1. VORTEX POPULATION VIABILITY ANALYSIS 7/2/20151

2. Introduction  It is the use of quantitative methods to predict the likely future status of a population  It estimates the vulnerability to extinction and explores management to ensure persistence  http://www.vortex9.org/vortex.html 7/2/20152

3. Methodology The modeling exercise requires a set of parameters to describe the biological characteristics and stochastic events of the herd:  Breeding system: Cattle are polygynous species whereby one bull mates with more than one cow at any single breeding season.  Age of first reproduction: VORTEX considers the age of first reproduction as the age of the first parturition. 7/2/20153

4. Methodology…  Age of reproductive senescence: An estimate of 15 years was chosen for modeling purpose.  Offspring production: Mean parity was set as one calf while the maximum parity was set as two calves. The sex ratio of male:female at birth was set at 50%.  Breeding Pool: The percentage of bulls in the breeding pool was estimated from the pedigree records using the number of male parents while the number of adult breeding females was calculated as the number of female calves born annually. 7/2/20154

5. Methodology…  Mortality: VORTEX requires detailed estimates of age- sex-specific mortality rates.  Catastrophe: Catastrophes are remarkable environmental events that are outside the limits of normal environmental variation affecting reproduction and/or survival (Miller and Lacy, 2005).  Carrying capacity (K)-It is used to define the upper limit for the population size above which additional mortality is imposed randomly across all age classes. 7/2/20155

6. Methodology  Population augmentation and harvest: Currently there is no importation into the Kenyan Sahiwal cattle breed and thus it can be referred to as a closed population, therefore no supplementation was modeled in the breed.  Iterations and years of projection: All population projections (scenarios) were simulated 500 times for 100 years. 7/2/20156

7. Methodology  Inbreeding depression: VORTEX includes the detrimental effects of inbreeding most directly through the reduced survival of offspring through their first year.  Initial population size: Obtained from the pedigree records. Because of fluctuations of herd size with time, sets of different population sizes were analyzed. 7/2/20157

8. Methodology Sensitivity Analysis  Each parameter is given variable levels while all other parameters are kept constant.  The sensitivity index for each parameter is calculated following Pulliam et al. (1992) as:  Where: ∆x/x is the change in the observed response resulting from a change of ∆P/P in input variable P 7/2/20158

9. Methodology… Input values for the baseline model and sensitivity analysis parameters ParameterBaseline modelSensitivity test Age of first offspring for males22-10 Carrying capacity30001500-6000 Initial population size1200250-3000 Maximum age of reproduction159-20 Percent adult females breeding855-85 Percent males successfully siring offspring2.50.5-5 Percent mortality of females from age 0 to 1year200-50 Percent mortality of females from age 1 to 2year50-50 Percent mortality of females from age 2 to 3year50-50 Percent mortality of males from age 0 to 1year220-50 Percent mortality of males from age 1 to 2 year50-50 Percent mortality of males from age 2 to 3 year50-50 7/2/20159

10. Results 7/2/201510 ParameterInput values Sensitivity Index Mean final NHePopulation r Carrying capacity1500-60000.750.0083.847 Initial population size250-30000.000400.34375 Female mortality (%)0-500.00970.0010.099 Male mortality (%)0-500.00370.0010.0063 % breeding females0.5-50.9270.0140.0344 % breeding males5-850.00060.0150.0116 Age of first offspring for males (years) 2-100.00080.0020.0064 Maximum breeding age (years)9-200.06880.0140.916