Stochastic metapopulation models and watershed estimates for playas on the Southern High Plains

TL;DRAbstract

Stochastic models incorporate the variability inherent in natural systems. Two types of stochastic modelling formats are studied and applied to populations: continuous time Markov chain (CTMC) and Itô stochastic differential equations (SDEs). CTMC models, which have discrete state space, are common in population biology. Recently, Itô SDEs, with continuous state space, have also been applied. SDE models have advantages over CTMC models, in that numerical simulations of SDE models are generally much faster than simulations of CTMC models, especially for large population sizes. In addition, the drift term in the SDE model relates directly to the population growth rate in a deterministic population model.
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\nDifferential equations for the moments of the distributions corresponding to the two types of stochastic models are derived and compared. These equations are not closed: each differential equation depends on higher-order moments. Closing the system to

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