Stochastic stage-structured population model
Kaskela, Kiyomi Otsuka
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The Larvae-Pupae-Adult (LPA) model is a system of difference equations that predicts the population dynamics of flour beetles. The deterministic LPA model assumes individuals in the population belong to a homogeneous group. Consequently, the deterministic LPA model does not include random variabilities that affect population dynamics, such as weather, diseases, deaths, births, or immigration. For this reason, stochastic LPA models have been developed by adding variability into the deterministic LPA model. We first analyze two such stochastic LPA models, environmental and demographic stochastic LPA models, that are based on a process known as a nonlinear autoregressive process (NLAR). These are two important types of stochasticities in biological modeling. Numerical examples have shown that demographic stochasticity is superior statistically to environmental stochasticity for the flour beetles. A second type of LPA model with demographic variability is instroduced, the Poissonbinomial LPA model. This latter model is a direct parametric interpretation of the deterministic LPA model with demographic variability. Poisson and binomial distributions are used to express the Poisson-binomial LPA model. The Poisson-binomial LPA model and the NLAR model with demographic stochasticity will be compared and investigated. Through numerical examples and statistical tests for the means, it is clear that the Poisson-binomial LPA model and the NLAR demographic model have different outcomes for the dynamics of the flour beetles. This paper summarizes the description given by Cushing et al. in their book Chaos in Ecology . Matlab programs were written for each of the models and extensive numerical simulations were performed. Numerical examples are presented of the NLAR environmental and demographic models and an analysis and a comparison of the NLAR demographic model and the Poisson-binomial LPA model.