Introduction to matrix population models

Matrix population models (MPMs) are currently used in a range of fields, from basic research in ecology and evolutionary biology, to applied questions in conservation biology, management, and epidemiology. In MPMs individuals are classified into discrete stages, and the model projects the population over discrete time-steps. A rich analytical theory is available for these models, for both the linear deterministic case and for more complex dynamics including stochasticity and density dependence. This chapter provides a non comprehensive introduction to MPMs and some basic results on asymptotic dynamics, life history parameters, and sensitivities and elasticities of the long-term growth rate to projection matrix elements and to underlying parameters. We assume that readers are familiar with basic matrix calculations. Using examples with different kinds of demographic structure, we demonstrate how the general stage-structured model can be applied to each case.