Cáceres Manuel O, Cáceres-Saez Iris
Centro Atomico Bariloche, Instituto Balseiro, Universidad Nacional de Cuyo, CNEA, CONICET, 8400 Bariloche, Argentina.
J Math Biol. 2011 Sep;63(3):519-56. doi: 10.1007/s00285-010-0378-0. Epub 2010 Nov 14.
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.
我们推广了具有随机元素（相关或不相关）的莱斯利矩阵情况下种群增长率的概念，即表征生命参数中的无序性。一般来说，我们提出一种微扰形式来处理线性非负随机矩阵差分方程，然后将其非平凡有效特征值定义为平均种群向量状态的长期渐近动力学，该有效特征值作为有效增长率给出。这个有效特征值是由久期多项式的最小正根计算得出的。给出了几种无序模型的解析（精确和微扰计算）结果。特别地，应用一个3×3的数值例子来研究表征生物种群模型长期动力学的有效增长率。当前的分析是一种在生命参数可能在种群间具有负协方差的情况下寻找有效增长率的微扰方法。
