# Gene flow and genetic drift Evolution Biology 4971/5974 D F Tomback

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1 Biology 4974/5974 Evolution Gene Flow, Genetic Drift, and the Shifting Balance Theory Figures from Hall and Hallgrimsson, 2014, Strickberger s Evolution Learning goals Understand how the following processes change allele frequencies within a population: Mutation Neutral selection Balanced polymorphism Gene flow (migration) Natural selection Genetic drift Know and understand: Why local populations may differ from one another. How to tell genetic differentiation from environmental effects. How genetic drift alters allele frequencies. How the Shifting Balance Theory maintains alleles within a population. How a deme moves from peak to peak. Demes Individuals of a species share a gene pool by definition. Demes and local populations may differ from one another because of genetic differences due to natural selection, mutation, and genetic drift. Gene flow reduces these differences. Variation in phenotype among populations of a species is known as geographic variation. Example: Populations of yarrow (Achillea lanulosa and Achillea borealis) vary in height and many leaf and flower traits. How can we tell whether this variation is genetically based or in response to environmental differences? 1

2 Different populations of yarrow in a transect across California. Fig Timberline = 3,050 m Mather = 1,400 m Stanford = sea level Fig Mutation One explanation for the origin and continued existence of genetic variation is gene mutation. The rates of forward mutation and back mutation are usually not equal. Mutation rates are low: one mutation per 100,000 copies of a gene. Each egg and sperm carries less than one new mutation on average. Assuming no difference in selection between alleles. p = frequency of A q = frequency of a A a, mutation rate is u; a A, mutation rate is v Δq = u p 0 v q 0 An equilibrium is reached between the two gene frequencies, based on the respective mutation rates: ^q = u/(u + v) ^p = v/(u + v) and ^p/^q = v/u Gene flow (migration) Alleles may enter a population through gene flow or gene migration. This will change allele frequencies. Factors that influence the recipient population, given one allele in a population: The difference in gene frequency between recipient (q 0 ) and migrant (Q) populations for that allele. The proportion of migrating genes incorporated each generation into the recipient population (m). Whether gene flow occurs once or repeatedly. If repeatedly, the gene frequency of the recipient population become q n. (1 m) n = q n - Q/ q 0 - Q Gene flow can oppose selection (oppose adaptation), for example. In other cases it can add important genetic variation or reduce inbreeding effects. 2

3 Random genetic drift Random genetic drift usually results in the loss of allelic variation. Random events (random variation) in populations can alter allele frequencies at a gene locus. The smaller the population, the more likely that genetic drift will cause changes in allele frequencies. Assume a diploid population, with two alleles for a gene, indicated by the frequencies p and q. The Standard Deviation in p and q caused by random variation each generation is calculated as: σ = pq/2n N is the number of parents; 2N is the total genes for that locus. Gene frequencies would assume a normal distribution with p and q the mean frequency and σ the variance around the mean due to random events. Drift when population is large N = 5,000 parents, and 2N = 10,000 genes examined. p = q = 0.5 are initial allele frequencies (p + q = 1). After one generation, the range of drift possible: σ = (0.5)(0.5)/10,000 = = This means that the values for p and q will vary around 0.5 ± 0.005,that is between to For a population with the extreme values for p and q, next generation: σ = (0.495)(0.505)/10,000 = Thus, p and q could become even more different by chance: ~ and The likelihood is that drift will fluctuate around 0.5 for each allele, back and forth over time. 100 populations, each starting with p = q = 0.5 T = 0 T = 1 N = 5,000 T = P 3

4 Drift when population is small In contrast, small populations: N =2 parents σ = pq/2n = (0.5)(0.5)/ = σ = 0.25 After one generation, p and q may vary in frequency: 0.5 ± 0.25 by chance. p or q may end up as low as 0.25 with the other allele as high as 0.75 in frequency. After the second generation, they could shift more: σ = (0.25)(0.75)/4 = Here, p ranges from 0.03 to 0.47 and q varies from 0.53 to Thus, in the extreme, p = 0.03, and q = 0.97 after two generations of genetic drift. Another generation and p could be lost and q = 1.0. Imagine 100 populations, each starting with p=q=0.5 T = 0 N = 2 T = 1 If p = 0, q = 1.0 If p = 1, q = 0 Allelic fixation T = P The outcome of random genetic drift Random genetic drift may drastically alter gene frequencies in small populations. Small populations may achieve allelic fixation: where the value for p and q becomes 0 and 1.0. Loss of alleles causes loss of heterozygosity. In small populations, this process is inevitable. The rate of fixation or probability of fixation is considered 1/2N, which gives the proportion of populations that eventually attain fixation. For the first example: 1/10,000 is very small; but for the second ¼ is very large. Genetic drift in small populations is strong enough to counter the effects of natural selection, i.e., the more fit allele may be lost by chance. 4

5 The effects of random genetic drift on the distribution of equilibrium gene frequencies, when selection is zero. Fig Laboratory study of random genetic drift: Buri s work on genetic drift in Drosophila at the bw locus For each breeding line, Buri began with p = bw = 0.5 and q = bw 75 = 0.5 He selected 16 parents (8 males, 8 females) at random each generation to continue each line. Set up 107 different breeding lines. Continued all lines for 19 generations. By generation 19, the bw 75 allele was eliminated completely from 30 lines (q = 0), and bw 75 was fixed at 28 lines (p = 1). Fig The Shifting Balance Theory Proposed by Sewall Wright to explain allelic variation at a particular gene locus. Demes occupy an adaptive landscape of peaks and valleys. Different genotypes occupy different adaptive peaks. Each peak has the potential to be the highest under the right environmental conditions. Movement of a deme from peak to peak is initiated by genetic drift, which changes allele frequencies. Drift moves a deme down a peak and maybe into a valley Gene migration into the deme changes allele frequencies further, and the deme crosses the valley. Selection drives the deme up the nearest peak. Environmental change alters the landscape, so peaks change in height (new genotypes may be best adapted.) 5

6 Adaptive Landscape illustrating the Shifting Balance Theory End Box 19.1 In this scenario there are four gene loci, each intended to be homozygous. Having capital letter alleles at two loci are required for a deme to be on the top of a peak. Study questions How does mutation maintain genetic variation? How does gene flow (migration) change allele frequencies? What are the important variables to know to calculate the new frequency (q n ). How does random genetic drift affect allele frequencies for a gene over time? Are frequency changes always unidirectional for an allele? Explain the implications of the Standard Deviation σ = pq/2n for allele frequencies p and q after one generation. Over more time? How does population size N affect drifting allele frequencies? Explain why genetic drift results in loss of heterozygosity? What other genetic mechanism reduces heterozygosity? Study questions, p. 2 Fig Can you explain what is happening to a population of N = 100,000, N = 10,000, N = 5,000, and N = 1,000 with respect to allele frequency q? Fig Explain the final distribution of alleles in the Buri Drosophila experiment based on what you known about genetic drift and its effects? How does the Shifting Balance Theory explain the maintenance of different alleles for a gene? How does a deme shift from one peak to another? How does an adaptive peak change height (fitness)? 6

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