caa a22 4500 445329971 CHVBK 20180317142734.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00285-010-0378-0 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0378-0 Random Leslie matrices in population dynamics [Elektronische Daten] [Manuel Cáceres, Iris Cáceres-Saez] 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. Springer-Verlag, 2010 Leslie matrix nationallicence Disordered vital parameters nationallicence Growth rate nationallicence Random environment nationallicence Marine mammals nationallicence Cáceres Manuel Centro Atomico Bariloche, Instituto Balseiro, Universidad Nacional de Cuyo, CNEA, CONICET, 8400, Bariloche, Argentina aut Cáceres-Saez Iris CRUB, Universidad Nacional del Comahue, 8400, Bariloche, Argentina aut Journal of Mathematical Biology Springer-Verlag 63/3(2011-09-01), 519-556 0303-6812 63:3<519 2011 63 285 https://doi.org/10.1007/s00285-010-0378-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0378-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cáceres Manuel Centro Atomico Bariloche, Instituto Balseiro, Universidad Nacional de Cuyo, CNEA, CONICET, 8400, Bariloche, Argentina aut NATIONALLICENCE 700 1- Cáceres-Saez Iris CRUB, Universidad Nacional del Comahue, 8400, Bariloche, Argentina aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 63/3(2011-09-01), 519-556 0303-6812 63:3<519 2011 63 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer