Nonnegative matrices as a tool to model population dynamics: classical models and contemporary expansions amg

Matrix models of age- or/and stage-structured populations rest upon the 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. A summary of
classical results in the theory of matrix models for population dynamics is presented,
and generalizations 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.