VORTEX
POPULATION 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 agesex-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:
S x  (x / x) /(P / P)
 Where: ∆x/x is the change in the observed response
resulting from a change of ∆P/P in input variable P
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Methodology…
Input values for the baseline model and sensitivity analysis parameters
Parameter
Baseline model
Sensitivity test
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
Age of first offspring for males
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Results
Parameter
Sensitivity Index
Input
values
Mean final N
He
Carrying capacity
1500-6000
0.75
0.008
Population
r
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 2-10
(years)
Maximum breeding age (years) 9-20
0.0008
0.002
0.0064
0.0688
0.014
0.916
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