Editing Leslie matrix (section)

==Random Leslie model==
There is a generalization of the population growth rate to when a Leslie matrix has random elements which may be correlated.<ref>M.O. Caceres and I. Caceres-Saez, Random Leslie matrices in population dynamics, J. Math. Biol. (2011) 63:519–556 DOI 10.1007/s00285-010-0378-0</ref> When characterizing the disorder, or uncertainties, in vital parameters; a perturbative formalism has to be used to deal with linear non-negative [[random matrix]] [[Matrix difference equation|difference equations]]. Then the non-trivial, effective eigenvalue which defines the long-term asymptotic dynamics of the mean-value population state vector can be presented as the effective growth rate. This eigenvalue and the associated mean-value invariant state vector can be calculated from the smallest positive root of a secular polynomial and the residue of the mean-valued Green function. Exact and perturbative results can thusly be analyzed for several models of disorder.