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The quasi-deterministic limit of population dynamics

Juan P. Aparicio, Mario A. Natiello, Hernán G. Solari

Abstract


We review, discuss and compare different, but related, approximations to the stochastic dynamics of populations, all of them having as limit the same deterministic dynamics. The diffusion approximation, linearized diffusion approximation and the Poisson approximation are briefly revisited and their quality as approximations for large, but given, populations is addressed analytically as well as with demonstrative examples. To this end we introduce the Integer-Gauss approximation to the Poisson approach and use it to discuss the relation among different techniques.

Keywords


Stochastic Population Dynamics, Feller Process, Poisson Approximation, Diffusion Approx- imation, Langevin approach, SDE.

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