The models described above (the simple birth-death process and the diffusion approximation for populations in a fluctuating environment) illustrate some generalizations about extinction risk that hold for many populations. However, these models are not sufficiently precise for risk analysis in most cases, because they are based on idealized populations with very simple properties. Although occasionally more complicated models will be analytically tractable, these cases are rare. More realistic models are therefore developed with the aid of computer programs designed to simulate stochastic population growth. In particular, a computational approach can be adopted to incorporate density dependence, spatial metapopulation structure, and diminishing fitness due to genetic inbreeding. There are several commercially available software packagers that incorporate some or all of these elements (Table 1). The reader is referred to the articles by Brook et al. for comparisons.
It is also reasonably straightforward to develop one's own models using a scientific programming language like MATLAB (www.mathworks.com) or R (www.r-project. org). The book Quantitative Conservation Biology by Morris and Doak provides an introduction to PVA programming
Table 1 Some software packages for population viability analysis Program Short description VORTEX
in MATLAB, many examples, and samples of code that can be tailored to different scenarios. Using approaches introduced there, one can incorporate important realistic features of population growth such as autocorrelation in environmental conditions; age, development stage, sex, and spatial population structure; genetic status; and density dependence. Of course, to effectively parametrize a model that includes all these components would require tremendous amounts of information. Thus, the most important tasks of the modeler are to identify which features are the most important and to develop a model that reasonably includes these and avoids unnecessary detail.
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