Population Viability Analysis (PVA) is the estimation of extinction probabilities by analyses that
incorporate identifiable threats to population survival into models of the extinction process. Extrinsic
forces, such as habitat loss, over-harvesting, and competition or predation by introduced species, often
lead to population decline. Although the traditional methods of wildlife ecology can reveal such
deterministic trends, random fluctuations that increase as populations become smaller can lead to
extinction even of populations that have, on average, positive population growth when below carrying
capacity. Computer simulation modelling provides a tool for exploring the viability of populations
subjected to many complex, interacting deterministic and random processes. One such simulation
model, VORTEX, has been used extensively by the Captive Breeding Specialist Group (Species Survival
Commission, IUCN), by wildlife agencies, and by university classes. The algorithms, structure,
assumptions and applications of VORTEX are described in this paper.
VORTEX models population processes as discrete, sequential events, with probabilistic outcomes.
VORTEX simulates birth and death processes and the transmission of genes through the generations by
generating random numbers to determine whether each animal lives or dies, to determine the number
of progeny produced by each female each year, and to determine which of the two alleles at a genetic
locus are transmitted from each parent to each offspring. Fecundity is assumed to be independent
of age after an animal reaches reproductive age. Mortality rates are specified for each pre-reproductive
age-sex class and for reproductive-age animals. Inbreeding depression is modelled as a decrease in
viability in inbred animals.
The user has the option of modelling density dependence in reproductive rates. As a simple model
of density dependence in survival, a carrying capacity is imposed by a probabilistic truncation of each
age class if the population size exceeds the specified carrying capacity. VORTEX can model linear trends
in the carrying capacity. VORTEX models environmental variation by sampling birth rates, death rates,
and the carrying capacity from binomial or normal distributions. Catastrophes are modelled as sporadic
random events that reduce survival and reproduction for one year. VORTEX also allows the user to
supplement or harvest the population, and multiple subpopulations can be tracked, with user-specified
migration among the units.
VORTEX outputs summary statistics on population growth rates, the probability of population
extinction, the time to extinction, and the mean size and genetic variation in extant populations.
VORTEX necessarily makes many assumptions. The model it incorporates is most applicable to species
with low fecundity and long lifespans, such as mammals, birds and reptiles. It integrates the interacting
effects of many of the deterministic and stochastic processes that have an impact on the viability
of small populations, providing opportunity for more complete analysis than is possible by other
techniques. PVA by simulation modelling is an important tool for identifying populations at risk of
extinction, determining the urgency of action, and evaluating options for management.
Effects of a Fluctuating Carrying Capacity on the Generalized Malthus-Verhulst Model
