VORTEXPOPULATION VIABILITY ANALYSIS

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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

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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.

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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.

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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.

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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.

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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.

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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

)//()/( PPxxSx

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Methodology…

Input values for the baseline model and sensitivity analysis parameters

Parameter Baseline model Sensitivity test

Age of first offspring for males 2 2-10

Carrying capacity 3000 1500-6000

Initial population size 1200 250-3000

Maximum age of reproduction 15 9-20

Percent adult females breeding 85 5-85

Percent males successfully siring offspring 2.5 0.5-5

Percent mortality of females from age 0 to 1year 20 0-50

Percent mortality of females from age 1 to 2year 5 0-50

Percent mortality of females from age 2 to 3year 5 0-50

Percent mortality of males from age 0 to 1year 22 0-50

Percent mortality of males from age 1 to 2 year 5 0-50

Percent mortality of males from age 2 to 3 year 5 0-50

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Results

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Parameter Input values

Sensitivity Index

Mean final N He Population r

Carrying capacity 1500-6000 0.75 0.008 3.847

Initial population size 250-3000 0.0004 0 0.34375

Female mortality (%) 0-50 0.0097 0.001 0.099

Male mortality (%) 0-50 0.0037 0.001 0.0063

% breeding females 0.5-5 0.927 0.014 0.0344

% breeding males 5-85 0.0006 0.015 0.0116

Age of first offspring for males (years)

2-10 0.0008 0.002 0.0064

Maximum breeding age (years) 9-20 0.0688 0.014 0.916