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B-1559
January 1987

The Texas A8rM Sheep
and Goat Simulation

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The Texas Agricultural Experiment Station, Neville P. Clarke, Director
The Texas A&M University System, College Station, Texas

in cooperation with

The United States Agency for International Development, Small Ruminant
Collaborative Research Support Program

Mention of a trademark or a proprietary product does notconstitute a guarantee or a warranty of the product by The
Texas Agricultural Experiment Station and does not imply its approval to the exclusion of other products that also
may be suitable.

All programs and information of The Texas Agricultural Experiment Station are available to everyone without
regard to race, color, religion, sex, age, handicap, or national origin.

 

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The Texas A&M Sheep And Goat Simulation Models
Texas Agricultural Experiment Station, Texas 77843

11.1). Blackburn, 11.0. Cartwright, can. Smitha, N. McC. Grahamb and F. Ruvuna

Acknowledgement:

The research reported in this bulletin was supported in part by the United
States Agency for International Development Title XII Small Ruminant
Collaborative Research Support Program under Grant No. AID/DSAN/XII—G—0049. In
addition to drawing heavily on the scientific literature, many scientists at
Texas A&M University contributed their expertise in the form of knowledge and
critique; their contribution is gratefully acknowledged.

a Present address: Box 353, Silverton, Texas 79257
b C.S.I.R.0. Division of Animal Production, Prospect, NSW Australia

FOREWORD

Historically, agricultural science has grown through small advances and
incremental progress, and the application of research results have often been
limited by the time and geographic location. In contrast, the models
reported here permit reaching beyond restrictive time and geographic
constraints. The models represent major directional progress in ruminant
production through quantitative description of animal performance. The
models will be useful to other scientists as research tools to evaluate and
develop new hypotheses. Also, the models reach across several disciplines
and the integration of knowlege from these disciplines is of scientific
interest in understanding the dynamics of growth, maturing and reproduction
cycles.

Clearly, the models are not intended for direct field use by producers.
Their application value lies in use by experts to examine effects of varying
nutrition, breeding, and management on practical production or development
problems encountered in the field. These applications are especially useful
for addressing problems in areas where production research results are
lacking and cannot be obtained because of time, funding, facility and
personnel constraints or complexity of the problem. These capabilities also
provide the means for examining practical problems of individual enterprises;
i.e., extending research results directly to the unique set of production
resources of individual producers.

These models are reported for their scientific accomplishment and
interest and for their use to enhance the capability to make decisions about
sheep and goat production that are relevant and practical and in quantitative
terms. From a broader perspective, the application of systems science in
agricultural research is being employed by TAES to both extend the frontier
of knowledge and to make the knowledge more accessible for practical

application.

Dudley T. Smith, Associate Director

Texas Agricultural Experiment Station

ii

PREFACE

Animal scientists have become increasingly aware of the need for
systematic consolidation of component knowlege obtained through the
traditional scientific approaches. Systems analysis is an orderly method of
structuring and organizing knowledge and interaction relationships.

The development of models of complex systems, which include sheep and
goat production, requires substantitive knowledge of the components which
make up a system. The models summarized in this publication were constructed
so that any breed of sheep or goat can be simulated for a wide range of
nutritional environments and management practices. The simulations reflect
the response of sheep or goats to a specified set of inputs and therefore,
may be used to evaluate the performance of breeds considered for introduction
into an area or to examine the effect of nutritional regimes or management
practices as well as the interactions among these variables. Results from
simulations allow biological interpretation in quantitative terms and are in
a convenient form for economic analysis.

These models have been validated and put into active, continuing use in
less developed countries (LDCs) using micro or minicomputers to simulate
various versions. Although systems analysis represents a high technology use
of science, at the same time it is appropriate for use in LDCs; it is a
method by which scientific knowledge from developed countries can be
transferred for practical application in LDC settings. "Production
experiments" can be simulated as a substitute for much research for which
funds, facilities and personnel are limited.

Models are reported in this publication for their scientific
accomplishment and interest and for their use to enhance the capability to
make decisions about sheep and goat production in quantitative terms.

Appreciation is expresed to nuerous coworkers in the United States and
host countries who participated in the development or validation of this
model. Additionally, graduate students, involved in this research made

valuable contributions.

T. C. Cartwright, Professor

Texas A&M University

iii

FOreWOrd o o o o 0 o o o o o o

Preface . . . . . . . . . . .

Chapter 1

Conceptual Overview of Model

a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
1.

Genetic Potential . . .
Maintenance . . . . . .
Growth . . . . . . . .
Maturing Rate . . . . .
Body Composition . . .
Pregnancy . . . . . . .
Feed Intake . . . . . .
Tissue Mobilization . .

TABLE OF CONTENTS

Partitioning of Nutrients

Lactation . . . . . . .
 I I I I I I I I I
Reproduction . . . . .

Chapter 2
Functions of the Model . . . .

a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
1.
m.
n.

Maintenance . . . . . .
Growth . . . . . . . .
Lactation . . . . . . .
Fiber Production . . .
Pregnancy . . . . . . .
Total Requirements . .
Feed Intake . . . . . .
Tissue Mobilization . .
Partition of Nutrients
Update Phenotype . . .
Reproduction . . . . .
Fiber Production . . .
Mortality . . . . . . .
Health . . . . . . . .

Chapter 3
Goat Model . . . . . . . . . .

Chapter 4
Parameter Specification . . .

a.
b.
c.
d.

Forage Parameters . . .
Genetic Parameters . .
Management Parameters .

Example of Parameters Specification

PAGE

ii

iii

13

14
15
21
26
27
29
30
33
39
41
42
54
56
59

75

80

80
80
81
81

PAGE

Chapter 5
Simulated OuCpUt-SUHIHIBIIIQGS o 0 0 o o o o 0 o o o o o o o a o o o o o o o 0 

Chapter 6
  O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 

I. Single Animal Version-SAV . . . . . . . . . . . . . . . . . . . . . 93
a. Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . 94
b. Simulated Results . . . . . . . . . . . . . . . . . . . . . . . 95
c. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . .111

II. Flock Model (FM) — Northern Kenya . . . . . . . . . . . . . . . . . 116
a. 1979 Results . . . . . . . . . . . . . . . . . . . . . . . . . 116
b. 1980 Results . . . . . . . . . . . . . . . . . . . . . . . . . 123
c. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 126

  O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 

[mm   [mum]

 

       

1. CONCEPTUAL OVERVIEW OF MODEL STRUCTURE AND FUNCTIONS

A major purpose of the sheep model is to simulate sheep performance for
a wide array of genotypes in a wide variety of environments with managerial
options implemented as desired. These capabilities make it possible to
evaluate performance of different genotypes in different areas employing
different production practices. The results from such simulations may be
used to develop packages of breeding strategies and feasible alterations in
management techniques that can be recommended to increase the productivity of
the system.

Two versions of the TAMU sheep model have been developed, the single
animal version (SAV) and the flock model (FM). Both models have the general
characteristics of a 15-day time increment for a period of simulation, with
conception and lambing occurring at the end of a period of simulation. The
length of the time increment was chosen because it closely matches the
reproductive biology of the sheep (150—day gestation and a 17-day estrus
cycle) and it makes a 360—day simulated year feasible. A shorter time frame
might add precision to the simulated results, however it would increase the
amount of memory, cost and time required for simulation. The SAV is capable
of simulating the biological response (maintenance, growth, work, gestation,
birth, lactation, fiber and death) of any portion of the life of a sheep.

For example, SAV is capable of simulating the biological response of one ewe,
her nursing offspring (until weaning) and any fetuses she may be carrying.
The FM incorporates the biological components of the SAV and adds to it the
accounting and flock management practices required to simulate flocks of
sheep. The FM has the capability to simulate six flocks of sheep with 12
classes of animals per flock. The classes in the FM represent differences in
age and sex of the simulated sheep. The flock may also be divided into
different management groups (e.g., supplemental feeding and pasture
assignments).

A conceptual overview of the sheep model is presented in figure 1 and
illustrates the interaction among the different biological processes modeled.
The physiological status of the sheep interacts with its nutritional intake,
partitioning the nutrients for various functions, which results in the final
output or sinks on the right hand side of the figure (milk and fiber produced

and protein and energy loss, etc.). In figure 1 it is possible to trace the

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division of nutrients for any type of sheep simulated. Sources and sinks are
illustrated by amorphous cloud shapes. The sources are parameters supplied
to the model. Sinks are losses or offtakes from the system.

The nomenclature used follows that described by Forrester (1968). All
rectangles represent state variables or physical products (e.g., kg of
protein or kg of body weight). The flow of material between levels is
denoted by a solid line. The flow of a material is regulated by the valve on
the solid line which is turned on or off by the auxiliary variables (circles)
or constants. Information flows are depicted by dashed lines and can pass to
an from a state variable. That is, information controlling the rate of
material flow is altered by an auxiliary or constant, but there is a feedback
from the state variable to the auxiliary which may increase or decrease the
material flow.

The logic flow of the FM follows a hierarchical design, with the main
program calling subroutines in a top down manner. Figure 2 illustrates this
concept for the entire program. Due to the importance of the biology and
management subroutines in the flock model, their hierarchical structures have
been diagrammed in more detail (figures 3 and 4) to show subroutines that are
called from biology and management. These two figures demonstrate, in broad
outline, the simulation process, the options and the capabilities of the
model.

The information for an individual in the FM is kept in one dimensional
arrays, with each sheep being assigned a specific position in that array.

The records of an animal's traits are connected together by doubly-linked
lists (Knuth, 1968). A doubly—linked list has two pointers, one to the
previous position in the array, and the other to the next position in the
array. These pointers allow individuals to be deleted frm any portion on
the list without having to reorder the entire list of animals. The
doubly—linked list procedure also allows the grouping of animals in the same
class and it reduces the computation time for a simulation. Mayfield (1979)
described this procedure in detail in his master's thesis at Texas A&M.

From the preceding discussion and flow charts, it can be perceived that
the sheep model is primarily a nutrition model. That is, the model is driven

by nutrients (just as the energy "driving" real sheep is derived from their

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nutrition), and the flow of nutrients can be followed from consumption to
their ultimate end point for a particular time step.

Any questions that might arise as to the rationale of the model
structure and functions may be more easily resolved if one over—riding point
is kept in mind; the simulated animal or flock is designed to respond to its
environment just as a real sheep or real flock would respond Qnot vice
versa). That is, the simulations are substitutes for real sheep.

The structure and biological processes of the model are described below;
first, in functional categories as an overview, where the effects of the
biological functions of the model are presented as mathematical expressions
along with the descriptions of the process functions, logic and structure.
The complete set of functions is presented as matheatical expressions in the
following section (Functions Of The Model), where order of presentation
follows a logical sequence of dependency progression rather than a
description by functional categories.

a. Genetic Potential

The production functions of an animal are growth and reproduction.
Growth includes all stages and all parts of the body (including hair or
wool); reproduction includes lactation, and maintenance as a necessary
overhead. These production functions and overhead are driven by or fueled by
nutrition. Growth and lactation patterns, including limits and rates, are
mediated by the genotype. The model functions are designed to simulate the
response of an animal to its nutritional environment in such a way that it
tends toward fulfilling its genetic potential for growth and reproduction
limited by both quality and quantity of nutrition, health impairments and
management restrictions. Since nutrition is usually limiting, the priority
of nutrient utilization is critical and the model functions promote survival
as an inherent mechanism. The genetic potential is set into the model for
the specific breed type being simulated. The key genetic potentials
specified are mature size (WMA or weight at the maturity asymptote of the
growth curve with specified body composition), milk production (GMLKL or
genetic potential for milk level at peak lactation, for an uninhibited
lactation curve of a mature ewe), ovulation rate (OVR), seasonality of estrus

(SEAEST), wool growth (GWOOL) and resistance to internal parasites (PRST).

These and other genetic parameters are discussed under appropriate headings
below.

The key parameters that must always be set in the model to specify the
genetic potential of a breed (e.g., WMA) are designed to represent each
specific breed and therefore reflect breed variability. Also, the
coefficients in many of the functions such as the ones above may be varied to
reflect any specific characteristic peculiar to a breed. For example,
research characterizing a breed may indicate that the male factor of 1.5
times WMA does not correctly reflect the sexual dimorphism characters for
that breed. Therefore, these coefficients would be appropriately "fine
tuned" in addition to the other breed parameters. The maturing rates of so
called "unimproved" indigenous breeds are usually different from "improved"
breeds on a relative as well as absolute basis.

b. Maintenance

The nutritional requirements of the simulated sheep are an accumulation
of minimal body maintenance costs (unavoidable losses), expenditures for
pregnancy, lactation, growth and fiber production. Maintenance (both protein
and energy) requirements, as used in this model are the sum of basal
metabolism (MB), endogenous urinary loss (UL) and work (WK). The work
component of the equation consists of, on a daily basis, the time spent
eating (EAT), distance travelled (DIST) and the time spent ruminating (RUM).
The maintenance requirements for protein (MTP) are first calculated as .0164
MTE. This first calculation provides a first estimate of the requirements so
that potential performance levels may be considered.

c. Growth

In order to simulate the growth of a sheep, a potential growth curve,
specified by a set of parameters describing the breed being simulated, is
placed in the model functions. This set of growth parameters specifies the
genotype or genetic potential for the growth of an individual. From birth to
50% of mature weight (WMP) potential growth rate is assumed to be linear;
after reaching WMP (the point of inflection), potential growth rate decreases
until the curve asymptotes at the simulated breed's average mature empty body
weight (WMA). This underlying growth curve represents animal growth with no

nutritional impediment, therefore an animal following this growth pattern is

 

considered to be in good condition, but not excessively fat. The body
composition for such a sheep is assued to be 3% fat at birth and 25% fat at
maturity; the deposition of fat from birth to maturity increases in
proportion to the degree of maturity (WM/WMA). The simulated individual has
two measures of body size. One is WM, which Sanders and Cartwright (1979a)
described as the structural size. The structural size attained at a given
age is a combination of the effects of the animal's genetic potential and the
enviroment (principally nutritional environment).

An animal's WM will increase at the rate set by its genotype if there is
adequate nutrition until it reaches maturity. The rate of change in WM may
be decreased in a growing animal if nutrition is limiting. However, once an
individual has obtained a given WM, it will never decrease from that value.
In the case of severe nutritional deprivation, stunting may occur and would
be reflected in zero increase in WM for that period. The second and more
dynamic measure of body size is EBW, which is the summation of the fat and
lean (lean includes bone) content of an individual and is a record of the
fluctuating empty body weight from period to period. Thus WMA is WM at
maturity (or at the asymptote) and when EBW (empty body weight) equals WMA,
fat composition is 25% of EBW.

d. Maturing Rate

The rate at which animals mature will influence the initiation and
cessation of their body functions. The influence of these factors was taken
into account in the development of functions to calculate maturing rates for
different breeds of sheep. Taylor (1965) showed that the time taken to reach
any particular degree of maturity tends to be directly proportional to an
animal's mature weight raised to the .3 power. In this model, rate of
maturing (RM), is considered to be inversely proportional to the .3 power of
WMA. Therefore, the time taken to reach the point of inflection (WMP(Ti)) on
the growth curve is proportional to the .3 power of WMA.

In the development of the model, the breed used as a base was patterned
after a fine wooled sheep (Rambouillet). It was assumed that this sheep had
a WMA of 60 kg and a Ti of 165 days (Ti = time of inflection) as base or
reference points. With this base and the WMA of the breed to be simulated,

the appropriate Ti and RM can be calculated for the breed. Males are

simulated as having a WMA 1.5 times that of females. Therefore, they also
have a larger WMP.
e. Body Composition

Both protein and energy are accounted for in the model; therefore, fat
and lean gains are calculated separately. These gains are subdivided into
essential and nonessential pools. The essential pool of an animal at one
period of time is used as the base for calculating gain in WM from that
period to the next period. The composition of this growth of WM must be at
least 3% fat and at least 65% of the lean growth expected for that period.
Growth in WM may range from these minima up to the full expected growth,
depending on the nutrition available. If nutrient requirements for these
minima can not be met, then zero growth occurs, representing stunting for the
period. It is possible to have greater growth of WM than of EBW; i.e.,
structural size may increase while condition is lost, a common occurrence,
because any portion of the nonessential fat or lean can be catabolized for
maintenance or production including growth in WM. Animals weighing less than
their structural size (EBW<WM, a thin condition) have an impulse to increase
intake striving to gain weight at a compensatory rate reflecting the
biological adaptation to tend toward a normal or surplus body composition
(EBW_Z WM).

f. Pregnancy

The sheep model simulates individuals from conception onward. A ewe may
have one to three lambs per pregnancy. The equation used to describe
expected growth in conceptus weight (DCW) was presented by Graham et al.
(1976). Conceptus weight change is calculated on a daily basis, and the
total of conceptus weights of all fetuses of a ewe are then accumulated over
each 15-day period.

The potential birth weight (BW) of a lamb is determined by the number of
fetuses, the potential mature size of the fetuses (WMA), and the structural
size of the ewe (WM). Birth weight is calculated by an equation similar to
one reported by Geisler and Jones (1979). Mammary gland growth is initiated

at 105 days of gestation and continues for 30 days after parturition.

10

g. Feed Intake

The model uses three factors to determine feed intake. The minimum
value of either the physiological limit, physical limit, or feed availability
determines the feed intake.

Availability is specified externally to the model and is defined as
being that amout of feed, of a given quality, available for an animal to
consume during a day. The availability for immature sheep is adjusted
downward to represent differences which exist in foraging range.

Physiological limit (PSOL) is the animal satiety factor; that is, body
condition of the sheep, feed quality, and energy requirements interact to set
a limit on feed consumption.

Physical limit (R2) represents the gut capacity of the sheep. The
equation used describes the amount of feed the gut will hold and contains an
adjustment that varies with feed quality, and may be interpreted as the
passage rate of nutrients.

The physical limit of pregnant ewes is adjusted downward depending upon
a ewe's age, the number of fetuses she is carrying and the period of
gestation. For lactating ewes, intake is adjusted upward and is a function
of time (postpartum interval) and potential milk production.

h. Tissue Mobilization

The model has the capability to mobilize tissue when protein and energy
intake is insufficient to meet the animal's nutritional requirements. Lean
may be catabolized for use as protein or as energy. Fat may only be utilized
as a source of energy. Tissue is catabolized in the order of 1) lean for
protein, 2) lean and fat for energy, 3) fat for energy, and 4) lean for
energy.

i. Partitioning of Nutrients

When the nutrients consumed and the tissue mobilized are still lower
than the animal's requirements, the existing nutrients are divided between
the various uses. This partitioning is accomplished by dividing the protein
and energy available according to functions represented by geometric
containers as shown in figure 11. These containers are adjusted to hold the
calculated nutrient requirements for the simulated animal. The protein and
energy present (from the feed consumed and tissue catabolized) are then

"poured" into a separate set of containers for protein and energy. The

ll

nutrient which is most limiting or fills its respective containers to the
lowest levels is the limiting nutrient. Performance is then adjusted
downward to the level of the limiting nutrient.

The shape of the containers and their positions relative to one another
are based on interpolations and indications from relevant research and
general experience.

j. Lactation

Milk production potential is a function of units of available lactation
capacity (ALC) and secretion rate (SR) per unit in a manner similar to that
developed by Bywater (1976). Genetic differences in milk level (GMLKL) and
period of lactation (LACPP) set an upper limit on ALC. Either the intake
capacity of nursing young (MLKLIM) or nutrition may restrict the ALC actually
used below that available. In addition, the number of units of lactation
capacity used the previous 15-day period (LCU) sets a lower limit on ALC. SR
is a function of ewe age in periods (AGEP), genetic difference in persistency
(PRS) and LACPP.

k. Fiber

The genetic potential for clean wool growth (GWOOL) is the maximu
growth (g/day) which can occur for a breed. It is adjusted for photoperiodi—
city (SCR), age, and degree of maturity (UCR).

The nutritional requirements are based upon clean wool being 100%
protein, which is assumed to be deposited with an efficiency of BVP. The
gross energy content of wool is assued equal to 6.0 Mcal/kg and to be
deposited with an efficiency of 20% (Graham and Searle, 1982).

1. Reproduction

The approach used in modeling reproduction was to identify the
components which had an influence upon reproduction and then to construct
mathematical functions to describe their responses. This method was
described and used by Sanders (1974) for beef cattle. A female has a
calculated probability of estrus cycling and conceiving if mated; if she
conceives, another probability determines the number of ova ovulated (1 to

3).

12

2. FUNCTIONS OF THE MODEL

The more basic functions are presented initially in order to establish
definitions and based upon which to build the functions that follow in
sequence. Some expressions of overall structure and functions were presented
in the preceding section for illustration and are repeated below.

The order of presentation begins with life-sustaining maintenance
followed by the production functions of growth, milk, fiber, pregnancy, and
their summation. Next are controlling functions that mediate the flow of
nutrients for the above functions and relate to the two sources of nutrients:
feed intake and mobilized tissue. The next section describes the mechanism
of setting priorities for use of nutrients; it operates in the interface
between nutrient "supplies" and nutrient "consumers" directing flow or
partition of nutrients. The next updates the animal for changes due to
growth, etc., that have taken place during the period. The final section

integrates the ewe reproductive functions with other functions.

13

a. Maintenance
Energy. Maintenance requirements for energy (MTE) are estimated as the
su of basal metabolism (MB), endogenous urinary loss (UL), and work (WK) in
terms of net availability of metabolizable energy (ME) for maintenance.
MB = .o5s3(EBw+xwT)-75 e"-°°125 AGEP + .046DME + .0446QEBW
UL = .Q8MB
WK = (.OO0526EAT + .O0O237RUM(DM) + .OO0598DIST) W
MB + UL + WK
KM

KM - 85 --—-_ME (MILK) + ( 546 + 3 ( s1 01c) ME (FEED)
' ‘ ME(TOTAL) ‘ ‘ ° ) ME(TOTAL)

MTE

where
EBW = empty body weight; W less fill, conceptus, fleece and
mammary gland, kg
XWT = rumen fill after fasting; min. (2, .2 AGEP), kg
AGEP = age in periods; period = 15 days
DEBW = change in EBW from the previous period, kg
DME = daily feed ME intake during last period
EAT = hours per day spent eating
RUM = hours per kg DM spent rmninating
DM = daily dry matter intake during last period, kg
DIST = distance walked each day, km
W = body weight, kg
DIG = feed dry matter digestibility
KM
The estimates for MB, UL and WK are the same as used by Graham et al.

net availability of ME for maintenance

(1976), except that (1) feed intake is the average of the previous 15-day
period rather than the previous day, (2) time spent eating is expressed on a
daily basis rather than on a per-kg—intake basis, and (3) for use in
conjunction with KM as defined by ARC (1980), the growth rate term in the
original equation for MB was set to zero.

The ME content of milk is calculated as 1.08 Mcal per kg from the
assumptions of gross energy of 4.8 kJ/g liquid milk with 94% metabolizability
(Graham et al., 1976). The net availability of ME from milk of .85 is

14

modified only slightly (Graham, personal communication) from the .84 used by
Graham et al. (1976). The ME content of dry feed is estimated as .81 times
digestibility and has an assumed net availability for maintenance of .546 +
.3 m: (Graham et al., 1976). 9
Protein. Approximate protein maintenance requirements (MTP) are first
estimated as .0164 MTE. After feed intake is estimated, MTP is recalculated
similar to the estimate used by Graham et al. (1976).
MTP = .44(EBW + FILL)2 + .01DM(1—DIG) + .0O04MLKTK
where:
FILL = 2
MLKTK = intake of milk, kg.

b. Growth
Potential. Growth potential (WMG) in structural size (WM) is assumed
linear from birth (BW) until a constant fraction (WMP) of mature size (WMA)
is reached and to decline monotonically after that point. WMA is a parameter
set as part of breed specification; see the next section on composition. The
rate of maturing (RM) is inversely proportional to the .3 power of WMA
(Taylor, 1965); hence, time taken to reach WMP (ti) in females is
proportional to the .3 power of WMA. Parameters for potential growth of
females are as follows:
BW = CIWMA; Cl = .06 as a base; set as part of breed
specification.

.50 as a base; set as part of breed
specification.

The constant C1 is the percent of mature weight which is attained at birth
of a lamb. The base estimate of .06 was based upon summary of literature
values (Sidwell and Miller, 1971; Dickerson et al., 1972; Hodgeson and Bell,
1973; Hohenboken et al., 1976; Stobart, 1983; Mathenge, 1981). The constant
C2 represents the degree of maturity attained by a sheep at the point of
inflection of its growth curve; C2 was set at .50 as a base. Most of the
data which were utilized to establish this base value were related to
attainment of puberty of ewe lambs and are cited in the section describing

the reproduction correction factors. The constants C1 and C2 may be

15

varied to more closely resemble the breed being simulated. In general, the
literature, as a whole, substantiates the use of .06 and .50 for C1 and

C2, respectively.

t = (WMA/WMA')-3 t'i t'i = 165 days as a base
WMA' = 60 kg as a base
if WM 3 WMP,
WMP - BW
WMG = -----
ti
if WM > WMP,
C — C
WMG = 2 1

T711357“

Potential growth of males is simulated by assuming an increase in WMA and WMP
with ti adjusted (ti') to provide a specified growth rate ratio (RSX).

WMA' and WMP' are the increased WMA and WMP.

WMA' = Q(WMA) Q = 1.5 as a base;
WMP’ =  
ti‘ = Pti
RSX _ (WMP'—BW)/Pti
(WMP-BW)/ti
P = C2Q-Q1
02 — cl RSX RSX = 1.15

Differences between sexes for birth weights are simulated, but these birth
weight differences are ignored in estimating potential postnatal growth
rate.

Baseline Body Composition. An animal that is never stressed by disease,

treatment, or nutrition (quality and quantity) is expected to be in "good"
condition. The percent body fat of an animal that is always in "good"
condition is assumed to increase linearly from 3% at birth to 25% at maturity
(Sanders, 1977). The minimum amount of fat a sheep must have at any age is
3%. The lower limit of 3% fat and the average unstressed mature level of 25%

fat correspond with data of Farrell and Reardon (1972), who undernourished

16

Merino ewes for 4 months and maintained them in that state for an additional
9 months at which time they were slaughtered. Two groups of undernourished
ewes had 9 and 5% body fat, respectively, compared to 27% for control ewes.
The 25% body fat for mature ewes in average "good" condition also corresponds
closely with data of Notter et al. (1984) who found body fat of Rambouillet,
Dorset and Finn to be 27.7, 24.4 and 21.6%, respectively. For an animal in
"good" condition, empty body weight (EBW) will equal structural size (WM);
hence, expected fat (XFAT) and expected lean (XLN) are functions of degree of

maturity (lean is defined as muscle).

Z1 = el e2 %¥§:gl-Ygfi) e1 f .83, minimum fat
—C1) WMA e2 — .
XFAT = zl (WM)
XLN = WM ~ XFAT

Composition Of Gain. The fat (FG) and lean (LG) gain associated with a

gain in WM can be calculated from expected normal compositions.
WMX WM + 15 WMG
_ (WMX-C1 WMA)

x " el + 92 fT:§Ij"wfiX--'

Zlx WMX — Z1 (WM)

WMG - FG

Z1

FG
LG

Partition Of Gain. FG and LG are partitioned between that amout which

is essential (FGE and LGE) for a unit growth in WM and the remainder which is
normal (FGN and LGN) (figure 5). A unit of WM growth must be at least 3% fat
and at least 65% of the expected lean fraction must be met. The percentage
fat considered minimal for body functions is that suggested by Sanders (1977)
and substantiated by Farrell and Reardon (1972). The percentage lean is
approximately equal to that fraction of body protein that can not be depleted

during protein starvation (N. Graham, personal communication).

FGE = e1 (WMG)

FGN = FG - (FGE)

LGE = p1 (LG); P1 = .65
LGN = LG - LE

17

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18

Hence, a unit's growth of WM is made whenever FGE and LGE are met. The ratio
of FG to LG is linearly proportional to degree of maturity with FG increasing
from 3% at birth to 25% at maturity.

Composition Correction. A necessary component of grazing ruminant

production is the capability for compensatory gain. This ability is vital to
an animal which must survive in an environment where forage quality and
quantity constantly change with seasons of the year. The ratio in which
protein and energy are lost during nutritional stress is variable, depending
upon the maturity of the sheep (Thorton et al., 1979). However, when
realimentation occurs, a sheep's impetus is to reach the normative
proportions of protein and fat for its given degree of maturity. This
biological mechanism is embodied in the conceptual structure of the TAMU
model. That is, a simulated sheep will always strive to attain its normative
condition, and if the nutrient supply permits, the sheep will accuulate body
reserves. The copensating rates of gain during compensatory growth are
varied. Graham and Searle (1975) reported that a compensatory group of lambs
gained 280g/day while the control gained 160g/day. Thorton et al. (1979)
reported a 330g/day gain for lambs undergoing realimentation vs the 60g/day
of their control. Both of the articles cited state that greater feed intake
during rehabilitation was the cause of compensatory growth and not an
alteration in efficiency of nutrient utilization or lower basal metabolism.
The rationale for the model structure and functions for feed intake for
under-conditioned animals is described in the section on the physiological
limit to feed intake and incorporates the concept of animal condition
determining feed intake.

In the model, animals that have fat and protein levels below amounts
expected for their structural size (WM) have a compensatory impulse to gain
fat (FGC) and lean (LGC) to bring their composition back to baseline
(realimentation ). The difference between empty body weight (EBW) and actual
lean weight (WL) is actual fat (AFAT). The redeposition of expected fat is
set at 1%/day (Sanders, 1977). The requirement for this gain does not lower
the physiological limit on intake and does not necessarily compete with other
energy requirements. The rate of lean coposition correction, which becomes
part of the upper limit on lean gain, is set at 2%, twice the rate for fat.

Further research may be required to obtain more precise estimates of the rate

l9

for compensatory growth; however, lean deposited at a faster rate than fat
agrees with Drew and Reid (1975).

Animals that have fat and protein levels above WM have a compensatory
dampening.

AFAT = EBW — WL

FGC = .O1(XFAT — AFAT)

FGC max (FGC,0.0)

LGC .02(XLN — WL).

Requirements. Energy requirements for gain are based upon ARC (1980)
requirements. The net availability of ME for gain (KG) is assued equal for
both fat and lean and to be dependent upon physiological status (lactating vs
nonlactating) of the animal and upon source and digestability of nutrients.
The energy content of gain (Mcal/kg) is assumed equal to 9.4 for fat and 5.7
for protein. The percentage protein of lean (PPL) is currently set equal to
20%. That is, 20% of the weight of lean (WL) is protein. This was the
estimate reported by Searle and Graham (1975) and Searle et al. (1979). The
efficiency of depositing protein is assumed to equal the biological value of

absorbed amino acids (BVP) which is set to .72.

Nonlactating

KG = .70  + (.03 + .81(.81(n1c)))  )
Lactating

KG = .95(.47 + .35(.81 DIG))
KF = 9.4/KG
KLN = 5.7PPL/KG
RGE = KF(FGE) + KI.N(LGE)

RGEX = KF(FGN + FGC) + KP(LGN + LGC)
GL = PPL/BVP
RGP = GL(LGE)
RGPX = GL(LGN + LGC)
The separation of requirements into those for essential gain and those for

nonessential (normal plus compensatory) gain allows assignent of different

priorities to these.

20

c. Lactation

Potential. Milk production is simulated as an interactive process where
the amount of milk produced is dependent upon the ewe's genetic potential,
body condition, age, nutrition, period of lactation, and the number of lambs
nursing. The concept used for modeling milk production was suggested by
Bywater (1976). Bywater's approach assumes that milk production is comprised
of two components, lactation capacity available (ALC), which is determined by
the environment and the genetic capability of the female, and secretion rate
(SR) which defines the rate and pattern of milk production for a given unit
of time.

The TAMU sheep model uses the same concepts of SR and ALC. However,
several modifications to Bywater's approach have been made. Secretion rate
may be viewed as the output of milk per uit, where units are defined as ALC.
Therefore, as lactation proceeds over time the milk produced per unit (ALC)
decreases. Secretion rate not only varies within an individual's lactation,
(figure 6) but there are a family of SR curves detenmined by ewe age. As a
ewe grows older the SR curve is increased. The incremental changes occur at
one, two, and over three years of age (figure 7). Secretion rate is

described by the following equation:

SR: (ARC)e-.Z2(1—P)(LACPP-Z)
10.0

where:

ARC=An age adjustment for the initial level of SR (figure 7).

ARC=. 6349+. OO5636AGE P—. 00O024O2AGEP2

P=Persistency currently set to zero.

LACPP=Period of lactation.
where:

AGEP=Age of the ewe in periods of 15 days.

Lactation capacity available describes the number of units available at
any one time to produce milk. Bywater (1976) states that these uits are not
alveoli but, conceptually, may be looked upon as performing the same
function. Lactation capacity available is initially expressed in percentage
until it is multiplied by the genetic potential (GMLKL). Figure 8 represents
the ALC curve. For this model the development stage is the first 30 days of

lactation, with day 30 being the lactational peak provided there are no

21

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Am¢>v mo<

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23

limiting factors on milk production. A peak lactation at day 30 would
closely agree with published values by Corbett (1968), Morag et al. (1970)
and Geentry and Jagusch (1974).

Breed specificity is introduced to the ALC equation via the genetic
potential for milk production (GMLKL). This term is defined as the peak
production of a ewe nursing twins with no nutritional impediment. If a ewe
is nursing a single lamb the product of ALC and GMLKL is adjusted downward by
25%.

The genetic potential for a breed is derived from previous research on
the breed being simulated, which meets th previously stated criteria.

Lactation capacity available is calculated by:

ALC=( 1 . 0+. l(LACPP—1)-. O444(LACPP—1)2)(GMLKL)
where:

LACPP=Period of lactation.

GMLKL=Genetic potential for milk production.

The curve for lactation capacity available describes the potential units of
milk production a ewe may utilize during her lactation. If a ewe does not
utilize her lactation capacity, she loses the ability to make these uits
functional. During a simulation, if the ewe's ALC (referred to as lactation
capacity used, LCU) is equal to the calculated ALC, then the ewe's LCU is set
equal to the potential value for the duration of the lactation. Figure 8
demonstrates this concept. In figure 8 the dotted line represents lactation
of a ewe. Before intersecting the potential ALC curve, the LCU is allowed to
vary depending upon nutrition and lamb intake. Once the two lines intersect
at the idealized ALC (the solid line), it is fixed at that level for the
duration of the lactation. In other words the ewes ALC (which is equal to
LCU) can vary within the bounds of the ALC curve, however, after they
intersect, lactation capacity is set for the duration of the lactation. The
major emphasis of this concept is that after a period of time if the ewe has
not been able to utilize her ALC she loses the ability to make them
functional. The extreme of this case is in period 7; at this time, if LCU
has not intersected ALC, milk production will cease.

The preceding section describes the maximum potential of milk
production. Determining the units of LCU is a function of the amount of milk

the lamb or lambs can consume and the plane of nutrition of the ewe. Milk

24

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muwummmu cowumuomfi Hmsuum wcu wcm Amcwfi wwfiomv xuwummmu cowumuumfi Hmwucwuom was

Qowmmm zoH@<~u<@

¢_ m w R @ n Q m N ~

1D
1r
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XlIOV&VD NOILVIDVT

25

taken from a ewe by hand is treated in the same way as that consumed by a
lamb except, of course, the lamb does not receive the nutrition.

The steps which interface these variables are as follows: First, an
estimate of ALC is determined for a particular breed. At the start of
lactation the LCU is estimated from the intake capacity of the lamb or lambs.
If LCU is greater than ALC, LCU is set equal to ALC. Milk production
(MILKPR) is then calculated as:

MILKPR = ALC(SR)

Requirements. Lactation requirements (LACRQE, LACRQP) are calculated by
assuming that milk contains 5.6% protein and 1.1 Mcal/kg energy (Graham et
al., 1976) and that the efficiency of protein utilization for milk production
equals the BVP and the net availability of ME for milk equals .47 + .284DIG,
(ARC, 1980).

1.1
KL = .47 + .2s4n1c
KPL .056
7 BVP

LACRQE = KL(MILKPR)

LACRQP = KPL(MILKPR)

If available nutrients are inadequate, milk production is prorated to
correspond with level of available nutrients.

Maintenance Correction. The aounts of energy and protein required for
maintenance are increased durin lactation in proportion to the ratio of
actual milk yield to potential peak yield (PMILK) which is assumed to equal
3.7 kg per day (Graham et al., 1976).

FMLC = 1.0 + 0.3 §EEEZ§
PMILK
MTE = FMLC(MTE)
MTP = MTP + .44(EBW + 2)-5(FMLc)

d. Fiber Production

Potential. Genetic potential for clean wool growth (GWOOL, g/day) is
adjusted for photoperiodicity (SCR), age and degree of maturity (UCR). The
photoperiod effect is taken from Nagorcka (1979) and requires specification

26

of amplitude (AMP) of seasonal differences (distance from equator effect),
frequency (FREQ) of pattern (once/year) and time of peak growth (PHAS,
mid-June in Northern Hemisphere). The adjustment for age and degree of
maturity is taken from a model by Christian et al. (1978).

UCR = (1 + e—165(AGEP—l))(wM/WMA).67

SCR = AMP (cos(120 FREQ (DAY—PHAS)))

AMP = .35GWO0L

FREQ = 2w/360 n=3.1416
PHAS = 165 FREQ
FGRTH = UCR(SCR + GWOOL)

Requirements. Clean wool is considered to be 100% protein that is
assumed deposited with an efficiency equal to BVP (Graham et al., 1976). The
gross energy content of grease wool is assumed to equal 6.0 Mcal/kg and to be

deposited with an efficiency of 20% (Graham and Searle, 1982).

 

KW = 6.0/.2
KPW = 1.0/BVP
FIBRQE = FGRTH
YIELD
FIBRQP = KPW(FGRTH)

Yield is the fraction of the fleece which is 100% wool. This parameter will
change with local conditions and the breed of sheep being simulated.

e. Pregnancy

Birth Weight. Potential birth weight (BW) is determined from number of
fetuses (N), potential mature size of the fetuses (WMA') and size of the ewe
(WM) in an equation similar to the one reported by Geisler and Jones (1979).

BW = .158(WMA')'83 (1 — 10'Y)

Y = (1.1/N)(wM/wMA')-83
BW is also adjusted for sex Qt .015) and for a random effect that can be
thought of as the effect of the number of cotyledons. This random effect is
necessary in order to simulate birth weight differences between twin—born

lambs of the same sex.

27

males,

BWm - 1.015BW
females,

BWf = .985BW

RX = N(1.0,.04)

Bw' = RX(BWm or BWf) M
Conceptus Growth And Requirements. Expected conceptus growth rate (DCW)§

is calculated based upon day (DAY) of gestation and total BW of all fetuses

(Graham et al., 1976) and accuulated by 15-day period.

d
new = 22 .0ooo3ss~§§§~nAY1'6
dl '

Energy and protein requirements for conceptus maintenance (RME, RMP) are

based upon conceptus weight (CW) at the beginning of the period. Energy and _
protein requirements for conceptus growth (RGE, RGP) are calculated daily andfi
averaged for the period. The net availability of ME for conceptus growth is l
assumed to be 0.7. Protein is assumed to be deposited with an efficiency
equal to BVP.

RME = .079 CW

d ZBW 2.66
RGE = %3_ Z2 .0Ql()7 m DAY

dl 4184 KLNG
KLNG = .7

RMP = .O164RME

d zsw 2.79
RGP = %3_Z2 .oo0o1s375 Zf§ DAY
d 1000 BVP

1
Mammary Gland Growth. Mammary gland weight (MGW) is assued to increase f

(DMGW) from .35 kg on day 105 of gestation through day 30 of lactation.
Growth rate is calculated separately for single and multiple births from
estimates provided by Rattray (1974).

MMGW — MGW

nmcw = cx (MGW - MGWI) MMGW

28

where,

multiple single
C .095 .110 (coefficient)
MGWI .20 .25 (initial wt)
MMGW 3.0 2.3 (maximum wt)

Requirements for mammary gland growth are calculated assuming 3 kcal/g
gross energy density, 13% crude protein and the same efficiencies of

depositing fat and lean as for weight gain.

 

 

RMGE 3. 0 mew
" KF

RMGP .13 nmcw
" BVP

Requirements for mammary gland growth are calculated only through parturition
based upon the assumption that the postpartum requirements would be offset by
tissue mobilized as the uterus regresses. No maintenance costs are made for
the regression of the mammary gland. MGW is added to body weight and is thus
included in the estimation of ewe maintenance requirements via the work
equation.

Conceptus And Mammary Gland Growth. Conceptus maintenance requirements
are added to ewe maintenance requirements and have equivalent priority of
nutrient use. The actual amount of conceptus and mammary gland growth is
dependent upon the fraction of their requirements (FRP) that is met after
nutrients are partitioned among all requirements.

MTE’ MTE + RME

MTP' MTP + RMP

PRGRQE RGE + RMGE

PRGRQP RGP + RMGP

CW‘ = CW + FRP(DCW)

MGW' = MGW + FRP(DMGW)

f. Total Requirements
Total requirements for energy and protein are summed including the
nonessential component of growth (RQEX, RQPX).
REQE = MTE + RGE + FIBRQE + LACRQE + PRGRQE
REQP = MTP + RGP + FIBRQP + LACRQP + PRGRQP

29

RQEX = REQE + RGEX
RQPX = REQP + RGPX.
g. Feed Intake

The estimation of feed intake for sheep is at best difficult, especially s

when they are free grazing on heterogenous pastures. Ellis (1978) stated
that "the inability to consistently predict voluntary intake of forage by
ruminants reflects an incoplete quantitative understanding of the dynamic
process". Prediction of intake deals with a vast array of variables that
include forage selectivity, physiological status of the sheep, forage quality
and its seasonal changes, and the availability of forage. These variables
are in turn affected by stocking rate.

The TAMU model uses three factors to determine feed intake of a
simulated sheep. The physical capacity of the rumen is the first of these.
The volue of the reticulorumen and the rates of chemical and physical
processes which determine the turnover of the content of this volue (Ellis,
1978) are reflected in the physical limit equation. For sheep in extensive
production systems, volue and turnover rate are the influential factors
determining feed intake, except for when forage availability is limiting.

The second limiting factor is physiological limit which is expressed as a
representation of metabolic control taking into account diet quality and
animal condition. Both physical an physiological limits are calculated
within th model. The availability of forage for grazing is the third factor
determinin intake. It is specified to the model on a 15-day (one period)
basis.

Physiological limit (PSOL). As digestibility of the diet increases,

voluntary intake is controlled less by physical factors and more by the
energy requirements of the animal (Freer, 1981). Ellis (1978) stated that
there is a transition point between gut fill control and metabolic control
which varies with the animal's physiological status. Physiological limit is
the metabolic control of feed intake. It is calculated as a function of the
sheep's body condition, nutritional requirements and the quality of the diet.
Physiological limits are expressed as:
PSOL = (REQE - RGE + MXEG/KG)/3.69

where

30

REQE

The total requirements for energy, and is calculated as the
summation of the requirements for maintenance, lactation,
gestation, fiber and growth.

RGE = The summation of essential fat and lean gains where each
component is multiplied by its respective efficiency factor to
determine the energy content of the gain. These values are 9.4
Mcal/kg for fat and 5.7 Mcal/kg for protein which is also
multiplied by 20%, the percent protein in lean.

KG

An efficiency factor representing the net availability of ME for
gain and is assumed to be equal for both fat and lean and to be
dependent upon physiological status (lactating vs nonlactating)
of the animal and upon the source and digestibility of
nutrients.
MXEG = The maximum possible daily energy gain.
The MXEG equation describes the maximum daily rate of energy gain in
mcal/kg/day when an animal's weight (EBW) equals its WM. This rate is
adjusted downward for mature animals and as condition increases:
MXEG = -03EBW(WM/WMA)'1O(1.6+.75714(EBW/WM)-1.35714(EBW/WM)2)

The quadratic portion of the MXEG equation sets the adjustment for condition.
Where EBW/WM = 1, this portion of the equation equals 1; when condition
(EBW/WM) > 1, this portion < 1; when EBW/WM < 1, this portion > 1. For
nursing lambs, the amount of energy obtained from milk is deducted from PSOL
to estimate feed intake for the physiological limit (R1). Milk is assumed
to have a gross energy concentration of 1.15 Mcal/kg with 98% digestibility
(Graham et al., 1976). R1 is set at a minimum of 1% of WM for nursing
young.

TM = a1MILK/3.69; a1=1.12; 3.69 is a conversion factor, Mcal ME to kg

P _ PSOL - "m
*1 fir"
R1 = MAX(Rl, 0.0mm)

Physical limit. The physical limit on feed intake (R2) corresponds to

gut capacity and rate of passage. It is calculated as:

31

The equation allows intake to increase as the digestibility of the forage
increases up to a maximum digestibility of .85, a limit suggested by Egan
(1977). Intake will also increase as structural size increases. The form of
this equation is similar to that used by Graham et al. (1976).

The variable TAU allows younger animals to consume feed as a larger
portion of their metabolic size and is calculated as:

TAU .09799(wMA/WM)-3964

TAU MAX(TAU, .12)

This adjustment has the greatest effect on intake for sheep between weaning

and 2 years of age, which is consistent with Hadjipieris et al. (1965) report i

that wethers from 4 to 5 mo age had greater intakes than 5 yr old wethers.

The estimate for R2 is not explicitly reduced for low protein diets,
however the high correlation between digestibility and protein will
indirectly result in adjustment for protein level for herbage. R2 is
increased in lactating ewes by FLACT, a function of milk production (MILKPR)
and lactation period (LACPP) and PNCR, a derived correction factor for each
period (lactation curve).

R2 = FLACT (R2)

MILKPR
FLACT = PNCR _______

MILKP
MILKP = the potential peak milk production
where,

LACTATION PERIOD: 1 2 3 1+ 5 6 7 s 9 10
PNCR: 1.3 1.65 1.6 1.55 1.5 1.4 1.3 1.2 1.1 1.0

Feed intake of a ewe is reduced by the developing fetus in the latter

stages of pregnancy. Forbes (1969) found a negative relationship between the é

volume of rumen contents and the volume of abdominal contents. His results
showed that after 120 days of pregnancy, intake is progressively reduced as
pregnancy advances.

After the seventh 15-day gestation period (PGEST), R2 is restricted
for all ewes except mature ewes carrying singles (NFET = 1).

RSTRC = a5 ((1—WM/WMA)/.4)+(NFET—1))(PGEST—1)
.0333
(l—RSTRC)R2.

a5
R2

32

WWW,J¢V¢I~E-9<q;,w/-I ><_-:_1_' A!  

Availability. The maximum amount of feed available to a mature ewe (AV,
kg/head/day) is set externally for each period (see section on Simulation
Parameters). It is adjusted downward in immature sheep.

R3 = AV(WM/WMA)a6, a6 = .15

Energy And Protein Intake. Total energy intake (DME, Mcal ME) equals
energy from dry matter intake (DM) plus energy from milk intake.

DM = MIN (R1, R2, R3); R1 = physiological limit,

R2=physical limit, R3=availability adjusted for immaturity

DME = DIG(DM) + TM
The amount of crude protein available for absorption in the small intestine
(DP, kg digestible protein) is estimated from ME and crude protein intake
(Hogan and Weston, 1981) of feed and added to that obtained from milk (CPM).
Milk is assumed to be 5.6% protein with 100% digestibility.

CPM = .056MILKPR

DP = .OO494(28.3(CP)DM + 29DME -5.2) + CPM

It has been well documented that sheep are selective grazers utilizing
grass, forbs and browse. Grazing behavior has not been included in the model
as an interactive component, but instead is accounted for in the
specification of the crude protein and digestibility which are model inputs.
h. Tissue Mobilization

Qasis. Body tissue, if available, is mobilized if either DME or DP are
inadequate to meet an animal's nutrient requirements for maintenance, fiber,
gestation, lactation and essential growth. Tissue is not mobilized to meet
requirements for the normal and compensatory (i.e., nonessential) coponents
of growth. The efficiency of using the energy stored in lean (KLNM) and fat
(KFM) is assued to be 100% when used for maintenance. Hence, for accounting
purposes, the gross energy content of the tissue is divided by the net

availability of ME for maintenance (KM).

 

KFM 9.4
' EH-

KLNM _ 5.7 PPL
" KM

33

Consequently, the efficiency of utilizing mobilized energy for requirements
other than maintenance is equal to the ratio of the efficiency of energy use
for production (KG, growth; KL, lactation; KW, fiber; KPG, gestation) to KM.

Mobilized lean is assued to have the same percentage protein as lean
deposited during growth. The efficiency of utilizing protein from lean is
assued to be 100% for all uses; hence, for accounting purposes, mobilized
protein is divided by BVP (biological value of protein) to convert it to the
uits of dietary requirements.

The order of calculating the amount of tissue mobilized is (1) lean for
protein, (2) lean and fat for energy, (3) fat for energy and (4) lean for
energy. The aount mobilized in each step is subtracted from the maximum
amount available.

Tissue Availability. Catabolism of tissue is dependent upon the
availability of fat (AVFAT) and the availability of lean (AVLN). Both of

these variables calculate the aount of non—essential tissue which can be
mobilized per day.
AVFAT = (AFAT—e1(WM))/15.0

where
AFAT = total fat
e1 = .03
AVLN = (WL-(P1)XLN)/15.0
where
WL = weight of lean
P1 = the amount of essential lean a sheep must have, 1.0-(.35 WM/WMA)
XLN = the expected lean of a sheep, WM—XFAT.

The following series of equations depict how lean and fat tissue are
catabolized. Once available lean and fat are calculated and sumed, the
fraction of available fat (FPC) is found.

FPC = AVFAT/(AVFAT + AVLN)

The total tissue that can be mobilized daily (WMBMAX) to meet a part of
maintenance energy requirements is calculated as

WMBMAX=FPC(MTE/KFM)+(1—FPC)(MTE/KLNM)

With WMBMAX known the maximum fat (FMBMAX) and lean (LMBMAX) that can be
mobilized daily in a fasting animal is: T
FMBMAX = (FPC)WMBMAX
LMBMAX = (1-FPC)WMBMAX

34

In a nonfasting animal, these maximu amounts are reduced in direct
proportion to the ratio of nutrient intake to the requirements for
maintenance, fiber, gestation, lactation and essential growth by the
equations:
ERATO
LRATO

(1.0-RE/(REQE))2"M°BXTR
(1_RP/(REQP))2-MOBXTR
For nonlactating sheep, MOBXTR = 1 and will be explained in the next

paragraph. The ratio of energy intake to requirements is, of course, used
for adjusting fat mobilization; whereas, the lesser of the energy or protein
ratios is used for adjusting lean mobilization.

FMBMAX ERATO (FMBMAX)

LMBMAX MAX (ERATO(LMBMAX),LRATO(LMBMAX))
The immobilizable portion of essential lean and fat (3%) components of WM
sets an additional upper limit on fat (AVFAT) and lean (AVLN) available for

mobilization.

AVFAT = MIN ((AFAT—e1(WM))/15, FMBMAX)

AVLN = MIN ((WL—P1(XLN))/15,LMBMAX)

Due to the increase of nutritional requirements during lactation, ewes
in poorer condition (EBW/WM) are not able to catabolize tissue at the same
rate or amount as those in better condition. This concept was incorporated

by the following equation:

MOBXTR = e2(actual condition T expected condition)_1
e2(1—expected cond1t1on)_1

The effects of this equation are shown in figure 9. To completely understand
the influence of MOBXTR one must examine how lactating ewes of different
conditions (EBW/WM) will mobilize tissue when the ratio of intake to
requirements is varied (figure 10). Figure 9 demonstrates how mobilization
would be reduced for ewes with various conditions, figure 10 represents the
values calculated from either the LRATO or ERATO equations.

Lean For Protein. If REQP exceeds DP, lean is mobilized for protein and

dietary energy is increased by the energetic value of the mobilized lean

(MBLN).
MBLN = MIN (REQP—RP)/GL, AVLN)
AVLN’ = AVLN — MBLN

35

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DP’ DP + GL(MBLN)
DME KLNM(MBLN)
Lean And Fat For Energy. If both are available, lean and fat may be

mobilized simultaneously in the same proportion as they would be deposited in
a normally growing animal of the same degree of maturity. Fat percentage
(FPC) at any degree of maturity is calculated from the assuption of a linear
increase in fat percentage from 3% at birth to 25% at maturity for animals in
good condition. The weight of tissue available for simultaneous lean and fat
mobilization (AVW) is the lesser of the amounts calculated from available
lean (AVWL) or fat (AVWF).
FPC = .03 + .22((ZWM-C1(WMA))/(l—C1)WMA)

AVWL §XE§_
‘ 1—FPC

AWF AVFAT
_ FPC

AVW = MIN (AVWL, AVWF)
The energy concentration (ECW) of the mobilized tissue and the energy deficit
of the animal set an additional limit on the weight actually mobilized

(MBW).
ECW = KFM(FPC)+KLNM(1-FPC)
MBW = MIN (§§9E:5E, AVW)
ECW
MBFAT = FPC(MBW)
AVFAT' = AVFAT - MBFAT
MBLNF = (l—FPC)MBW
AVLN = AVLN - MBLNF
MBLN = MBLN + MBLNF
RE‘ = RE + KFM(MBFAT)+ KLNM(MBLNF)

Fat For Energy. If AVLN limits lean and fat mobilization below that
amount needed by the animal, extra AVFAT can be independently mobilized.

REQE-RE
MBFX = MIN Q----, AVFAT)
KFM
MBFAT' = MBFAT + MBFX
RE = RE + KFM(MBFX)

38

Protein For Energy. If AVFAT limits lean and fat mobilization below
that amount needed by the animal, extra AVLN can be independently mobilized.
REQE — RE

 

MB = MI AVLN

LX N ( ICLNM ’ )
MBLN = MBLN + MBLX
RE’ = RE + KLNM + MBLX

i. Partition of Nutrients

If intake plus tissue mobilization of energy and protein (DME, DP) fail
to meet an animal's requirements (REQE, REQP), the available nutrients are
partitioned among the various uses. Sanders and Cartwright (1979a)
partitioned energy between lactation and WM growth. They depicted this
partition as two tanks of different shapes and elevations that are
simultaneously filled with liquid. Their concept has been extended for the
sheep model to also include fiber, gestation and nonessential growth and to
partition protein as well as energy.

The relative shapes and positions of the geometric figures (containers)
representing each physiological function in figure 11 depict the relative
priorities assumed in the model. The shape of the front face of a container
is constant but the depth, front to back, is such that the volume equals the
requirement for the particular function and period. Containers may have zero
depth for certain ages or classes. The relative shapes and positions of the
different figures are based primarily upon general experience and intuition.
The model can easily accommodate changes in these relative priorities to
correspond to differences aong breeds. For instance, the container for
lactation could be widened at the bottom to reflect characteristics of breeds
resulting from long term selection for milk production.

Essential to the joint accouting of protein and energy effects is the
assumption that the relative priorities are the same for both. Hence, the
model assumes two sets of identical, adjustable—depth containers with the
volume of one set equal to energy requirements for that period and the volume
of the other set equal to protein requirements. The total availability
(intake plus mobilized) of energy and of protein are "poured" into the
respective container sets. The set filled to the lowest level identifies the

limiting nutrient. The fraction of the volume filled for each container in

39

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this set determines the fraction of potential productivity attained for that
function. If protein is the limiting nutrient, the energy above the level
limited by protein is deposited as fat. The proportion of this extra energy
that came from mobilized fat is redeposited with the same efficiency with
which it had been mobilized (i.e., as if it had never been mobilized).
j. Update Phenotype

Protein and energy requirements are recalculated based upon actual
levels of production and amount of essential growth and subtracted from the
amounts available from intake and/or tissue mobilization. The remaining
amounts are used for nonessential growth and fat deposition. The ratio of
nonessential lean gain to nonessential fat gain can not be greater than the
expected ratio of the "normal" components of gain (LGN:FGN) based upon the
degree of maturity of the animal. Energy in excess of the amount required
for this proportional lean and fat gain, is stored as fat.

Net gain or loss equals essential plus nonessential gain minus mobilized
tissue. Weight, EBW, WM and WL are updated at the en of each 15-day

period.

41

k. Reproduction

Research in the area of reproductive physiology has made it apparent
that the reproductive process of the ewe is influenced by many factors.
Numerous papers have been written on the effects of breed, nutrition,
management and environmental stress on reproduction in sheep. From these
results we can conclude that the reproductive process is a sequence of
component events, each of which must occur at a particular level of intensity
for a successful completion of the reproductive cycle. If one of these
components falls below a critical level, then the level of reproduction will
be reduced or, in severe cases, the reproductive processes will be
terminated.

The general approach in modeling reproduction has been to account for
many of the components which exert an influence on reproduction. Once these
components were identified, mathematical functions were developed which
described their effects. The functions developed depict the dynamic
properties of the component by establishing the range of values and the rate
of change between values within the range. These equations are each designed
to demonstrate the behavior of a component independent of all other
components assuing that the covariance between these components is zero, or
that it is possible to disassociate the effects of one component from the
other.

The fertility subroutine deals with two aspects of the reproductive
process. First, it calculates the probability that a ewe may exhibit estrus,
and if she has, the probability of conceiving. Secondly, provided the ewe
has conceived, the ovulation rate is determined.

Estrus. The basic equations used to describe reproduction are expressed
as the ewe's functional capability of exhibiting estrus for a current period.
A series of equations determine if a given ewe exhibits estrus and is able to
conceive. The equation

PEST = .85(CFW)(CFDW)(CFT)(CFM)(CFL)(CFS)
represents the probability of estrus (PEST) in ewes that did not exhibit
estrus during the preceding 15-day period. The constant .85 sets the upper
limit on the probability of a ewe initiating estrus which can occu when
every factor equals 1.0, the maximum value. These remaining factors are

correction factors each of which range from 0.0 to 1.0 but is usually less

42

 

than 1.0, especially for stressing conditions (see below). The probability
of estrus in animals that exhibited estrus during the preceding 15-day period
is calculated as:
CCYC = (cFw-1)(cFDw-1)(cFs)
Conception. The probability of conception given estrus and breeding:
PCON = .75(cFT-5)(cFw-Z)(cFnw-2)(MB)(cFs-2)
where:
MB = The specified management breeding season, with values of 0.0 or 1.0.

Cobining the probabilities of CCYC and PEST for an open ewe, the fonn

becomes:

ACC = CYCC(ACC + PEST)(l — ACC)
where

ACC = ACC from the previous period

The rate at which animals mature influences the initiation and cessation of
their body functions. A sheep's maturing rate can influence the time at
which it attains puberty. In American and British breeds, ewe lambs reach
puberty when they reach 60 to 65% of their WMA or mature weight (Southam et
al., 1971; Cedillo et al., 1977). However, Hawker and Kennedy (1978)
indicated that Merinos reached puberty at 55% of their mature weight.

The purpose of incorporating the CFM is to prevent young ewes which are
physiologically immature from cycling. Sanders (1974) showed how the age and
weight related to a heifer attaining puberty. In sheep, within a breed, age
and weight are factors influencing the age at puberty, but in addition,
seasonality may be influential in determining when this event is initiated
(Hulet and Price, 1974).

Dufour (1975) indicated that ewe lambs reached puberty more as a
function of season than of a specific age. Furthermore, shortening day
length may trigger estrus at a relatively constant calendar time, but, at
varying ages and weights. This would cause lambs born late in the season to
cycle at younger ages and lighter weights, than older and heavier
contemporaries (Cedillo et al., 1977). Land (1978) proposed two genetic
effects that control sexual maturation; one controls the response to a given
photoperiodic change, given that an individual is sufficiently mature to

respond, and a second that determines whether she is able to respond.

43

Age is an important component in attaining puberty. An animal's age
provides an individual an opportunity to express its inherent potential for
growth and maturation within its particular environment (Fitzhugh, 1976).
Estimates of age at puberty were collected from a variety of sources. It was
apparent from these data that breed and environmental effects influence the
time when ewe lambs attain puberty. Estimates of age at puberty ranged from
157 to 400 days (Wiggins et al., 1970; Southam et al., 1971; Dickerson et
al., 1975; Evans et al., 1975; Cedillo et al., 1977). Estimates which are
close to the upper boundary of this range may be due to ewe lambs being born
immediately prior to or during the breeding season. Ewe lambs which are born
in the spring and early summer have been shown to display estrus between 160
and 250 days of age.

The third component of ewe lambs attaining puberty is weight. Estimates
of weight at puberty are just as variable as estimates of age at puberty.
They are subject to breed and environmental conditions. Reports by Foote et
al. (1970) and Southam et al. (1971) exemplify these differences, in their
reports, Rambouillet ewe lambs reached puberty at 41.8 kg and 55 kg,
respectively.

The literature reviewed indicates that ewe lambs reach puberty from 40
to 60% of their mature weight. These estimates are within the ranges given
by Sanders (1974). Using degree of a maturity as a basis, the following
equation was derived:

((WM/.6WMA) — .67)
(1-.67)

WM/WMA is the degree or fraction of maturity of the ewe lamb.

CFM =

The graph of this equation is shown in figure 12.

Correction Factor For Weight (CFW). The CFW is an adjustment for body

condition of the ewe. As she loses body tissue (both fat an lean) the ratio
of EBW to WM decreases resulting in a lower level of fertility. The CFW is a

reflection of past nutritional levels. The equation for this correction is:

e-6((EBW/WM)—(MIN WT/WM))_1_O
CFW =

e-6(1—(MIN WT/WM))-1_O

where

44

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Figure 12. The change in CFM as an animal becomes more mature.

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Figure l3. The change in CFW as the body condition of a female
changes.

45

 

MIN WT= is the minimu weight of lean and fat a sheep needs to stay alive.
EBW/WM is a fraction that measures body condition and MIN WT/WM is a fraction
describing the lowest condition a sheep may have before death. At this point
all lean and fat reserves are exhausted. The graph of CFW is shown in figure
13.
Correction Factors For Weight Change (CFDW). Weight change is a

reflection of the nutritional regimen during the period being simulated. It
is possible to evaluate weight gain for the current period because the
fertility subroutine is called after the feed consumption and nutrient
division between various sinks for an animal has been completed.
CFDW = 1 - (lOO(DWM - DEBW)/WM)
where
DWM
DEBW

Correction Factor For Time Since Parturition (CFT). This correction

the change in WM for the current 15 day period

the change in EBW for the current 15 day period.

accounts for the length of time taken for the involution of the uterus in
preparation for the next pregnancy.

Smith (1964) was able to rebreed Peppin Merino ewes (4-6 yrs old) at an
average postpartu interval of 46.1 days (range 30-67). This estimate was
obtained while the ewes were still lactating. Whiteman et al. (1972)
experimented with twice—a—year lambing using Dorset, Rambouillet and D x R
ewes. In the fall, 85% of the ewes came into estrus with an average
postpartum interval of 32 days. When Gallagher and Shelton (1974) rebred
Rambouillet ewes after lambing in October, the average postpartum interval
was 39 days; however, the interval was 53.5 days for ewes lambing in December
and January.

In South Africa, Joubert (1962) found the average postpartum interval
for Merino, Dorset Horn x Merino, Persian, Dorset Horn x Persian to be 103.3,
42.0, 90.1 and 51.0 days, respectively. The percentages of ewes coming into
estrus during the breeding season were 64, 100, 82 and 100, respectively. In
a later study with Dorper sheep, it was found that after autumn lambing, the
postpartum interval was 61.8 days (Joubert, 1972).

Attempts have been made to rebreed Karakul ewes (with lambs removed)
during the peak of their breeding season. The reported average postpartum

interval was 27.5 days (Nel, 1965). However, the conception rates remained

46

low. The percentage of ewes conceiving at 30 and 40 days and between the
ranges of 40-59 and 60-109 days were 7.7, 27.8, 42.9 and 72.2, respectively.

Seasonal effects can influence the length of the postpartum interval.
Differences between spring and summer were shown by Joubert (1972) and
Gallagher and Shelton (1974). These workers showed spring postpartum
intervals to be 117-129 days and 62.8 days, respectively, with a shorter
summer postpartum interval of 81-97 and 58.8 days, respectively. It is
speculated that the shortening of the postpartm interval is most likely due
to the decreased daylight in the smmer.

A third effect on the postpartum period is lactational status of the
ewe. Torell et al. (1956) found no significant differences for postpartum
interval for Rambouillet x Merino ewes with or without lambs. These two
groups had postpartum periods of 55.4 and 50.3 days, respectively. It should
be noted that these ewes lambed in the spring, therefore it is likely that
the effects of season and lactation are confounded. Restall (1971) found in
fall lambing ewes that nonlactating ewes had a shorter postpartum period than
lactating ewes. The nonlactating ewes exhibited behavioral estrus and
ovulation at 17 vs 34 days. Ford (1979), used Finn cross ewes to detect any
differences between the lactational effects of ewes. This work indicated
that some nonlactating ewes reach estrus by 20 days postpartum and that
lactating ewes started to show heat by 30 days postpartum. Furthermore, all
ewes exhibited estrus by days 60 and 45 for lactating and nonlactating ewes.

Sanders (1974) developed an equation to describe CFT for cattle. This
form was adapted to fit the biology of the sheep as follows:

b
CFT = 1-ea(15(P_1))

where

P = the periods since lambing

a =—.OO0000125, a constant

b =—5.2740378, a constant
This equation allows 45% of the ewes to cycle 30 days after parturition and
all of the ewes to cycle at 45 days postpartum provided all other correction
factors are 1.0 (figure 14).

Correction Factors For Lactation (CFL). As previously discussed, there

is a lactational influence upon estrus. The correction factor for lactation

47

HTH")

PERIOD SINCE LRMBING

Figure l4. The correction factor for postpartum interval (CFT).

48

(CFL) has been accounted for in the model as a constant of .95 for all
lactatin ewes. For nonlactating ewes this value is 1.0. At the present
time a functional relationship for CFL has not been developed for the sheep
model. This is, in part, due to a paucity of data. Boyd (1983) has recently
developed a function to describe this event in beef cattle and perhaps this
equation can be incorporated into the sheep and goat models.

Correction Factors For Season (CFS). For many breeds of sheep the
cyclic change in photoperiod (seasonality) is the main determinant keying
estrus activity. Breeds vary not only in breeding season length but also in
the intensity of their cycles. The photoperiodic response within a breed
will also be altered with a change in latitude or the light/dark ratio; these
responses were discussed in the comprehensive review by Hafez (1952).

As stated earlier, Land (1978) proposed that the response of ewes to
photoperiodic changes are genetically controlled. This response is believed
to be mediated via the pineal gland and its secretion of melatonin (Rollag et
al., 1978; Barrell and Lappwood, 1979). CFS is therefore a genetic parameter
specified in the model as input as a characteristic of the cyclic pattern of

the breed in the environment that is being simulated. The input required for

ranges from 0 to 1.0. This method provides the capability to specify the
exact cyclic pattern for the sheep or goats simulated. As an example of how
photoperiod influences breeding season, the response of two sets of
Rambouillet ewes in different latitudes is given in figure 15. The CFS array
which could be constructed from these data is presented in table 1. These
values would then be used in calculating PEST and CCYC.

Ovulation Rate. Prolificacy in sheep has been shown to be genetically
mediated (Turner, 1969; Land, 1981; Piper and Bindon, 1982). A major
component in the chain of physiological responses resulting in multiple
births is ovulation rate. The sheep model utilizes the genetic differences
in ovulation rate to simulate breed differences in prolificacy. In the
development of a method to assign an ovulation rate (OVR), as a genetic
parameter for the breed being simulated, several factors were considered.
One important consideration was embryonic mortality. In 1969, Edey reviewed

the literature on embryonic mortality. Basal embryonic losses were found to

49

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51

range from 20 to 30%. The greatest loss of embryos was found to occur in the
first month of pregnancy. These losses were attributed to genetic
abnormalities. Further experimentation was conducted to determine when
embryonic loss was at its peak. The results revealed that one—half of all
losses were before day 13 with most of the remainder occurring by day 18
(Edey, 1976). Work by Coop and Clark (1969) confirmed Edey's results in that
the majority of embryonic loss was before day 18 of pregnancy.

Because the sheep model uses a 15-day time step it was not feasible to
directly model this important reproductive loss. However, the loss was
accounted for by considering the genetic parameter of ovulation rate as an
effective ovulation rate; that is, the value used as OVR is adjusted downward
'by 20% to compensate for the mortality of unimplanted embryos.

Two approaches can be taken to estimate OVR. First, if the actual
ovulation rate of the breed to be simulated is known, this value may be
reduced by 20% and then used as a model input. Second, if lambing rates
(lambs born/ewes pregnant) for the breed are known and there has been no
environmental stress on the ewes, this value may be used directly as OVR. In
the case where environmental conditions are harsh, the lambing rate should be
adjusted upward to account for additional embryonic deaths and abortions.

Calculating the ovulation rate in the model (RATE) is, like other
components of reproduction, an interactive process. The manner in which
ovulation rate is calculated represents this concept:

(1.O—CFS)CFS.7)(CFC.5)(CFM.5)

RATE = OVR(CFW'7)(CFDW)

The RATE equation combines the effects of breed, seasonal variation,
body condition and maturity. Periodic environmental (nutrition) changes are
mediated through the CFDW portion of the equation. The effects of current
weight change (CFDW) can be over—ridden when photoperiod effects are optimum;
i.e., CFS = 1.0.

Edey (1968) showed how increases in body weight (therefore condition)
increased ovulation rate. However, this response was sigmoidal in shape and
not linear as reported by Coop (1962). Gunn and Doney (1975) reported
significant differences in ovulation rate for ewes which had three different
condition scores. Earlier work by Gunn et al. (1969) led the authors to

conclude that there was a threshold of body condition above which the level

52

of food intake has no effect on ovulation rate and below which food intake is
important.

Reeve and Robertson (1953) reported that maturity, measured as age,
influenced ovulation rate. With four breeds of sheep, they showed how there
is a curvilinear response in ovulation rate as ewes grow older. Not only is
there an increase in ovulation rate to approximately 5 years of age, but
thereafter there is a decrease in ovulation rate at a slower progression than
the increase.

Gunn et al. (1969) found an interaction between age and condition for
ovulation rate. They stated that the ovulation rate of young ewes was more
sensitive to the influence of body condition than of older groups of ewes.

Reeve and Robertson (1953) showed that season influenced ovulation rate.
As the middle of the breeding season is approached, the percentage of twins
born from ewes bred at this time increases; at the extremes of the breeding
season the percentage of multiple births declined.

Once RATE has been calculated the following equations are used to

determine the actual ovulation rate:
TRP = (e.7(RATE-1.0)_l)/(e2(.7)_l)

TWN = (RATE — 1) — 2 TRP
SNG = (1 — TRP) - TWN
where
TRP = 3 ova
TWN = 2 ova

SNG = 1 ovu

These equations generate numbers between 0.0 and 1.0. The values for
TRP, TWN and SNG are then compared to a random nuber (RI) which is generated
from a uniform distribution ranging from O to 1.0. The following IF
statements show the final steps in calculating ovulation rate:

IOVR = 1

IF (RI > SNG),IOVR = 2

IF (RI > (l—TRP)),IOVR = 3

From this point the subroutine CONCV is called to initiate body

parameters for the number of fetuses conceived.

53

l. Fiber Production
Potential. The model simulates wool production for breeds which grow

wool. The genetic potential for wool growth (GWOOL) is similar to other
genetic parameters used in the model in that it specifies maximum (or
potential) wool growth per day for the simulated breed when all other factors
influencing wool growth are at an optimal level.

Photoperiod Effect. Fleece growth is adjusted or modified by

photoperiod (SCR) and age and degree of maturity (UCR). Nagorcka (1979)
derived an equation describing the photoperiodic effect. For this equation,
amplitude (AMP) of seasonal differences (distance from the equator),
frequency (FREQ) of day light pattern (once/year) and time of peak growth
(PHAS, mid—June in Northern Hemisphere, day 165; and mid—December in Southern
Hemisphere, day 345) must be specified:

SCR=AMP(cos(120(FREQ (DAY-PHAS))))

where
AMP=.35GWOOL; for 35 degree latitude
FREQ=21r/360 1r= 3.1416

DAY=day of the year
PHAS=165 FREQ
Using the photoperiod reported by Shelton et al. (1973) the following
example of wool growth for Rambouillet sheep in Texas and Idaho may be
generated. The parameters used are:
GWOOL = .0076 kg given that a ewe shears 5.45 kg of grease fleece which
has a yield of 50% thus producing 2.725 kg of clean wool which
is divided by 360 to put wool growth on a per day basis.

AMP = .31(.0076) for Texas and .42(.O076) for Idaho; 31°N and 42°N are
the latitudes, respectively.
FREQ = 2w/360 — .0174533
PHAS = 165 FREQ = 2.8797933

Figure 16 illustrates how photoperiod may affect wool growth. The effect on

the same breed is illustrated for 3 latitudes: 15°N, 31°N and 42°N.
Age And Degree Of Maturity. The influence of age and degree of maturity

are calculated by the following equation;

UCR = (l+e-.165(AGEP)-1))(WM/wMA).67

"ml;

vTYvvvYvrIVIVTYIIIVIIIIVIYFI-IIVIIIVIII!lIIYVIIIIYITIIIVIIIIIIIIYVIYTIIIIIIIIITYIIIIIIVIIYIYfVVIIIvvIIvYI-TvvrvIvvvvvvvvvr

0 2 U 6 8 10 12 1U 16 18 20 22 2%

PERI00 0F THE YERR
Figure 16. The influence of photoperiod on wool growth.

   

= 12 periods of age
= 24 periods of age
48 periods of age

WCUG

Z

\.|

l‘
ll

IvuvuvvvvrIvuvuvvuvr‘vvvv|vvvv|vvvvv vvIvvvrvrvvv-I-rvvvvvvyvl

0.0 0.1 0.2 0.3 0.H 0.5 0.6 0.7 0.8 0.9 1.0
UEGHEE 0F MRTUHITY

IYIYvvIvvYvIvvvYTvYvIrYYYvIv-vvvr-rrrf

Figure l7.“Age and maturity effects on wool growth.

55

Figure 17 shows how wool growth is adjusted for various ages and degrees of
maturity. It also demonstrates that this equation has a larger influence on
younger sheep.

Using the results from the UCR and SCR equations, fleece growth (FGRTH)
may be calculated by the following equation:

FGRTH = UCR(SCR + GWOOL)

Wool Growth. After FGRTH has been calculated, the nutritional
requirements to meet fleece growth are calculated. In this process it is
assumed that clean wool is 100% protein and deposited with an efficiency
equal to BVP (Graham et al., 1976). The gross energy content of grease wool
is assumed to equal 6.0 Mcal/kg and to be deposited with an efficiency of 20%
(Graham and Searle, 1982). From these assumptions we can calculate the
efficiencies used in calculating nutrient requirements. For protein (KPW)
and energy (KW), these are:

KW 6.0/.20

KPW 1.0/BVP

The nutritional requirements for energy (FIBRQE) and protein (FIBRQP) are
calculated as:

FIBQRE = KW(FGRTH/YIELD)
FIBQRP = KPW(FGRTH)
where
YIELD = The percentage of grease fleece weight which is clean wool.

m. Mortality

DIE Subroutine. The DIE subroutine provides the basis for determining
deaths in a flock based on physiological and nutritional status. This
subroutine does interact with other functions but it has more empirically, or
statistically, based characteristics and it also has stochastic elements.
Mortality rates based on experience of the area and prevailing practices are
necessary inputs at the present time, the only specific "health effect" in
the program is that due to internal parasites (haemonchus); its effects on
mortality is mediated via effects on physiological status and therefore the
DIE subroutine.

A predisposition to death associated with each animal is calculated;
this variable, FD (fraction dead), ranges from 0.0 to 1.0. To calculate if

death occurs the variable FD is compared to a random number drawn from a '

56

uniform distribution between 0.0 and 1.0. If FD is greater than the random
number, the animal dies.

Empirical Death Factors. At the beginning of the DIE subroutine all

animals start with FD = .001; this value is then modified by a series of
"death factors" which increase FD, therefore raising the chance of death
occurring. These factors are: body condition (CFW), period of the year (CT),
age of the sheep over 1 year (CA), sheep under 1 year of age (CL) and
lactation (C11). Factors CT, CA and CL are vectors which are based on
experience for that area and practices employed. The vectors depict changes
in the probability of death other than direct nutritional reasons (e.g., heat
stress, lack of water, and disease outbreak). Therefore the vectors change
from area to area and from one production system to another. Determination
of the die vectors is empirical and requires adjustment for simulations run
for each area and set of production practices.

Interacting Correction Factors. Body condition (CFW) is calculated

within the DIE subroutine by the same equation used to calculate body
condition in reproduction (EBW/WM). Body condition alters FD (FD1 = FD) by
the equation:

FD2 = FD1 (A—(A-1) CFW)
where

A = 4
This equation is a linear function except that CFW is curvilinear. The value
of A, set at 4, produces the desired slope seen in figure 18. Note that
death occurs when CFW reaches .54 due to enaciation per se; the probability
of death increases as CFW decreases toward .54 so that few animals would ever
reach CFW = .54.

The lactation status of a ewe increases her FD in the first period of
lactation only using the equation

FD3 = FD2(C1l)
where

C11 = 1.25

Newborn lambs are exposed to higher levels of mortality if milk
consumption does not meet their nutritional requirements. A result of this

situation would be a stunting of lamb growth which may also reduce their

57

UYCF-T)

UII-IIDFFIC Z~— TYIUIDTTIIF7ZP-I

..... ..P.".".q.".".","..".q."".".V."."",".".H.V.n."","".".q.".".wr
0 1 0.2 0.3 0 Q 0.5 0 6 0.7 0 8 0 9 1 0
CFH

Figurel8. The increase in FD as body condition worsens.

IVIIYIITYvvIIVIIYIIIIIVIVIYYYYIYVVV['7' YYYYI

0.5 0.6 0.7 0.8 0.9 1.0

vIIVfYI-YVIVIIIIVITVYIIII

0.1 0.2

vvrvvvrvvvvvlvvvv

0.3 0.0
NM / ENM

The increase in FD as stunting becomes more severe
in young lambs.

Figurel9.

58

survivability. This concept was modeled by using an equation to increase the
likelihood of death, FD, for lambs which have not grown in WM. The equation
compares the expected WM (EWM) to the actual WM for lambs between 1 and 4
periods of age. The PLUS equation is defined as follows:

PLUS = 1_((e-8(WM/EWM—.3)_1)/(e—8(.7)_

l)
where

EWM = BW + 15EDW(AGEP)
and

EDW=expected growth in WM and is calculated as (WMP-BW)/TI
The PLUS curve is shown in figure 19. PLUS is added to FD where all other
factors are multiplied (FD+PLUS).

The subroutine LMDIE calculates the probability of a lamb being
stillborn or dying within the first 24 hr after parturition (PROBD). The
probability is calculated as:

PROBD = CB(CBA)

where
CB = A vector containing probabilities of death in newborn lambs due to
the time of year.
CBA = A vector containing probabilities of death in newborn lambs due to

the age of its dam.

PROBD is then compared to a random number, uniformly distributed ranging from
0.0 to 1.0, if PROBD is greater than the drawn number the lamb dies.

Abortion. Situations arise where pregnant ewes are severely
undernourished. In such an instance fetal growth is reduced or halted. When
this happens the chance of abortion is increased. The model monitors this
situation by accountin for and storing the potential and actual conceptus
weight. When the ratio of actual conceptus weight to potential conceptus
weight is less than .5 the ABORT subroutine is called and the ewe aborts her
lamb. Abortion may be triggered at a higher ratio and, if this is the case,
the .5 base can be appropriately increased.

Early embryonic mortality is part of the PCON subroutine. Additional
abortion may be specified at an mpirical rate.
n. Health

Limitations. The interactive health component of the model is currently

limited to the effects of internal parasites, more specifically the helminth.

59

The important impact that helminths have on sheep and goats is of major
hportance on a worldwide basis (Preston and Allonby, 1979).

The functions in the parasite subroutine are developed around concepts
for which there is less basis in the literature and less experience—based
knowledge than for any other equations used in the model. The equations
developed depict animal response to parasitic load and, although a
considerable amount of biology is known by parasitologists, experimental
quantification of the effects parasites have on the biology of sheep and
goats is limited. Therefore, the cooperation of consulting parasitologists
was paramount in developing the approach and methodology. However, the
subroutine developed does provide the opportunity of quantitatively assessing
the effect of health regimens and, perhaps more importantly, it provides
parasitologists an opportunity (incentive) and basis to further investigate
the interaction between parasite and host; i.e., it "... throws information
gaps into sharp relief, thus guiding future data collection exercises towards
the most critical areas" (Hallam et al., 1983).

Population. An overview of the health component is presented in figure
20. The program first establishes the worm population of an animal, which
is a summation of previously acquired worm count and the larvae intake for
the current period. The existing population may be reduced by the
administration of anthelmintics which have varying levels of efficacy, where
this level is an input parameter. Larvae intake is also an input parameter
(based on data or experience) which varies as the situation (e.g., season)
dictates.

The effective worm population count is also conditioned by the animal's
immune status that determines its resistance to the parasite. The modeled
immune response is a function of age, body condition, pregnancy status,
lactational status and genotype. The effective wonm population is the number
of worms surviving and having an influence upon the animal.

Several avenues are utilized in the model to express the effect of the
parasites on the individual. The physiological limit of feed intake is
reduced as the worm burden becomes heavier. Also, there is a reduction in
energy absorbed due to damage to the gut. This effect is small with

haemonchus; however it is programmed in a fonn such that it may be increased

60

 
  

  
   

i 
X
Updated I
Worm t \
Population l i \
I
i, Etiective '
___________ ___ Worm
{ Ir ———————— -- Population
i I it
i i ii
I
Feed v Feed i i
Resource ‘ Intake i i
ll
A J

     

 

Nutrients
Available
tor
Absorption

 

 

tor Animal
Use

Figure 20. A flow chart of the effects of parasites on productivity.

61

hen other types of internal parasites are simulated. The maintenance
requirements of the host are increased to reflect the loss of blood absorbed
by haemonchus.

Effects. Each sheep has a potential parasite population (PWPOP) which
is a function of body size. The maximum nuber of worms that can implant
themselves in the gut wall is set at 11,000. The equation describing PWPOP
is:

PWPOP = 11000(1-e"-°45WM) (1_e"-°45WM))
The intake of worms in a period (WINTK) an the existing worm population
(WPOP) in the sheep may not exceed PWPOP.

Each breed of sheep has a genetically based resistance (PRST) to
internal parasites. Preston and Allonby (1979) demonstrated this effect and
cite other research reports that show similar results. For simulation, a
breed is assigned a level of resistance indicative of its ability to maintain
resistance to population build up of the parasite population relative to
level of infestation. The "genetic resistance" of each breed, PRST, ranges
from O to 1.0, a 0 PRST means no resistance and 1.0 means complete resistance
to infestation.

As stated previously, the animal's immune response is a combination of
factors. One of these is the influence of age (CIMAGE) on immunity.
Information from T. M. Craig (personal communication) was used to develop the
CIMAGE equation:

CmAGE = e(AGEP-9)/(e1.OO5_1)

The CIMAGE equation allows animals to increase resistance to parasites as age
increases (figure 21). Body condition has been established as an important
factor in determining resistance. Body condition is a reflection of several
factors. When condition is high, EBW/WM close to or greater than 1.0, it is
an indication that the forage resource is not limiting, therefore the sheep
do not graze the forage close to the ground and increase the chance or rate
of larval consumption. Furthermore, it is general knowledge that animals in
good body condition have a higher resistance to diseases and parasites, and

their debilitating effects, than animals in poor condition.

62

LTJCJPZZHO

HGE IN PERIODS
Figure 21. CIMAGE, the increase in resistance due to the animal's age.

TICJF1Z{'—'\’W

A1111

vvIvwvvv ‘vvvwwvwvvIvvwvvvvvvlvvvvvvvvvIv v '

IvvvvvvvvvlvvvvfvtvvIvivvvvvvvIrvYvvv

0.0 0.1 0.2 0.3 0.14 0.5 0.6 0.7 0.8 0.9 1.0
EBW/WM
Figure 22. CIMCON, the correction factor for condition in worm
burdened animals.

63

The equation describing the influence of body condition (CIMCON) on

resistance to parasites is:

CIMCQN = (e20(1-EBW/WM)_1)/(eZ0( .4)_1)

Figure 22 shows the shape of the curve described by CIMCON.

Lactation status has an important impact upon a ewe challenged by
haemonchus. During a lactation a ewe loses her immunity and then regains it
later in lactation as the "self—cure phenomenon". Figure 23 illustrates the
shape of the curve and the equation describing lactation effect is presented
below:

CIMLAC = 1.0 —.583LACPP + .l167LACPP2
where:

LACPP = the period of lactation.

The final adjustment made to the immune status of a ewe is for pregnancy
(CIMPR). As a ewe reaches the last period of gestation her imunity drops
from 1.0 to 0.60.

The product of the mediating factors previously described are used as
the actual resistance to the parasite load (ARST).

ARST = PRST(CIMCON)(CIMAGE)(CIMPR)(CIMLAC)

The value of this equation ranges from 0.0 to 1.0. The value for ARST is
then used to reduce the potential worm population to obtain the effective
worm population (EFFWOP), the number of worms which have an effect on the
host:

EFFWOP = WPOP — ARST(WPOP)

Once the worm burden, or effective parasite population, has been
established, the effect on the host is calculated. Reduction in the
physiological limit effect (WRR3) is given by:

WRR3 = _O1e4.60517(EFFW0P/PWPOP)
The range of WRR3 is from 0.0 to 1.0 and the maximum effect on physiological
limit is 20% (figure 24a).

Another effect of internal parasites is damage to the gut wall which
decreases the host's ability to absorb energy (WRRE figure 24b). This effect

is represented by the following equation:

64

 

r>>-H Z|#<1

_ 13.2»

JLLLLAA

PERIOD OF LRCTHTION

Figure 23. The fluctuation in ewe resistance during lactation.

65

i a
0.751
W
R 0.50
R
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0.0 0.1 0.2 0.3 0.0 0.5 0.6 0.7 0.8 0.9 1.0
Fraction of Maximum Worm Population,EFFWOP/PWPOP
b

P1712151

1.001
.
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.
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.
.
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0.0 0.1 0.2 0.3 0.U 0.5 0.5 0.7 0.8 0.9 1.0
Fraction of Maximum Worm Population, EFFWOP/PWPOP

Figure 24. The influence of parasites on feed consumption, (a). The
fractional reduction in energy utilization as worm burden increases, (b).

66

1_ef3@0543(EFFWQP/PWPQP)
WRRE =

WORTYP is a term that denotes the extent of damage to the lining of the gut.
Haemonchus does not damage the lining as severely as other species of
parasites and the WORTYP value is set at .02. The effect of other species
may be set higher (or lower) depending on their characteristics. The maximu
value of WRRE is therefore .02; that is, the digested nutrients of a
particular sheep could be reduced by 2% due this effect.

The final simulated effect of parasites on the sheep is an increase in
maintenance requirements to account for the loss of blood absorbed by
haemonchus. The additional requirements for energy (WRQE) and protein (WRQP)
are calculated as:

WRQE MTE(EFFWOP/PWPOP)/(.25 + (EFFWOP/PWPOP))

WRQP .0164WRQE
The term (EFFWOP/PWPOP)/(.25 +( EFFWOP/PWPOP)) ranges from 0 to .8; i.e.,

under maximum haemonchus load of a sheep with zero level of immunity, etc.,
the energy requirement for maintenance increases 80%.

Simulations. A series of simulations was performed with the SAV to
determine how the model would respond to the parasite subroutine. A goat was
used for the simulations (goat model will be described in the next section).
A similar response was obtained when a sheep was used. The model input
parameters were set to simulate a dual purpose goat which had a WMA of 45 kg
and either 100, 50 and 10% PRST (figure 25). Larvae intake was 2000 per
period. Simulations were of single nonreproducing does of each PRST which
were drenched at 6-month intervals with an 80% effective anthelmintic. The
100 and 50% PRST does were either completely or partially resistant to the
parasite load therefore the anthelmintic had little or no effect on their
body weight (figure 26).

Does of PRST of 10 and 50% were then simulated to be bred and forced to
have single and twin kids to determine the influences of pregnancy and
lactation on doe weight (figures 27 and 28). These results show that the
"50%" doe was able to regain some weight while the "101" doe continued to
lose weight and would have a high probability of dying (condition decreased
to 70%; i.e., EBW/WM = .7). Further simulations involving similar does

giving birth to singles and being wormed at 3-month intervals with a drug

67

effectiveness of 80% were performed (figure 29). Under this health
management, both "IOZ" and "SOZ" does were able to maintain sufficient body
weight and remain in reasonable body condition.

The changes in the host's worm population are plotted in figure 30. The
graph illustrates the genotypic difference in PRST and how the anthelmintic
reduces the worm population.

These simulations can not be taken as validations since they are not
compared with real data; nonetheless, they do appear to represent the form
and magnitude of effects expected by experienced small ruminant
parasitologists. Currently, experiments with the TAMU/SR CRSP Breeding
Project in Kenya have been designed to provide feedback information to refine

this component of the model.

68

I-IZ '<UOU$ MOD

Ks

SS

50

us

HO

35

30

Figure 25.
Te$1$tan¢e (PRST) levels of 10 (solid line), 50 (dashed line) and 100
(dotted line).

PERIOD OF THE TEHR

Non-reproducing doe body weights with no drenching. Genetic

69

HS *<UOUU [TJOU

Ks

55.0 1

52.5

50.0

U\

Q7.

PERIOD OF THE YERR

Figure 26. Drenching effects on non-reproducing does with a PRST of
No drench (solid line) and drench (dashed line) treatments.

70

_\_ 1_P\m4Q [~.A\_Qll£) mlLlznln4m/nflnnfln

v-IZI '-<CJOW [TJOU

Ks

 

60 -+
SS -
so i
us l
n0 l
3S -
3o l
TFTTP |IvIIIIT|IIIIIvIIYIITIIIIIIIIIrYYITIYIIIVIIVYI-I I I 1 I I I III I I v I I I I Iv] v I r I I Y I 11' I r r Y T Y I III v 1 1 v v r . vvlvrvvv.wrv~r
O 2 *4 5 E! 1O 12 ll! 16 18 2O 22 214
PERIOD 0F THE YEFIH
Figure 27. The influence of kidding on doe body weight when PRST = l0.

Doe with a single kid (solid line) and doe with twins (dashed line).

71

S7
0
E

S1
B
O
D
Y US
W
T us
K8

H2

Figure 28.

PERIOD OF THE YERR

The influence of kidding on doe body weight when PRST = 50.

Doe with a single kid (solid line) and a doe with twins (dashed line).

72

51

CHOU

H8

r-lfi v<UObd

K8
39

PERIOD OF THE YEHR

Figure 29. The effect of drenching,on reproducing does which gave birth
to singles, at 3 month intervals. PRST = 10 (solid line) and PRST = 50

(dashed line).

73

ZQ--4DF'CI'UCJ"U "_-I'_'.1l.'JZC

i
t")
l?)
F)
L:

5050

    

(T:

_'|

c1
if: “
l_'-A..A.l..|..i_44 .L_L.|.J. A-LJ-A-l. 1.4. 04.4.4.1 _

,...»
.-

  

t
\ A A
0000 \ / \ /
/ / \
\ / \ (/ \ _
\ / .- — /
\ / \y" f  \ ’
2000 ,2 /  \ /
\ / ,»"' \/ ‘\_ /
__________ --V_(_--_---___.—" v 
----- "\/
0-1
     
0 2 u s a 10 12 1n 1s 1a 20 22 2n

PERIOD OF THE YERH
Figure 30. The periodic changes in reproducing doe's worm population.
Genotypes PRST = l0, no drenching (solid line); PRST = 10, drenched every
3 months (dashed line); and PRST = 50, no drench (dotted line).

74_

3. GOAT MODEL

The production resources utilized by sheep and goats and the variability
of production systems (e.g., extensive vs intensive) for sheep and goats are
similar. In many situations these species are treated as one production
unit. The literature indicates that there are biological similarities
between the two species, but recent experimental results have more clearly
identified biological differences. The following section describes these
primary differences and how they were incorporated into the construction and
functions of the goat model.

Much of the success of biological discovery has been based on the
separation of the components of a biological unit and examining the
components free of interference from other components. However, a
functioning biological unit depends upon the integration and contribution of
all its components. Therefore, component Aqmay influence component C by an
inconspicuous pathway. Such an example can be illustrated with fat
composition of an individual animal. Taken by itself, it may appear that fat
composition has influence only as an energy store and on carcass quality.
However, fat content has been shown to influence feed intake, reproductive
rate, the ability of the animal to survive stressful periods and other
functions. Similarly, in the conversion of the sheep model into a goat model
each single change tends to have pervasive effects because the model is
constructed to represent the animal as a biological entity. That is, a
single altered equation may have many indirect effects, as well as a direct
effect, upon an animal's simulated response.

The program structure, logic, flow and subroutines of the goat model are
the same as those in the sheep model. The management subroutine is also the
same in both models. The flexible manner in which the management subroutine
was constructed allows it to facilitate simulation of management alternatives
which can occur in either species. Anticipatin production systems where
sheep and goats are maintained as one flock, the model structure and
programming were designed to allow simulation of both species simultaneously
in the same computer run.

The reproductive processes of sheep and goats have many similarities.

Shelton (1978) reported average estrus cycle length from 19 to 21 days which

75

is similar to the 16 to 17 day cycle of sheep. In the same report, an
average gestation length of 149 days was given. As with sheep, seasonality
(photoperiod effects) and breed affect a doe's cycle. In equatorial regions
goats display year—round sexual activity. Goats in temperate regions display
a restricted breeding season for a portion of the year (Doney et al., 1981).
Breed effects have been shown to influence breeding season; e.g., Sengar
(1976) reported that Jamnapari does were more seasonal than Beetal, Barbari
and Black Bengal does.

Does often have a high rate of multiple ovulations. Ovulation rate is
genetically mediated but is also influenced by environental effects.
Ricordeau (1981) summarized breed differences in litter size, an indicator of
ovulation rate minus embryonic death and abortions. Mean litter size ranged
from 2.45 to 1.11 kids. Ovulation rate may be affected by body condition and
maturity of the doe (Shelton, 1978; Shelton and Groff, 1974).

From the information reviewed it is apparent that the same environmental
factors influence estrus an ovulation rate in sheep and goats. Therefore,
the general method used to simulate reproduction in sheep can be used for the
goat. It is assumed that the equations used in the sheep model fertility
subroutine are applicable to the goat. Further simulations may indicate that
some of the assumptions do not hold within close limits. If this occurs, the
model will help identify the knowledge voids for which experiments can be
designed to answer specific questions about reproductive processes or provide
more definitive quantitative values.

Morand—Fehr (1981) discussed growth in the goat. He stated that there
have been no systematic studies of fetal development. However, the
information that does exists indicates that fetal growth is very similar in
both species. Eighty percent of fetal kid growth was reported to occur in the
last 8 weeks of gestation (Morand-Fehr, 1981) which is in agreement with the
report on fetal lamb growth by Rattray et al. (1974).

As with other livestock species, birth weight is highly variable and
influenced by genetic and environmental factors. The primary influence on
birth weight of kids is related to the form and size of adults of the breed
to which it belongs (Morand-Fehr, 1981). Morand—Fehr (1981) stated that, on
average, birth weight was 1/15 (6.7%) of adult weight. The sheep and goat

76

 

model uses 6% of WMA (base adult weight) to establish the target birth
weight. Simulated kid birth weight varies according to sex, number of litter
siblings and nutrition of the dam.

The growth and development of body tissues in goats are similar to those
observed in other ruminants. The proportion of lean weight as a fraction of
empty body live weight is similar to sheep (Morand—Fehr, 1981) but definite
differences exist for fat deposition. Morand-Fehr (1981) stated that kids
deposit fat earlier in the loin of the carcass and slower in the leg when
compared to lambs. When comparing fat deposition to empty live weight it is
apparent that fat development of goats is lower than that of lambs. However,
it tends to increase linearly with empty live weight but at a slower rate of
increase when compared to lambs (Morand—Fehr, 1981).

Naude' and Hofmeyr (1981) reported that Boer goats at approximately 250
days of age and weighing 41 kg had 12.9% fat. Gaili et al. (1972)
demonstrated that Sudan Desert sheep had a larger percentage of fat in their
carcass when slaughtered at "young", yearling and mature ages than goats
(8.9, 16 and 24.5% in sheep and 5.5, 10.7 and 19.1% in goats, respectively).

In converting the sheep model to a goat model, body composition and
growth have a key differentiating role. Fat composition of a goat in an
average, "normal" (nonstressed) condition is assumed to be 3% at birth and to
increase to 15% at maturity with a maximum fat content attainable of 25%. In
the sheep model, fat is assumed to be 3% at birth and increases to 25% at
maturity with a maximum of 40%. As with the sheep model, 3% fat is the
minimu level required to sustain life at any age.

As discussed earlier, growth rates of goats are slightly less than
sheep. This difference is at least partially a result of slower (less) fat
deposition. The lower growth rate of a goat was modeled by reducing the
maximum daily rate of energy gain from .0125 Mcal/kg/day to .00625
Mcal/kg/day, a reduction of 1/2. The effect of this reduction is expressed
in the equation for maximum energy gain (MXEG):

MXEG=CFI1(.0l25)(EBW)(WM/WMA)-45(3(WM-.882 EBwH/wm
where

CFI1 = .5

77

The calculated value for MXEG is used to calculate the physiological limit
(PSOL). The influence of MXEG on PSOL is to lower the satiety level in the
goat.

Another major difference incorporated into the goat model is an increase
in the physical limit for feed intake. This increase is facilitated in the
goat by having a faster passage rate of intake through the digestive system.
The faster passage rate in goats is associated with a smaller rumen and
reticulum. In synchrony with their gut size, goats have evolved as highly
selective grazers (Kothann, personal communication).' Singleton (1961)
measured the flow of digesta through the duodenum of goats and sheep. He
reported that goats had a flow rate of 12-15 l/day vs 11 l/day for sheep for
the diet used in his study. Information from Geoffray (1974) showed that
goats have a higher frequency of eating than sheep; however the dry matter
intake and organic matter digestibility were not significantly different.

The increased frequency of feeding implies that the goats were feeding to
their physical limit but were not meeting their nutritional requirements;
therefore they were only partially digesting the consumed feed (compared with
sheep), thus allowing them ruen space to consume more forage. Huston (1978)
also found that goats have a greater passage rate that results in a capacity
for greater food consumption at more frequent intervals.

In the goat model the physical limit (R2) for feed intake is adjusted
upward by the variable CFI2:

R2 = CF12 (J2 WMJS) e-5.s(.s5-n1s)2
where

CFI2 = 1.4; In the sheep model this variable is set at 1.0.

The protein and energy requirements are calculated essentially the same
in both models, but the results differ due to the alterations previously
described. The NRC requirements of goats (1981) repeatedly refer to the
similarity between sheep and goat data for maintenance, pregnancy and growth.
This precedent is currently accepted as the soundest basis for designing the
nutritional component. As more nutrition research with goats is reported,
model modifications which are indicated and supported by data will be made.

Also, as simulations and validations proceed, more precise indications of

78

nutritional differences between sheep and goats as well as the nature of the
differences, will become evident and may be incorporated into the model.
Similarities between the goat model simulations and reports from the
literature of basal metabolic requirements of a doe, are illustrated in the
following example where the maintenance requirement for energy for a 50 kg

doe consuing feed of 60% digestibility was calculated.

Method source ME Requirement Location
NRC (1981) 1.91 Mcal/day U.S.A.
Sengar (1980) 1.757 Mcal/day India
Morand-Fehr (1981) 1.76 Mcal/day France
Goat Model 1.72 Mcal/day

Although direct comparison between ME requirements should not be made, due to
differences in breed of goats, type of feed and the age of goats used, it is
interesting to see how closely these values are grouped. Also, it should be
noted that the goat model has more refined provisions to account for
differences in physiological status (e.g., pregnancy and lactation) and
activity (e.g., greater distance traveled to grazing or water).

Important differentiations between the sheep and goat models are
contained in the specification of input parameters. The values used as input
parameters are equally as important as the model equations for they specify
characteristics of the breed being simulated and take into account the goat's
feeding behavior. The genetic parameters are specified to reflect inherent
differences between breeds; e.g., maturing rate potential independent of size
potential is characteristically slower in tropically adapted breeds and must
be properly specified for the breed simulated.

Differences between sheep and goats in diet quality and quantity have
been shown to exist (Bryant et al., 1979; Bryant et al., 1980). It is
finportant that these differences be taken into account when specifying forage
input vectors for either species.

Limited research and general experience indicate that goats are more
agile and active than sheep (Huston, 1978). Therefore their activity factor,
expressed as distance walked, should be higher than the factor used for
sheep. The higher activity factor of the goat indicates that they have a
higher maintenance cost than sheep. On the other hand, goats are more agile

allowing them a larger more diverse foraging range; the effects of these

79

grazing behavior characteristics are reflected in the forage availability
vector. For a "cut and carry" confinement system, a differential selectivity
is often observed but has not been sufficiently quantified for inclusion as
an interactive component of the model (or inclusion in NRC requirements or
other objective considerations of goat nutrition), but may be accommodated in
simulations through input vectors to the extent that observations are
available.
4. PARAMETER SPECIFICATION
a. Forage Parameters

Three sets of data must be specified as input parameters in order to
perform simulations. These are forage, animal and management parameters.
The forage parameters are crude protein, digestibility and availability.
Crude protein and digestibility estimates are of th forage plus any
supplements in the diet. These are usually obtained from forage research
reports or forage scientists experienced in the geographic area.
Availability is the amount of forage, measured in kg/head/day, that is of the
given quality of the diet for that period, which is available for an animal
to consume. The estimation of availability is difficult because measures of
the total biomass or stratified layers of biomass estimates are not directly
useable. These tend to overestimate the forage availability because the
actual diet selected from the total does not include the lower quality plant
components. In addition these estimates do not include the effects of
selective grazing on diet quality. One method used to adjust forage
availability for free-grazing animals has been to collaborate with persons
experienced in the production environment and have then identify critical
times of the year, such as the last month of a dry season. When the critical
times of forage production have been identified the input availability is
adjusted downward to correspond with the level of severity.
b. Genetic Parameters

The genetic parameters provided vary with the breed being simulated.
The genotype of each animal has been set equal to the mean of its breed. The
components of genotype are mature size (WMA), milk production (GMLKL),
ovulation rate (OVR), seasonality of estrus (SEAEST), wool growth (GWOOL) and

resistance to parasites (PRST). These genetic potentials are estimated as

80

 

the values for mature females in good condition that have never been
restricted by nutrition or health. These values are estimated at the
location in question if possible but may be obtained from the literature,
unpublished or other data, or estimates of knowledgeable persons (actually,
usually a combination of these sources).

c. Management Parameters

Management options are the third set of input parameters. These
parameters specify breeding season, weaning date or weight, feed
supplementation, sale policy, culling policy, pasture rotation and flock
assignments. Age, weight or time of year can be used to determine when the
previously mentioned parameters are fimplemented.

d. Example Of Parameters Specification

An example of how input parameters are established is given for a series
of simulations in northern Kenya. The genetic parameters were initially
ezewsmktemei. flaws general. 53123219)?» $25 mes 22b 5:1)» 2710a? >2se2 00 flare
relevant information sources. The breed simulated was the Somali Blackhead.
Mason and Maule (1960) describe this breed as a fat-rumped hair sheep, with a
mature ewe weight ranging from 33 to 52 kg and milk production ranging from
200 to 300 g per day.

Field (1979) studied the characteristics of this breed in northern
Kenya. She reported that mature pregnant ewes weighed 35.3 kg in the wet
season and 31.7 kg in the dry season. It was estimated that ewes produced
58.8 l of milk in 5 months. Season and sex effects appeared to be present.
Rams born in the rains or in the dry season had a preweaning weight gain of
107.1 and 91.9 g/day, respectively. Ewe lambs gained 91.9 and 86.5 g/day in
the respective seasons. Carles (personal communication) has recorded weights
of Soali Blackhead ewes at Kabete, Kenya and found them to have an average
mature weight of 35 kg.

The seasonal factors which affect the productivity of East African
Blackhead sheep were examined in western Uganda (Trail and Sacker, 1966a).
Lambs born to ewes exposed to dry conditions during the last 2 months of
pregnancy had mean birth weights of 2.61 vs 2.63 kg for those born in the
remainder of the year (P>.O5). At two months of age those lambs which
suckled during the dry season weighed 9.64 kg compared to 10.25 kg (P<.05)

for lambs not nursing in the dry season. If lambs were born before the dry

81

season but were still nursing during the dry season (age 2 to 5 mo),
seasonality was nonsignificant. Sacker and Trail (l966a) provided estimates
of the growth rates for the same group of lambs. Single born lambs had a
range in weight gain from birth to eight weeks of age of .095 to .136
kg/day.

Mortality rates from birth to 5 months of age of single lambs from ewes
lambing for the first time was 21.6% with 6.5% occurring from birth to 21
days of age (Trail and Sacker, 1966b).

from aged ewes was 15.8%, with 4.6% occurring from birth to 21 days.

The mortality rate for single lambs
Those
ewes producing twins had a 27.5% loss of which 10.2% came before day 21.

Lamb mortality was higher in the dry season than in the remainder of the year
(31 vs 20%).

The Somali Blackhead or varied strains of it have been used outside of
Africa. Estimates of mature ewe weights from South America range from 27.6
to 31.3 kg (Butterworth et al., 1968; Fitzhugh and Bradford, 1983). Birth
weights were reported to range from 1.9 to 3.0 kg. Butterworth et al. (1968)
reported that the milk production of ewes on a high and low nutritional plane
was 67.9 and 37.8 kg for a 12-week lactation.

The literature reviewed indicated that the genetic parameters for mature
size (WMA) and the genetic potential for milk (GMLKL) should be set at 35 kg
and 1.30 kg, respectively. The value used for WMA agrees with Carles
(personal communication) whose sheep were under very little stress allowing
them to express their genetic potential. The 1.30 kg level for GMLKL (which
is the peak milk production level) would produce an average milk production
within the range of reported values. The ovulation rate for the Somali
Blackhead was set at 1.1, which would result in very few multiple births.
The seasonality of reproduction in the Somali Blackhead is not influenced by
photoperiod. Therefore, seasonality of estrus in the model is set to 1.0 for
24 periods which allows the sheep to breed year around.

The forage parameters used in the simulations were provided by the IPAL
staff. They hand plucked the plant species that sheep and goats were
observed foraging. The crude protein and digestibility levels of those
plants are given in table 2. As stated previously, obtaining forage
availability estimates were difficult. In situations where the exact

availability is unknown, several steps can be used to construct these

82

4 . lslnpngillulatmai-walflihan 

parameters. Of primary importance is the input from on—site personnel who
know, in general terms, what month, or combination of months, forage quantity
may be limiting. An indirect indicator is the fluctuation of mature ewe
weight. Ideally these two sources coincide. Rainfall pattern and amount,
and stocking rate may also be valuable in fine tuning forage estimates. The
availability of forage for the IPAL runs were derived by using a combination
of all the factors listed (table 3).

The inputs for the management subroutine were obtained from the IPAL
staff. These inputs comprise the management practices used on the IPAL
flock. They included year—round breeding, weaning all lambs at 10 periods of
age (150 days), utilizing 1/4 of the ewes milk for dairy production and
setting the minimum age for breeding ewe lambs at 1 year. Model stipulations
placed upon milk extraction for dairy purposes were: the ewe must be at least
1 year of age, the lamb's body condition (EBW/WM) must be .85 or greater and
the maximum amount of milk to be extracted was set at 1/4 of the total amount
produced. These stipulations reflect the basis on which herdsmen make
decisions about whether to milk a ewe.

The management subroutine can transfer animals to other classes when
deemed necessary by the simulator. In the IPAL simulations there are several
classes that both sexes can go through (figure 31). The transfers are
determined by either age, weight, or a proportion of total flock size.
Setting culling and sales policies are important in simulating the production
situation, but also they provide a means of establishing a flock in steady
state. A flock in steady state is defined as one where there is very little
fluctuation in the number of mature ewes. It is necessary to simulate a
flock in steady state for validation against actual results. More
importantly, the effects of alterations in management practices or other
simulated effects can be more clearly compared with the baseline (validation
run) when a steady state is simulated unless, of course, the effect of
interest is the process of change.

With the IPAL input data in the model, simulations for that production
system may be run. The first computer runs will be a validation or

comparison of model results with the actual results.

83

TABLE 2. weighted Average of Crude Protein and Digestibility for Sheep Diets

1979 1980
Z Diet Z Diet
Month C.P. Z DIG Z accounted for C.P. Z DIG Z accounted for
Jan 9.46 50.90 87.0 12.14 56.57 56.0
Feb 14.53 54.35 87.0 8.87 42.57 61.0
Mar 10.25 39.89 83.0 5.66 40.59 34.0
Apr 11.61 48.38 74.0 14.40 56.71 42.0
May 10.36 43.43 80.0 13.66 64.71 51.0
Jun 9.86 46.53 76.0 7.47 54.07 47.0
Jul 7.34 42.50 31.0 6.65 47.52 62.0
Aug 6.60 43.97 37.0 6.09 50.32 40.0
Sep --- --- --- 6.50 54.90 73.0
Oct 8.25 45.77 91.0 5.90 54.46 68.0
Nov 12.50 56.50 65.0 4.67 50.49 80.0
Dec --- --- --- 12.65 47.36 25.0

84

TABLE 3. FORAGE AVAILABILITY FOR IPAL SHEEP kg/hd/day.

Month 1979a 1980
January 1.1 1.7
February 7.5 .4
March 7.5 3.7
April 7.5 4.0 -.9°
May 7.5 .7
June 7.5 8.0
July 7.5 2.1
August 3.9 .5
Septemberb 1.9 .1
October 2.7 1.0
November 1.0 12.0
December 1.0 9.3

a Values greater than 2.0 indicate availability is unlimited.

September availability values were increased by .25 kg to represent
the consumption of Acacia tortilis pods.

C .9 is the availability for the second period of April.

85

ursing ewe
lambs trans-

ferred at 10
periods of age

Replacement
ewe lambs.
Transferred at

1 year of age

Breeding ewes
culled by age
and low

fertility

Cull ewes
sold or eaten

EWES

Excess ewe
lambs sold or
eaten at 1
year of age

RAMS

Nursing ram
lambs trans-

ferred at 10
eriods of ag)

Replacement
ram lambs.

Excess rams

sold or eat

Transferredat|

1 year of age]

at 1 year

Breeding rams
culled at 5
years of age

Figure 31. The age transfer of animals through the flock.

86

of age

- 

5. SUMMARIES OUTPUT - SUMMARIES

Summaries of the results from a simulation are printed in the run
summary, the flock summary, the lamb sumary, the management report and the
year summary. These summaries allow the user to examine output on ax
periodic, yearly or a total run basis. The user has the option as to when
the reports are printed.

The simulation output is printed in a specific order. For a simulated
period, if all summaries are printed, the order of the output is the flock
summary, lamb summary and management report. The year and run summaries are
printed at the en of output.

Before printing the flock summary (table 4) the individuals are sorted_
by pregnancy status, within lactation status, within age and within class.
The averages of these subclasses are printed in the summary. This grouping
allows closer examination of sheep in different physiological states.

The lamb summary (table 5) provides information on lambs that are not
weaned. A lamb's (or group of lambs’) growth pattern can be followed from a
period of age until they are weaned. Lambs are categorized in the summary by
birth period, sex, age of ewe and type of birth.

The management summary (table 6) provides information on flock dynamics
(the number of births and deaths), transfers from one class to another and
the number of sheep sold from each class.

The year sumary (table 7) lists every class in the flock by period of
the year. All animals within the class are averaged together, regardless of
age or physiological status.

The run (table 8) summary accumulates flock data and prints it out
yearly. This summary provides the user with an overview of total flock
performance. Printed are total births, deaths, animals marketed and feed
consumed. This information can be used for evaluating biological efficiency
(total kg of liveweight and milk harvested/total kg of dry matter consummed)
of the flock.

The data printed in the summaries are intended to meet the information
requirements of most users. However, more information can be placed in these
smmaries as the user desires. For example, the total weight of lean and fat
for all sheep sold can be included in the run summary. Furthermore,

shortages of energy and protein for particular body functions (i.e.

87

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92

lactation, growth and maintenance) may be printed out. Such information
would be useful in planning feed supplementation policies.
6. MODEL VALIDATION f

A critical area of systems analysis is validation. For use of the Texas
A&M Sheep or Goat Production Systems Model, the validation process examines
how closely simulated results match actual data thus testing both model
structure and functions and input parameters. Closeness of correspondence
establishes the level of confidence in the simulated results. When the
simulation data match with reasonable closeness the actual production levels
and fluctuations in those levels in every phase of the production system in
the area of intended use, experimental simulations can be conducted with more
confidence.

I. Single Animal Version — SAV

Before validating the flock model (FM), the SAV was tested to determine
if the biological assumptions and equations are representative of a sheep's
biology. One of the model components of the SAV least tested is the method
used to calculate milk production. In the process of validating milk
production, it was possible to also evaluate the model's response for ewe
body weight, feed intake and lamb growth.

Two experiments were chosen to validate the basic structure and
functions of the milk portion of the SAV model. These experiments were
selected because they included information on milk production, ewe body
weight, feed intake and feed quality.

Barnicoat et al. (1949a,b) reorted a series of experiments involving
the milk production of Romney ewes. The portion of this paper selected for
simulation involved 42 five-year—old ewes. The experimental treatments
consisted of placing the ewes in two groups on a high or low level of feed
intake prior to and after lambing. The ration was composed of lucerne hay
and a concentrate. The study started 51 days prior to lambing and lasted 84
days after lambing. After lambing, every alternate ewe in each group was
transferred to the other treatment group. Lactation data were collected for
12 weeks. Milk production was measured 6 times in 24 hr, once every week,

using the weighr suckle—weigh technique.

93

The results from Barnicoat et al. (1949a) indicate that type of birth
and ration had highly significant effects on milk production from O to 6
weeks. During the last half of lactation (7 to 12 weeks) differences were
found for ration (P<.01). These workers concluded that feed level during
pregnancy is second in importance for maintaining milk yield, that feed level
during lactation is the primary factor influencing both initial and total
milk yield, and that the maximum yield is obtained only by liberal feeding
during late pregnancy and throughout lactation.

Treacher (1970) reported the second experiment used for validation. He
utilized 32 Scottish half—breed ewes (Border Leicester x Cheviot) which were
all pregnant for the third time and all of which were carrying twin fetuses.
Three treatments were used to determine the effects of nutrition in late
pregnancy on milk production. The treatments consisted of feeding ewes
during the last six weeks of pregnancy so they would gain 20, 10, and 0% of
their initial live weight. The ewes were individually fed during pregnancy
and fed ad lib after parturition.

Milk production was measured by milking the ewes twice daily using a
milking machine. Lambs were removed shortly after birth. The level of milk
production for treatment groups ranked 20, 10, and OZ for peak milk
production during the six—week lactation period.

a. Model Parameters

To simulate the experiments performed by Barnicoat et al. (1949 a,b) and
Treacher (1970) genetic, management and forage parameters had to be
specified. For Barnicoat et al. (1949a), digestible organic matter and crude
protein were 57 and 17%, respectively. The WMA and genetic potential for
milk were set at 60 kg and 2.2 kg/day at peak lactation. These levels were
derived by examining
other reports in the literature which involved Romney sheep (Jagusch et al.,
1972; Geentry and Jagusch, 1974).

Treacher (1970) fed his ewes a ration which consisted of 60% digestible
organic matter and 25% crude protein. Due to the breed type used in this
experiment (Border Leicester x Cheviot) it was difficult to find
corroborative values for mature size and peak milk production. Therefore the
values used for WMA and GMLKL were set at 70 kg and 1.8 kg/day. These values

appear to be reasonable when the mature weight and milk production of the

94

parental breeds are considered. The availabilities of feed were set equal to
the actual intakes of ewes reported in the respective papers by Treacher
(1970) and Barnicoat et al. (1949a) (figures 32, 36, 37 and 38).

In both simulated sets, the ewes were bred and fed at nutritional levels
so that they would be at the same stage of pregnancy and approximately the
same weight at the beginning of the experiment.

b. Simulated Results.

The simulated results from the Treacher experiment generally indicate a
close agreement with the actual data. For all treatments the simulated feed
intakes mimicked the shape and the magnitudes of the actual changes in intake
(figure 32). The largest difference occurred in the 20% treatment where the
difference between simulated and actual intake is approximately 10% for the
fourth through the seventh period of simulation. The remaining treatments
had very close agreement between simulated and actual results.

The ewe body weights (figures 33 and 34) tend to parallel the reported
results. The magnitude of differences averaged less than 10% across all
treatments for the duration of the experiment.

After parturition there was close agreement between the actual and
simulated body weights for the ewes of this experiment. There was a tendency
for the simulated ewes on the 20% treatment to gain more weight on less feed
than the actual ewes in the postpartum period (figure 34).

The simulated results for milk production were similar for all three
treatment groups (figure 34 and 35). The closest agreement with actual data
was in the 20% treatment. The differences between actual and simulated data
increased as the percent body weight gain in pregnancy decreased. A possible
explanation for the differences which exist in the 0% gain group is that
Treacher's ewes were in poor condition and therefore partitioned a greater
percentage of their nutrient intake to body reserves and less to milk
production. However, the SAV does allow a ewe to redeposit lean and fat
while producing a relatively large quantity of milk. Other discrepancies may
be present due to the machine milking of the ewes, therefore depriving the
ewes of the continuous suckling stimulus that they might otherwise have.

The feed intakes for the Barnicoat et al. (1949a) ewes are shown in
figures 36, 37 and 38. Not shown are the intake of ewes on the L/L ration

since the simulated and actual intakes of this group were equal and

95

 

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97

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98

 

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fed to gain O and 10% of their body weights, respectively.

99

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100

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Figure 38. Feed intake of ewes fed L/H ration: actual intake
(solid line), simulated ewes bearing twins (dashed line) and
simulated single bearing ewe (dotted line).

101

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PERIOD OF 5IHULHTION

Figure 37. Feed intake of ewes fed H/L ration: actual intake
(solid line), simulated ewes bearing twins (dashed line) and
simulated single bearing ewe (dotted line).

102

consistent at 1.12 kg/day. The simulated intakes of the H/L, H/H and L/H
ewes were in general agreement in shape and fluctuation of the actual data,
but there were magnitude differences for all three groups. During the later
stages of pregnancy, intake of the simulated H/L ewes carryin twin fetuses
decreased. This is a programmed adjustment of the rumen capacity which
increases during gestation to represent the decrease in rumen volue due to
the increased conceptus size.

Before parturition the differences between actual and simulated intakes
were 26 and 34% for single— and twinrbearing ewes. After lambing, simulated
feed intakes had an earlier and lower plateau than Barnicoat et al. (1949a)
ewes. Compared to the actual intake the difference between the peak and
ending simulated intakes were 14 and 26% for ewes nursing twins and 22 and
30% for those nursing singles, respectively (the original work did not
separate the intake levels of single— and twin—bearing ewes).

Although the model appears to be simulating the fluctuations and levels
of feed intake reasonably well it is necessary to address the differences
observed. Before parturition both groups increase feed consumption, however,
the intakes of simulated ewes level off sooner.

The simulated ewes had a lower level of feed intake because the physical

limit of their rumen had been reached. This difference increased when the

 
   
  
 
  
 
  
   
  

physical limit was reduced as a result of increasing conceptus weight.
Differences between actual and simulated feed intake during lactation also
exist. Here also the physical limit of the simulated ewes prevented any
further increase in feed intake. Ewes were fed in groups so that there must
have been wasted and left—over feed, but there is no indication that this
feed was taken into account; therefore intake may have been over—stated by
Barnicoat et al. (1949a).

V Over all treatments, the simulated ewe body weights closely followed the
Qpweight and weight fluctuations of the Romney ewes with mean differences of
ggless than 10% (figures 39 and 40) at any time. Divergence of the simulated
{Lad actual results occurred during the later stages of gestation and in the
jéater periods of lactation.

g The H/H simulated ewes consistently gained more weight than the actual
fwes as the postpartum interval lengthened. Comparing the single and twin
éimulations within a treatment, the effects of bearing and nursing twins are

103

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Figure 39. a) Ewe body weights for the H/H ration
b) Ewe body weights for the L/H ration. For
each graph actual weight (*), ewe bearing
twin lambs (A) and ewe bearing a single
lamb (U).

104

 

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body weights for the L/L ration.
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Figure 40. a) Ewe
b) Ewe

105

 

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Figure 41. Milk production of ewes fed H/H ration, a) ewes
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106

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107

 

 

 

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Figure 43. Milk production of ewes fed L/H ration a) ewes
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108

 

   

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0-0 . . . . . . . . . . . . . . . . . . . . . . WT
, ....... .w ....... --, ....... .., . , , ,
0 1 2 3 u 5 0

PERIOD OF LACTATION

Figure 44. Milk production of ewes fed L/L ration a) ewes
nursing singles and b) ewes nursing twins. * Actual,U Simulated

109

 

evident. Twin—bearing ewes weighed more than single—bearing ewes prior to
parturition, this situation was reversed after parturition. The simulated
results follow this same pattern.

Comparisons of simulated and actual milk productions were made for each

ration and nuber of lambs nursing within a treatment (figures 41 through
44). In general, the simulations produce close representations of the
reported data. For all ewes fed a high nutrition diet during lactation there
was close agreement between simulated and actual results for the duration of
lactation. There was a tendency for the simulations to underestimate milk
production in the first period of lactation for ewes fed the high nutrition
diet. Two explanations for this behavior are that simulated feed intake did
not increase as rapidly as the actual, resulting in less nutrients available
for milk production, or the Romney ewes mobilized more body stores during the
initial stages of lactation than the simulated ewes.

The simulated milk production for ewes fed the low (H/L and L/L)
nutrition diet followed the magnitude and trend of the actual results.
However, there were greater differences between these values and those for
the ewes fed the high nutrition diet. The greatest difference between actual
and simulated results is for the H/L twinrbearing ewes. Here the simulated
ewes produced more milk than the actual ewes in the first four periods of
lactation. The Barnicoat et al. (1949a) L/L twin ewes produced more milk in
the first period of lactation than the H/L twin ewes (1.7 vs. 1.3). It
would seem logical for the ewes fed the H/L ration to have more body stores
to be catabolized during lactation. If this were the case, then the H/L twin
ewes should logically produce more milk than the L/L twin ewes. The
"unexpected" actual results could well have been due to sampling or
experimental error which is familiar to all experienced animal scientists.
(It is well to note at this point that the modeler must be especially
cautious and question simulated data even though these data may appear, and
often are, more logical than the actual biological data that are subject to a
vast array of real life, often cryptic, effects.)

Comparing the simulations between different rations, the simulated
output agrees with the conclusion of Barnicoat et al. (1949a) that the

current level of feeding is more important than the previous level of feeding

llO

 

for the determination of total milk yield. However, it would be expected
that those simulated ewes which were fed on a high nutrition diet before
parturition would yield more milk than those on the opposite treatment due to
more body reserves. Milk production for the simulated H/H twin and the L/H
twin ewes were different indicating that the H/H twin ewe was able to
catabolize fat at a faster rate and for a longer period of time than the L/H
twin ewe and/or to partition more nutrients for milk production. Simulated
ewes nursing single or twin lambs fed the H/L ration produced more milk at
the beginning of lactation than L/L ewes due, most likely, to more fat being
catabolized by the H/L ewes. The simulated results of the ewes fed the L/L
ration represent the weakest set of validations. Although they follow the
trend of the actual data, the differences are the greatest for these
simulations.

The final product of the production system examined by Barnicoat et al.
(1949b) was the weight of lamb produced. Lamb growth largely determines the
efficiency of the biological system. The model simulated this growth
accurately (figures 45 through 48).

The largest discrepancy between actual and simulated results was for L/L
single lamb. In this comparison the simulated lamb had a faster growth rate.
This would correspond to the higher level of milk production of the simulated
ewe during the middle periods of lactation.

The lambs produced in the study by Barnicoat et al. (1949b) were
Southdown x Romney crosses. The model does not currently accout for the
effects of heterosis so that the mature weight and maturing rate functions of
the simulated lambs are the same as their dams, whereas the actual lambs
would be expected to have had a relatively faster maturing rate and a lighter
mature weight than their dams. Therefore the absolute growth and maturing
rates were assumed to be approximately equal.

c. Conclusions

This series of validations for the SAV of the sheep model displayed the
model's capability of simulating the fluctuations and magnitude of changes of
real data sets. It was evident from these simulations that the end product
of the system (lamb growth) was simulated accurately, as were the
intermediate steps and components (feed intake, ewe body weight and milk

production) that influence lamb growth.

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AGE IN PERIODS

Figure45. The growth curves of lambs whose dams
were fed H/H ration. a) single lamb
b) twin lamb.
* Actual,E]Simulated

112

 

25 -
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LAMB 15
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25 - b
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Figure 46. The growth curves of lambs whose dams were
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* Actual,F]Simulated

113

 

 

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Figure 47. The growth curves of lambs whose dams were
fed H/L ration. a) single lamb b) twin
lamb.

* Actual,5 Simulated

114

 

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The growth of lambs whose dams were
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b) twin lamb.

* Actual,U Simulated

115

The simulation of data reported by Barnicoat et al. (1949a,b) and
Treacher (1970) indicate that simulated ewe performance was responsive to the
feed resource.

Also, simulated ewes, when placed under nutritional stress, lost weight
similarly to that lost by the actual ewes. However, with this data set it
cannot be determined if fat and lean were catabolized in similar proportions
and at proportional rates in the simulated ewes as in the real ewes.

The simulated results of milk production indicate that the technique
proposed by Bywater (1976) is viable. That is, the SAV is capable of
simulating milk production and, perhaps more importantly, lactation curves
accurately. This capability implies that this method can be used over a
broad range of production situations.

The results of these validations indicate that the SAV is adequately
simulating the biology of the breeds of sheep reported in the two studies.
Further testing of the SAV components is needed but must await acquisition of
new comprehensive data.

II. FLOCK MODEL (FM) - NORTHERN KENYA

The first validation with the flock model utilized sheep data collected
in northern Kenya on the IPAL project. The actual forage and anhnal data
were collected in 1979 and 1980 and are described by Blackburn (1984). To
reduce the amout of stochastic "bounce" or variability in results, the
simulation was run with a flock size of 300 ewes. The simulations were run
for 10 years in order to attain a steady state flock structure for both 1979
and 1980.

a. 1979 Results

Ewe Body Weight. Body weights of actual and simulated ewes were

compared for the entire year. The simulated ewe weights used were fro the
4.5 year age group. This was the youngest group where WM = WMA = 35kg,
meaning that the ewes had reached their maximum structural size. Also, for
most research results ewes of this age group are at their peak producing
ability. Empty body weight (EBW) and full weight (W) were compared to the
actual ewe weights (figure 49). It is necessary to compare all three curves

in figure 49 because actual ewe weights were recorded in the morning after

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being enclosed all night in a pen and, therefore represent an intermediate
weight. I

For the greatest part of the year there is consistent agreement between%
the simulated and actual weights. The largest divergence between simulated I
and actual results occurred in the last 3 months of 1979. At first
inspection the decrease in actual weight does not appear to be logical,
because the crude protein and digestibility were increasing. An explanationég
for this response is that 40% of the actual ewes gave birth and/or were x
lactating at this time. Therefore lambing and lactational stress caused the 5
reduction in actual weights. Sixteen percent of the ewes in the simulated A
flock gave birth at this time; therefore, the weight increase and decrease
were not as great as in the actual data. To further substantiate the
agreement between simulated and actual ewe weights, the weights of simulated
ewes lambing in September and October were plotted against the actual data.
Figure 50 clearly shows that simulated ewes in a similar reproductive phase
as the actual ewes display the same pattern of weight loss.

Milk Production. The average actual and simulated lactation curves are

in figure 51. Both of these curves are averaged over the entire year.
Actual lactation data were available only for the months of April, May and
November.

In general the simulated and actual lactation curves were in agreement.
The decrease and following increase of actual milk production did not occur
in the simulated lactation curve. To determine the cause of fluctuation, the
actual curves were divided and replotted as November and April and May. From
these curves it is apparent that the fluctuation is the result of the April
and May lactation curve. For comparison, the simulated November, April and
May lactation curves were plotted with their respective counterparts. The
November curves show a greater uniformity of agreement (figure 52) than the
April-May curves (figure 53). The simulated April-May curve shows a similar
decrease in milk production but it does not increase in milk production
during period 4. The cause of this increase is not clearly explainable,

because feed quality does not significantly change during this time. Due to

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simulated (dashed line) lactation curves.

120

 

 

 

 

PERIOD OF LACTATION

Figure 52- November lactation curves for actual (solid
line) and simulated (dashed line) ewes.

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Figure 53. April and May lactation curves for actual (solid
line) and simulated (dashed line) ewes.

122

 

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the small number of lactations, it is possible that the increase was due to a
peculiar artifact not counterbalanced as would be expected for a larger
sample size.
Lamb Growth. One of the final products of this system is lambs
produced. A comparison of the least squares means of the actual lamb weights
and the simulated W and WM weights averaged over the year was made (figure
54). There is close agreement between actual and simulated weights up to 300
days of age. The close agreement between actual and simulated data for
preweaning, birth to 10 periods (150 days of age) of growmh has additional
implications. The close agreement based on a larger sample size indicates
that real milk production levels for actual and simulated ewes were more
similar than indicated.
The IPAL flock had a 130% lamb crop (live lambs

The simulated flock had a 132% lamb crop.

estimates of reproductive efficiency were not obtainable from the actual

Reproduction.
born/ewes) for 1979. Further
data. Additional simulation output indicated that lambs weaned/ewe in the
flock was 120% while lambs weaned/lambs born, a measure of lamb survival, was
76.4%. The actual reproductive rate was higher than the regional average due
to IPAL ewes receiving higher levels of management (e.g., drenching and
dipping). The simulated lamb survival to weaning is closer to the regional
mean (IPAL, personal communication).
b. 1980 Results

Ewe Body Weight. The 1980 year was drier than 1979, and the effects of
Also, the altered
The simulated

ewes emulated the actual ewe body weight fluctuations (figure 55). The

the drier year resulted in lower ewe body weights.

environment resulted in a different ewe body weight pattern.

decreases and increases that occurred in ewe body weight for 1980 fit more
closely than for the 1979 data. The 1980 simulated ewe weights had a greater
change in magnitude between the high and low weights especially for the
weights in June (periods 12 and 13). It appears that the simulated ewes were
given (in the input forage vector) greater access to forage than the real
ewes. The difference between the actual weight and simulated weight in June
was 16.8% which, taken with the pattern for the entire year, was considered

to be a close validation.

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125

Milk Production. The shape of the 1980 lactation curve is different

than the 1979 curve in that it lacks an increase after the peak had been
reached (figure 56). In general, the simulated lactation curve was higher
than the actual data curve. The greatest divergence occurred during the 2nd
through the 4th periods of lactation. The divergence implies that the
simulated ewes were able, either through catabolism of body tissue or access
to higher quality forage, to produce more milk during these times.

Lamb Growth. Average simulated and actual lamb growmh are in close
agreement throughout the time of comparison (figure 57). Compared to the
1979 lambs, the 1980 lambs had a faster more prolonged growth. At 300 days
of age the 1980 simulated lambs were heavier than the 1979 lambs. The
difference was likely due to two causes. First, the forage quality was
higher in 1980 allowing young lambs to take greater advantage of grazing.
Secondly, in 1979 the lambing pattern was more uniformly distributed
throughout the year, causing more lambs to be born in seasons of lower
quality forage so that they could not take as much advantage of grazing as in
1980.

Reproduction. The reproductive rate of the simulated vs. the actual was
in close agreement (119 vs 118%). The difference between th two years is
partially explained by lower ewe body weights which would result in lower
conception rates. The lambs weaned/lambs born was 70.0% indicating a greater
loss of nursing lambs in 1980 compared to 1979.

C. Conclusions

When the simulation results from both years are considered in their
entirety, it can be concluded that there is close agreement between the
actual and simulated data. Differences at specific points do occur, but the
magnitude of the differences is not great. More importantly the simulations
follow the trends and major seasonal fluctuations which occurred with the
Somali Blackhead. These results are encouraging in terms of model validity
in two areas. The IPAL data set demonstrates that limited experimental
numbers, but with major production characteristics measured, can be
successfully utilized as baseline data for the model. This is critical if
data from smallholder production systems are to be used. There is a paucity
of data on fat—tailed or fat rumped hair sheep, therefore the majority of

data reviewed in the development of the model was from wooled breeds which

126

 

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PERIOD OF LACTATION

Figure 56. The 1980 average lactation curve for actual
(solid line) and simulated (dashed line) ewes.

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128

originated in temperate regions. These simulations indicate that the manner

in which the biology of the sheep was modeled does apply to hair sheep as
well as the wooled breeds.‘


?
E.
2

129

 

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Barnicoat, C. R., A. G. Logan and A. I. Grant. 1949b. Milk secretion
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Barrell, G. K. and K. R. Lapwood. 1979. Effects of various lighting regimes

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Coop, I. E. 1962. Liveweight—Productivity Relationships in Sheep. I.
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131

Field, A. C. 1979. IPAL sheep and goat project preliminary report on the
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Fitzhugh Jr., H. A. 1976. Analysis of growth curves and strategies for
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i;



i
3

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