Approximating the distribution of population size in stochastic multiregional matrix models with fast migration

Author:

Alonso Juan Antonio1,Sanz Luis1

Affiliation:

1. Departamento de Matemáticas, E.T.S.I. Industriales, Universidad Politécnica de Madrid, José Gutiérrez Abascal, 2, 28006 Madrid, Spain

Abstract

In this work we deal with a multiregional model in discrete time for an age-structured population which lives in an environment that changes randomly with time and is distributed in different spatial patches. In addition, and as is often the case in applications, we assume that migration is fast with respect to demography. Using approximate aggregation techniques we make use of the existence of different time scales in the model and reduce the dimension of the system obtaining a stochastic Leslie model in which the variables are the total population in each age class. Literature shows that, under reasonable conditions, the distribution of population size in matrix models with environmental stochasticity is asymptotically lognormal, and is characterized by two parameters, stochastic growth rate (s.g.r.) and scaled logarithmic variance (s.l.v.), that, in most practical cases, cannot be computed exactly. We show that the s.g.r. and the s.l.v. of the original multiregional model can be approximated by those corresponding to the reduced stochastic Leslie model, therefore simplifying its analysis. Moreover, we illustrate the usefulness of the reduction procedure by presenting some practical cases in which, although the explicit computation of the s.g.r. and the s.l.v. of the original multiregional model is not feasible, we can calculate its analogues for the reduced model.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Stochastic matrix metapopulation models with fast migration: Re-scaling survival to the fast scale;Ecological Modelling;2020-02

2. Conditions for growth and extinction in matrix models with environmental stochasticity;Ecological Modelling;2019-11

3. Aggregation may or may not eliminate reproductive uncertainty;Ecological Modelling;2017-11

4. Approximate Aggregation Methods in Discrete Time Stochastic Population Models;Mathematical Modelling of Natural Phenomena;2010

5. From biological and clinical experiments to mathematical models;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2009-12-13

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