A Markov Contingency-Table Model for Replicated Lotka-Volterra Systems Near Equilibrium

This paper proposes a translation of the deterministic Lotka-Volterra equations for the interaction of populations of two species in a single environment into a formally equivalent Markovian model for the interaction of populations of two species in an ensemble of similar environments. Unlike several discussions of the Lotka-Volterra equations, this paper explores the evolution of such an ensemble of interacting populations when some of the parameters of interaction are considered as subject to natural selection. The purpose of this theoretical development is eventually to illuminate interactions of infections in parasitized, particularly human, hosts, and the following exposition will speak of individuals (hosts) with various kinds of infections. But interactions of any species distributed in discrete, or patchy, and approximately similar environments could also be studied in the same way (Section 6).

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