Evolutionary Formalism from Random Leslie Matrices in Biology

CÁCERES, M.O.; CÁCERES-SAEZ, I.

Report of the International Centre for Theoretical Physics (ICTP), Trieste, Italia

United Nations Educational, Scientific and Cultural Organization (UNESCO) & International Atomic Energy Agency (IAEA)

Lugar: Miramare,Trieste; Año: 2008 vol. 46 p. 1 - 35

We present a perturbative formalism to deal with linear random matrix difference equations. We generalize the concept of the population growth rate when a Leslie matrix has random elements (i.e., characterizing the disorder in the vital parameters). The dominant eigenvalue of which defines the asymptotic dynamics of the mean value population vector state, is presented as the effective growth rate of a random Leslie model. This eigenvalue is calculated from the largest positive root of a secular polynomial. Analytical (exact and perturbative calculations) results are presented for several models of disorder. A 3x3 numerical example is applied to study the effective growth rate characterizing the long-time dynamics of a population biological case: the Tursiops sp.