Notes for Lecture #5:

        Population Genetics -- Selection and Drift

        Copyright 1996. May not be reproduced for commerical purposes

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        The best way to gain an understanding about drift (finite population size) and selection is to play around with them. Try different population sizes (e.g., 5 vs. 25 vs 100 vs 1000) and different survival probabilities in the Hardy-Weinberg simulator . This is a product of our good friends at the University of Chicago. Have fun!

        Evolutionary forces that can change allele frequencies

        Population genetics constructs mathematical models for how these forces change allele frequnecies

        • Selection
        • Drift
        • Mutation
        • Migration

        Selection

        Haldane, Fisher & Wright independently showed how selection changes genotypic frequencies. In particular, unless the heterozygote has the highest fitness (leaves on average the most offspring), selection fixes the most favored allele.

        In general, genotype with the highest fitness is fixed if possible.

        Selection against a recessive

        Overdominant Selection

        Here, the heterozygote has the highest fitness

        • This results in selection maintaining both alleles

        • If frequency is below its equilibrium value, it increases up to this value. If it is above the equilibrium value it decreases down to the eq. value. For example, suppose the heterozygote Aa has the highest fitness (the fitnesses used here are 0 : 1 : 0.6)

        Worked example
        Suppose the genotypes AA, Aa, and aa leave, on average, 
6, 10, and 3 offspring each.    What is the equilibrium frequency of A?

First, standardize the fitness so the heterozygote has fitness one,
			AA		Aa		aa
# Offspring		6		10		3
 Fitness		6/10		1		3/10

Next, to obtain the equil. freq of A = s/(s+t),  solve for 
s and t given these fitnesses.   

			AA		Aa		aa
    Fitness		0.6		1		0.3
			1-t		1		1-s
Hence 1-t = 0.6  or t = 0.4;   1-s = 0.3, or s = 0.7

Equilibrium freq of A =   s/(s+t) = 0.7/(0.7 + 0.4) = 7/11.

        Genetic Drift

        • Most populations are finite. As a result, allele frequencies change by chance each generation.
        • Sewall Wright worked out the basics of drift in the 1930''s.

        Examples:

        Drift and finite population size

        • Drift eventually fixes one allele in a population. Thus, drift removes variation, and mutation is required to introduce new variation.
        • The larger the population, the longer time it takes drift to remove variation.
        • In very small populations, drift can overpower natural selection.