Stochastic versus Deterministic Modeling in Population Biology

Shay Gueron

Department of Mathematics
University of Haifa
Haifa, 31905, Israel   
shay@math.haifa.ac.il
   


The field of Mathematical Ecology deals with the dynamics of populations, which typically exhibit stochastic behavior. Thus, many population biology models can be viewed as a description of coupled stochastic processes, although this interpretation is not always made explicitly. A well known example is the class of reaction diffusion equations, such as the Lotka-Volterra predator-prey models.

Stochastic processes are often modeled by means of deterministic differential equations that describe the time evolution of the stochastic process. The use of such approach is now standard. These deterministic models hope to approximate the expectation of the underlying stochastic process, at least for large populations. However, various examples demonstrate that this is not always the case, and the consistency of the deterministic approximations is therefore not obvious. For this reason, the justification of explicit omission of stochasticity in order to obtain deterministic model equations is an important theoretical modeling question.

This session is devoted to the study of the interrelations between stochastic and deterministic modeling approaches in population biology. Examples where discrepancies occur, and proofs for cases where these modeling approaches are equivalent.


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