Laboratory of Mathematical Ecology
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NONNEGATIVE MATRICES AS A TOOL TO MODEL POPULATION DYNAMICS: CLASSICAL MODELS AND CONTEMPORARY EXPANSIONS
Logofet D.O. and Belova I.N.
Summary Matrix models of age- or/and stage-structured populations rest upon Perron - Frobenius Theorem for nonnegative matrices, and the life cycle graph for individuals of a given biological species plays a major role in model construction and analysis. Presented is a summary of classical results on the theory of matrix models for population dynamics and the generalisations are proposed which have been motivated by a need to account for an additional structure, i.e., to classify individuals not only by age, but also by an additional (discrete) characteristic - size, physiological status, stage of development, etc.Matrix models of age- or/and stage-structured populations rest upon Perron - Frobenius Theorem for nonnegative matrices, and the life cycle graph for individuals of a given biological species plays a major role in model construction and analysis. Presented is a summary of classical results on the theory of matrix models for population dynamics and the generalisations are proposed which have been motivated by a need to account for an additional structure, i.e., to classify individuals not only by age, but also by an additional (discrete) characteristic - size, physiological status, stage of development, etc. |