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remain within the population, and the average heterozygosis and gene diversity (or 

"expected heterozygosis") relative to the starting levels. 

VORTEX 

also monitors the 

inbreeding coefficients of each animal, and can reduce the juvenile survival of 

inbred animals to model the effects of inbreeding depression. 

 

VORTEX 

is an individual-based model. That is, 

VORTEX 

creates a representation of 

each animal in its memory and follows the fate of the animal through each year of 

its lifetime. 

VORTEX 

keeps track of the sex, age, and parentage of each animal. 

Demographic events (birth, sex determination, mating, dispersal, and death) are 

modeled by determining for each animal in each year of the simulation whether 

any of the events occur. (See figure below.) Events occur according to the specified 

age and sex-specific probabilities. Demographic stochastic is therefore a 

consequence of the uncertainty regarding whether each demographic event occurs 

for any given animal. 

VORTEX Simulation Model Timeline

 

Breed                    Immigrate      Supplement

 

^- Age 1 Year 

^————^ Census

 

Death               Emigrate         Harvest   Carrying 

Capacity Truncation

 

 

 

 

 

 

 

 

 

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Events listed above the timeline increase N, while 

events listed below the timeline    

                                                           decrease N.

 

VORTEX 

requires a lot of population-specific data. For example, the user must 

specify the amount of annual variation in each demographic rate caused by 

fluctuations in the environment. In addition, the frequency of each type of 

catastrophe (drought, flood, epidemic disease) and the effects of the catastrophes on 

survival and reproduction must be specified. Rates of migration (dispersal) between 

each pair of local populations must be specified. Because 

VORTEX 

requires 

specification of many biological parameters, it is not necessarily a good model for 

the examination of population dynamics that would result from some generalized 

life history. It is most usefully applied to the analysis of a specific population in a 

specific environment. 

Further information on 

VORTEX 

is available in Lacy (1993a) and Miller and 

Lacy (1999). Dealing with Uncertainty

 

It is important to recognize that uncertainty regarding the biological parameters of a 

population and its consequent fate occurs at several levels and for independent 

reasons. uncertainty can occur because the parameters have never been measured 

on the population. Uncertainty can occur because limited field data have yielded 

estimates with potentially large sampling error. Uncertainty can occur because 

independent studies have generated discordant estimates. Uncertainty can occur 

because environmental conditions or population status have been changing over 

time, and field surveys were conducted during periods which may not be 

representative of long-term averages. Uncertainty can occur because the 

environment will change in the future, so that measurements made in the past may 

not accurately predict future conditions. 

 

Sensitivity testing is necessary to determine the extent to which uncertainty in input 

parameters results in uncertainty regarding the future fate of the pronghorn 

population. If altemative plausible parameter values result in divergent predictions 

for the population, then it is important to try to resolve the uncertainty with better 

data. Sensitivity of population dynamics to certain parameters also indicates that 

those parameters describe factors that could be critical determinants of population 

viability. Such factors are therefore good candidates for efficient management 

actions designed to ensure the persistence of the population. 

The above kinds of uncertainty should be distinguished from several more sources 

of uncertainty about the future of the population. Even if long-term average 

demographic rates are known with precision, variation over time caused by 

fluctuating environmental conditions will cause uncertainty in the fate of the 

population at any given time in the future. Such environmental variation should be 

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incorporated into the model used to assess population dynamics, and will generate a 

range of possible outcomes (perhaps represented as a mean and standard deviation) 

from the model. In addition, most biological processes are inherently stochastic, 

having a random component. The stochastic or probabilistic nature of survival, sex 

determination, transmission of genes, acquisition of mates, reproduction, and other 

processes preclude exact determination of the future state of a population. Such 

demographic stochastic should also be incorporated into a population model, 

because such variability both increases our uncertainty about the future and can 

also change the expected or mean outcome relative to that which would result if 

there were no such variation. Finally, there is "uncertainty" which represents the 

alterative actions or interventions which might be pursued as a management 

strategy. The likely effectiveness of such management options can be explored by 

testing alterative scenarios in the model of population dynamics, in much the same 

way that Sensitivity testing is used to explore the effects of uncertain biological 

parameters. 

Results 

Results reported for each scenario include: 

Deterministic r — The deterministic population growth rate, a projection of the 

mean rate of growth of the population expected from the average birth and death 

rates. Impacts of harvest, inbreeding, and density dependence are not considered in 

the calculation. When r == O, a population with no growth is expected; r < O 

indicates population decline; r > O indicates long-term population growth. The 

value of r is approximately the rate of growth or decline per year. 

The deterministic growth rate is the average population growth expected if 

the population is so large as to be unaffected by stochastic, random processes. The 

deterministic growth rate will correctly predict future population growth if: the 

population is presently at a stable age distribution; birth and death rates remain 

constant over time and space (i. e., not only do the probabilities remain constant, 

but the actual number of births and deaths each year match the expected values); 

there is no inbreeding depression; there is never a limitation of mates preventing 

some females from breeding; and there is no density dependence in birth or death 

rates, such as a Allee effects or a habitat "carrying capacity" limiting population 

growth. Because some or all of these assumptions are usually violated, the average 

population growth of real populations (and stochastically simulated ones) will 

usually be less than the deterministic growth rate. 

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