VORTEX POPULATION VIABILITY ANALYSIS 7/2/20151

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  7/2/20152

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

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

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

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

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

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

Methodology… Input values for the baseline model and sensitivity analysis parameters ParameterBaseline modelSensitivity test Age of first offspring for males22-10 Carrying capacity Initial population size Maximum age of reproduction Percent adult females breeding Percent males successfully siring offspring Percent mortality of females from age 0 to 1year 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 1year Percent mortality of males from age 1 to 2 year50-50 Percent mortality of males from age 2 to 3 year /2/20159

Results 7/2/ ParameterInput values Sensitivity Index Mean final NHePopulation r Carrying capacity Initial population size Female mortality (%) Male mortality (%) % breeding females % breeding males Age of first offspring for males (years) Maximum breeding age (years)