Basic Population Model
Slide 42 of 47
Leslie matrix models (Leslie 1945, 1948; Usher 1966; Lefkovitch 1965; Caswell 1989; Manly 1990) are commonly used as the modeling framework for population viability models. Density dependence must be incorporated into the model, i.e., basic parameters must be a function of population size. Thus, the resulting model is not a true Leslie matrix. Each iteration of the calculation also requires a temporal variance component, and making the parameters of the Leslie matrix into random variables (Burgman et al. 1993) is the standard approach, but eradicates the analytical results that normally are benefits of Leslies creative work. If multiple patches are modeled, each patch requires a spatial variance component. Demographic variation can be built into the model. However, the resulting model doesnt resemble the elegant matrix model that Leslie originally developed.
However, use of the Leslie matrix framework ignores individual heterogeneity, and thus is likely to underestimate persistence. Incorporation of individual heterogeneity requires an individual-based model (e.g., DeAngelis and Gross 1992), and thus, is conceptually different from the basic Leslie matrix approach. Individual-based models can be spatially explicit (e.g., Conroy et al. 1995, Dunning et al. 1995, Holt et al. 1995, Turner et al. 1995), providing another approach to incorporating spatial stochasticity into the model.