Week 12 - Building a model

Our population is haploid (each individual will carry one allele type: either A or a) · The allele affects survival to maturity (i.e., there is viability selection in the population), but has no effect on rates of offspring production among individuals that survive · Generations are discrete (non-overlapping), with the following series of events occurring during the life-cycle of our population: (1) birth, (2) viability selection, (3) reproduction of surviving individuals immediately followed by death of parents, (4) the newly born offspring comprise the population of the next generation · We assume that natural selection accounts for all evolutionary change in the population (we ignore effects of genetic drift, mutation and migration, on allele frequency change)

The fundamental unit of time in our model is a generation. By modelling changes in population size and allele frequency across a single generation, we can determine: · Conditions under which each allele type will increase within the population · Conditions leading to an increase vs. a decrease in population size · Rates of evolutionary and population size dynamics

We will consider two variables in our model: · The frequency of the A allele at birth, which we will refer to as p · The population size at birth, which we will refer to as N

Because there are only two allele types in our population, we do not have to separately keep track of the a allele frequency, which can be inferred from the frequency of A (i.e., if p is the frequency of A then 1 – p must be the frequency of a).

The parameters of our model will be: · wA: the probability that an individual carrying an A allele survives to reproduce · wa: the probability that an individual carrying an a allele survives to reproduce · R: the number of offspring that each surviving adult produces (which, as noted, is independent of genotype). We will assume that individuals reproduce asexually.

Calculate the numbers of a and A bearing adults Calculate A and a frequencies among adults Each adult produces R offspring and then dies. To complete the recursion calculate: the total number of offspring produced (N’) and the allele frequency among offspring (p’)