Equilibrium distributions and simulation methods for age structured populations

Fredrik Olsson; Ola Hössjer

doi:10.1016/j.mbs.2015.08.003

Equilibrium distributions and simulation methods for age structured populations

Math Biosci. 2015 Oct:268:45-51. doi: 10.1016/j.mbs.2015.08.003. Epub 2015 Aug 11.

Authors

Fredrik Olsson¹, Ola Hössjer²

Affiliations

¹ Department of Mathematics, Division of Mathematical Statistics, Stockholm University, Stockholm, Sweden. Electronic address: fredriko@math.su.se.
² Department of Mathematics, Division of Mathematical Statistics, Stockholm University, Stockholm, Sweden.

PMID: 26275600
DOI: 10.1016/j.mbs.2015.08.003

Abstract

A simulation method is presented for the demographic and genetic variation of age structured haploid populations. First, we use matrix analytic methods to derive an equilibrium distribution for the age class sizes conditioned on the total population size. Knowledge of this distribution eliminates the need of a burn-in time in simulations. Next, we derive the distribution of the alleles at a polymorphic locus in various age classes given the allele frequencies in the total population and the age size composition. For the time dynamics, we start by simulating the dynamics for the total population. In order to generate the inheritance of the alleles, we derive their distribution conditionally on the simulated population sizes. This method enables a fast simulation procedure of multiple loci in linkage equilibrium.

Keywords: Age structured population; Demographic variation; Genetic variation; Matrix analytic method; Simulation method.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Gene Frequency*
Genetics, Population*
Models, Genetic*