Appendix 1

This Appendix describes the structure of the simulation model used to assess the effect of an aseasonal breeding regime on the distribution of pregnancies in goat herds throughout the year. The assumed length of kidding interval was 10 months. Doe mortality was not taken into account. The flow from one mating season (MSn , n=1,...,6) to another is a function of the observed conception rate (ConRateMSn) in each mating season group. Exposed females that failed to conceive (BarrenMSn) were assumed to be re-bred during the immediately following mating period (i.e., two months later). Pregnant females (ConMSn) stay for 10 months in the reproductive cycle (RepCycleMSn) before making the transition (NextBreedingMSn) to the next mating period.

The model was implemented with the graphical simulation software STELLA, Version 5.0 (High Performance Systems Inc., Hanover, 1997). The model-diagram is depicted in Figure A.1. The model equations are given below. Note that a bi-monthly simulation time step was used. The simulation run started with an initial population of 1000 does in MS1, and 0 animals in all other states. The model converged to the following stable distribution, independently of the initial state distribution of 1000 animals choosen:

State Variables and flows

MS1(t) = MS1(t - dt) + (NextBreedingMS2 + FailConMS6 - FailConMS1 - ConMS1) * dt“

INIT MS1 = 0

INFLOWS:
   NextBreedingMS2 = CONVEYOR OUTFLOW
   FailConMS6 = (1-ConRateMS6)*MS6

OUTFLOWS:
   FailConMS1 = (1-ConRateMS1)*MS1
   ConMS1 = ConRateMS1*MS1

MS2(t) = MS2(t - dt) + (NextBreedingMS3 + FailConMS1 - FailConMS2 - ConMS2) * dt“

INIT MS2 = 1000

INFLOWS:
   NextBreedingMS3 = CONVEYOR OUTFLOW
   FailConMS1 = (1-ConRateMS1)*MS1

OUTFLOWS:
   FailConMS2 = (1-ConRateMS2)*MS2
   ConMS2 = ConRateMS2*MS2

MS3(t) = MS3(t - dt) + (NextBreedingMS4 + FailConMS2 - FailConMS3 - ConMS3) * dt“

INIT MS3 = 0

INFLOWS:
   NextBreedingMS4 = CONVEYOR OUTFLOW
   FailConMS2 = (1-ConRateMS2)*MS2

OUTFLOWS:
   FailConMS3 = (1-ConRateMS3)*MS3
   ConMS3 = ConRateMS3*MS3

MS4(t) = MS4(t - dt) + (NextBreedingMS5 + FailConMS3 - FailConMS4 - ConMS4) * dt“

INIT MS4 = 0

	Figure A.1. Forrester-Diagramm of the simulation model used to assess the effect of an aseasonal breeding regime on the distribution of pregnancies in goat herds.

INFLOWS:
   NextBreedingMS5 = CONVEYOR OUTFLOW
   FailConMS3 = (1-ConRateMS3)*MS3
OUTFLOWS:
   FailConMS4 = (1-ConRateMS4)*MS4
   ConMS4 = ConRateMS4*MS4

MS5(t) = MS5(t - dt) + (NextBreedingMS6 + FailConMS4 - FailConMS5 - ConMS5) * dt“
INIT MS5 = 0
INFLOWS:
  NextBreedingMS6 = CONVEYOR OUTFLOW
   FailConMS4 = (1-ConRateMS4)*MS4
OUTFLOWS:
   FailConMS5 = (1-ConRateMS5)*MS5
   ConMS5 = ConRateMS5*MS5

MS6(t) = MS6(t - dt) + (NextBreedingMS1 + FailConMS5 - FailConMS6 - ConMS6) * dt“
INIT MS6 = 0
INFLOWS:
   NextBreedingMS1 = CONVEYOR OUTFLOW
   FailConMS5 = (1-ConRateMS5)*MS5
OUTFLOWS:
   FailConMS6 = (1-ConRateMS6)*MS6
   ConMS6 = ConRateMS6*MS6
RepCycleMS1(t) = RepCycleMS1(t - dt) + (ConMS1 - NextBreedingMS1) * dt“
INIT RepCycleMS1 = 0“
   TRANSIT TIME = 4“
   INFLOW LIMIT = INF“
   CAPACITY = INF
INFLOWS:
   ConMS1 = ConRateMS1*MS1
OUTFLOWS:
   NextBreedingMS1 = CONVEYOR OUTFLOW

RepCycleMS2(t) = RepCycleMS2(t - dt) + (ConMS2 - NextBreedingMS2) * dt“
INIT RepCycleMS2 = 0“
   TRANSIT TIME = 4“
   INFLOW LIMIT = INF“
   CAPACITY = INF
INFLOWS:
   ConMS2 = ConRateMS2*MS2
OUTFLOWS:
   NextBreedingMS2 = CONVEYOR OUTFLOW

RepCycleMS3(t) = RepCycleMS3(t - dt) + (ConMS3 - NextBreedingMS3) * dt“
INIT RepCycleMS3 = 0“
   TRANSIT TIME = 4“
   INFLOW LIMIT = INF“
   CAPACITY = INF

INFLOWS:
   ConMS3 = ConRateMS3*MS3
OUTFLOWS:
   NextBreedingMS3 = CONVEYOR OUTFLOW
RepCycleMS4(t) = RepCycleMS4(t - dt) + (ConMS4 - NextBreedingMS4) * dt“
INIT RepCycleMS4 = 0“
   TRANSIT TIME = 4“
   INFLOW LIMIT = INF“
   CAPACITY = INF
INFLOWS:
   ConMS4 = ConRateMS4*MS4
OUTFLOWS:
[page 174↓]   NextBreedingMS4 = CONVEYOR OUTFLOW

RepCycleMS5(t) = RepCycleMS5(t - dt) + (ConMS5 - NextBreedingMS5) * dt“
INIT RepCycleMS5 = 0“
   TRANSIT TIME = 4“
   INFLOW LIMIT = INF“
   CAPACITY = INF
INFLOWS:
   ConMS5 = ConRateMS5*MS5
OUTFLOWS:
   NextBreedingMS5 = CONVEYOR OUTFLOW

RepCycleMS6(t) = RepCycleMS6(t - dt) + (ConMS6 - NextBreedingMS6) * dt“
INIT RepCycleMS6 = 0“
   TRANSIT TIME = 4“
   NFLOW LIMIT = INF“
   CAPACITY = INF
INFLOWS:
   ConMS6 = ConRateMS6*MS6
OUTFLOWS:
   NextBreedingMS6 = CONVEYOR OUTFLOW

Parameters (conception rates)

ConRateMS1 = 0.962

ConRateMS2 = 0.827

ConRateMS3 = 0.857

ConRateMS4 = 0.889

ConRateMS5 = 0.930

ConRateMS6 = 0.861