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Genetic Management of Fragmented Animal and Plant Populations$

Richard Frankham, Jonathan D. Ballou, Katherine Ralls, Mark Eldridge, Michele R. Dudash, Charles B. Fenster, Robert C. Lacy, and Paul Sunnucks

Print publication date: 2017

Print ISBN-13: 9780198783398

Published to Oxford Scholarship Online: September 2017

DOI: 10.1093/oso/9780198783398.001.0001

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(p.A7) Appendix 2 VORTEX simulation software for population viability analysis

(p.A7) Appendix 2 VORTEX simulation software for population viability analysis

Source:
Genetic Management of Fragmented Animal and Plant Populations
Author(s):

Richard Frankham

Publisher:
Oxford University Press

Population viability analysis (PVA) is a systems modeling approach for predicting the fate of a population (including risk of extinction) due to the combined effects of all its systematic and stochastic threats (Shaffer 1981; Beissinger & McCullough 2002; Frankham et al. 2014). Typically, population size, means and standard deviation of birth and death rates, density feedbacks, plus risks and severity of catastrophes, inbreeding depression, etc. are entered into a software package and many replicates projected over multiple generations using stochastic computer simulation. It is used as a management and research tool in conservation biology (Lindenmayer et al. 1993; Menges 2000; Ralls et al. 2002; Traill et al. 2007; Frankham et al. 2010; Pierson et al. 2015). PVA may be done with purpose written software, or generic software packages, such as VORTEX or the RAMAS family of software (Akçakaya 1994; Lacy & Pollak 2014). The software relevant to our concerns here are individual-based packages with genetic factors incorporated, such as VORTEX.

VORTEX (Lacy et al. 2015) is often used to model demographic and genetic dynamics of populations, especially by the Conservation Breeding Specialist Group of the Species Survival Commission of the IUCN. It can be used to model fragmented populations and estimate population genetic structure. VORTEX is an individual-based simulation of the effects of demographic, environmental, and genetic stochastic events on wildlife populations. VORTEX models population dynamics as discrete, sequential events that occur according to probabilities that are entered by the user. It simulates a population by stepping through a series of events that describe an annual cycle of a typical sexually reproducing, diploid organism: mate selection, reproduction, mortality, increment of age by one year, dispersal among populations, removals, and supplementation. The population simulation is iterated many times and over many years to generate the distribution of fates that the population might experience. Demographic (N) and genetic (H, F) metrics are tracked. Multiple sub-populations can be modeled based on the historical events of those sub-populations, and users can evaluate the effects of different gene flow strategies between sub-populations for use in developing genetic management recommendations.

The VORTEX program runs on computers running the MS Windows operating system and is available as freeware at www.vortex10.org/Vortex10.aspx. Below is an example of VORTEX input data for a simple case of a metapopulation with dispersal between the two fragments, with output graphs showing the trajectories of population size and gene diversity. (This example is a minor modification of the sample scenario that is created by VORTEX as default case when a new project is created.)

(p.A8) Input

VORTEX 10.2.1.0—simulation of population dynamics

Project: New Project

Scenario: TestScenario

2 populations simulated for 100 years for 100 iterations

Sequence of events in each time cycle:

  • EV

  • Breed

  • Mortality

  • Age

  • Disperse

  • Harvest

  • Supplement

  • rCalc

  • Ktruncation

  • UpdateVars

  • Census

Extinction defined as no males or no females.

Inbreeding depression with a genetic load consisting of

6.29 total lethal equivalents per individual, of which

50% are due to recessive lethals, and the remainder are lethal equivalents not subjected to removal by selection.

Correlation of EV among populations = 0.5

Both sexes disperse, from age 1 to age 5

Survival during dispersal: 50

Dispersal rates (as percents), from source (row) to destination (column):

Fragment1

Fragment2

Fragment1

10

Fragment2

5

Reproductive system:

  • Polygyny, with new selection of mates each year

  • Females breed from age 2 to age 10

  • Males breed from age 2 to age 10

  • Maximum age of survival: 10

  • Sex ratio (percent males) at birth: 50

Correlation of EV between reproduction and survival = 0.5

Population specific rates for Fragment1

  • Percent of adult females breeding each year: 50, with EV(SD): 10

  • Percent of adult males in the pool of breeders: 100

  • Normal distribution of brood size with mean: 2.5 with SD: 1

(p.A9) Female annual mortality rates (as percents):

  • Age 0 to 1: 50 with EV(SD): 10

  • Age 1 to 2: 10 with EV(SD): 3

  • After age 2: 10 with EV(SD): 3

Male annual mortality rates (as percents):

  • Age 0 to 1: 50 with EV(SD): 10

  • Age 1 to 2: 10 with EV(SD): 3

  • After age 2: 10 with EV(SD): 3

Catastrophe 1: Catastrophe1

  • Local impact

  • Frequency (%): 1

  • Reproduction reduced by severity multiplier: 0.5

  • Survival reduced by severity multiplier: 0.9

Initial population size:

Age

0

1

2

3

4

5

6

7

8

9

10

Total

Females

0

5

5

3

3

3

1

2

1

1

1

25

Males

0

5

5

3

3

3

1

2

1

1

1

25

Carrying capacity: 100

with EV(SD): 0

Population specific rates for Fragment2

  • Percent of adult females breeding each year: 50, with EV(SD): 10

  • Percent of adult males in the pool of breeders: 100

  • Normal distribution of brood size with mean: 2.5 with SD: 1

Female annual mortality rates (as percents):

  • Age 0 to 1: 50 with EV(SD): 10

  • Age 1 to 2: 10 with EV(SD): 3

  • After age 2: 10 with EV(SD): 3

Male annual mortality rates (as percents):

  • Age 0 to 1: 50 with EV(SD): 10

  • Age 1 to 2: 10 with EV(SD): 3

  • After age 2: 10 with EV(SD): 3

Catastrophe 1: Catastrophe1

  • Local impact

  • Frequency (%): 1

  • Reproduction reduced by severity multiplier: 0.5

  • Survival reduced by severity multiplier: 0.8

(p.A10) Initial population size:

Age

0

1

2

3

4

5

6

7

8

9

10

Total

Females

0

5

5

3

3

3

1

2

1

1

1

25

Males

0

5

5

3

3

3

1

2

1

1

1

25

Carrying capacity: 100

with EV(SD): 0

Genetics options:

  • Genetic management for population: Fragment1

  • Pairs restricted to those with inbreeding of F < 0.12

  • Maximum number of times to try to find a mate = 10

Results

Appendix 2 VORTEX simulation software for population viability analysis

(p.A11) References

Akçakaya, H.R., 1994. RAMAS/metapop: Viability Analysis for Stage-Structured Metapopulations (Version 1.0). Applied Biomathematics, Setauket, NY.

Beissinger, S.R., McCullough, D.R., 2002. Population Viability Analysis. University of Chicago Press, Chicago, IL.

Frankham, R., Ballou, J.D., Briscoe, D.A., 2010. Introduction to Conservation Genetics, 2nd edn. Cambridge University Press, Cambridge, UK.

Frankham, R., Bradshaw, C.J.A., Brook, B.W., 2014. Genetics in conservation management: Revised recommendations for the 50/500 rules, Red List criteria and population viability analyses. Biological Conservation 170, 56–63.

Lacy, R.C., Pollak, J.P., 2014. VORTEX: A Stochastic Simulation of the Extinction Process. Version 10.0. Chicago Zoological Society, Brookfield, IL.

Lacy, R.C., Miller, P.S., Traylor-Holzer, K., 2015. VORTEX 10 User’s Manual. 15 April 2015 update. IUCN SSC Conservation Breeding Specialist Group, and Chicago Zoological Society, Apple Valley, MN.

Lindenmayer, D.B., Clark, T.W., Lacy, R.C., et al., 1993. Population viability analysis as a tool in wildlife conservation policy: with reference to Australia. Environmental Management 17, 745–758.

Menges, E.S., 2000. Applications of population viability analyses in plant conservation. Ecological Bulletins 48, 73–84.

Pierson, J.C., Beissinger, S.R., Bragg, J.G., et al., 2015. Incorporating evolutionary processes into population viability models. Conservation Biology 29, 755–764.

Ralls, K., Beissinger, S.R., Cochrane, J.F., 2002. Guidelines for using population viability analysis in endangered-species management. In: Population Viability Analysis. eds S.R. Beissinger, D.R. McCullough, pp. 521–550. University of Chicago Press, IL.

Shaffer, M.L., 1981. Minimum population sizes for species conservation. Bioscience 31, 131–134.

Traill, L.W., Bradshaw, C.J.A., Brook, B.W., 2007. Minimum viable population size: A meta-analysis of 30 years of published estimates. Biological Conservation 139, 159–166.