title: Random Leslie matrices in population dynamics.
abstract: We generalize the concept of the population growth rate when a Leslie matrix has random elements (correlated or not), i.e., characterizing the disorder in the vital parameters. In general, we present a perturbative formalism to deal with linear non-negative random matrix difference equations, then the non-trivial effective eigenvalue of which defines the long-time asymptotic dynamics of the mean-value population vector state is presented as the effective growth rate. This effective eigenvalue is calculated from the smallest positive root of a secular polynomial. Analytical (exact and perturbative calculations) results are presented for several models of disorder. In particular, a 3 × 3 numerical example is applied to study the effective growth rate characterizing the long-time dynamics of a biological population model. The present analysis is a perturbative method for finding the effective growth rate in cases when the vital parameters may have negative covariances across populations.
authors.affiliation: Centro Atomico Bariloche, Instituto Balseiro, Universidad Nacional de Cuyo, CNEA, CONICET, 8400 Bariloche, Argentina. caceres@cab.cnea.gov.ar
authors.forename: Manuel O
authors.initials: MO
authors.lastname: Cáceres
authors.forename: Iris
authors.initials: I
authors.lastname: Cáceres-Saez
mesh_terms: D000818:Animals; D008954:Models, Biological; D011157:Population Dynamics; D016019:Survival Analysis; D050685:Whale, Killer / Q000254:growth & development*