Moran Process - Rate of Evolution

Rate of Evolution

In a population of all B individuals, a single mutant A will take over the whole population with the probability

If the mutation rate (to go from the B to the A allele) in the population is u then the rate with which one member of the population will mutate to A is given by N x u and the rate with which the whole population goes from all B to all A is the rate that a single mutant A arises times the probability that it will take over the population (fixation probability):

\begin{align} R = N \cdot u \cdot \rho = u \quad \text{if} \quad \rho = \frac{1}{N}. \end{align}

Thus if the mutation is neutral (i.e. the fixation probability is just 1/N) then the rate with which an allele arises and takes over a population is independent of the population size and is equal to the mutation rate. This important result is the basis of the neutral theory of evolution and suggests that the number of observed point mutations in the genomes of two different species would simply be given by the mutation rate multiplied by two times the time since divergence. Thus the neutral theory of evolution provides a molecular clock, given that the assumptions are fulfilled which may not be the case in reality.

Read more about this topic:  Moran Process

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