There are two basic approaches to PVA. First, simple theoretical models can be used to explore general ideas about the factors that affect population fluctuations.
Solutions to these simple models can be used to identify general patterns in the causes of population decline or risk factors for extinction. However, models that are sufficiently complicated to realistically represent the drivers of fluctuations in real populations are rarely analytically tractable. Thus, to perform PVA for a real population, simple theoretical models are supplemented with computational models that simulate population dynamics. An exception to this rule is the linear diffusion approximation for age-structured populations in a fluctuating environment. In summary, theoretical models are typically used to identify general principles of extinction risk while simulation models are used to model extinction risk for real populations.
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