AICME II abstracts
From individuals to populations and communities
From individuals to populations and communities
Time scales in multiregional models with environmental stochasticity Luis Sanz1 and Rafael Bravo de la Parra2 . In this work we extend previous results on the reduction of multiregional models with two time scales and subjected to environmental stochasticity. We contemplate an age structured population evolving in a multi-patch environment which varies randomly according to a Markov chain, in such a way that the migration among the different patches is fast with respect to the growth of the population. Using techniques already explored by the authors that make use of the separation of time scales, we can reduce the dimension of the dynamical system obtaining a so called aggregated system with a number of variables equal to the number of age classes. The main contribution in this work is the obtention of relationships between the so called ”stochastic growth rate”, the main parameter that characterizes the growth of the population, for the original and reduced system . In this way we prove the validity of the reduction technique employed in terms of the separation of time scales. We also explore the relationship between the variance of the population size for the two systems.
1 Departamento de Matem´ aticas, E.T.S.I. Industriales, U. Polit´ecnica de Madrid Jos´e Guti´errez Abascal 2. 28806 Madrid, Spain (e-mail:
[email protected]). 2 Dep. de Matem´ aticas, Universidad de Alcal´ a, Campus Universitario, Fac. de Ciencias, 28871, Alcal´ a de Henares, Madrid, Spain (e-mail:
[email protected]).
08-Saz-a
08-Saz-b
AICME II abstracts
