Coalescent Theory

Random variation in reproduction causes random fluctuation in allele frequencies. Can describe this process as diffusion: (Wright 1931) showed that the equilibrium distribution of the allele frequency of p, where alleles mutate: P → Q at rate µ and Q → P at rate υ, can be described by:) 1 4 () 1 4 () Pr(− − = µ υ e e N N q cp p (c is a constant that normalizes the area under the curve to one) Drift is more efficient in small populations (pushes alleles toward fixation: 0 or 1) Without mutation all alleles would eventually reach 0 or 1 µ υ υ µ υ υ µ υ υ + = + = + =) (4 4 4 4 4) (Ne Ne Ne Ne Ne p E So the expectation (mean) is independent of effective population size. (note: the variance is not) Here we see that if the composite mutation parameter, θ = 4N e µ, is less than 1 then drift dominates, but if θ is greater than one, then mutation prevents fixation. We will see θ pop up later… Notice that a range of N e and µ satisfy the equation: µ θ Ne 4 = What are we after? In general, we would like to be able to make inferences about evolutionary processes that maintain or erode genetic variation in natural populations. We gain intuition about these processes by creating models of idealized scenarios. Hopefully, our models capture the important evolutionary processes that produce the data that we see. We might