Equilibrium distributions and simulation methods for age structured populations

•Demographics and allele frequency dynamics of age structured population is simulated.•The simulation method applies to a haploid population, and it needs no burn in time.•Equilibrium distribution of age class sizes is derived, given total population size.•Equilibrium distribution is derived, at each marker, of alleles over all age classes.•Multiple polymorphic loci can be simulated independently.

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.