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Transcript
January 27th, 2010 Bioe 109 Winter 2010 Lecture 9 Microevolution 2 - mutation & migration Natural selection and mean population fitness - we can examine what happens to the mean population fitness as natural selection fixes an advantageous allele. - rather than plotting the frequency of the selected allele over time we can plot how wbar changes. - when we plot wbar over time as selection acts on a favorable allele we see that natural selection acts in a manner that maximizes mean population fitness (see Box 6.7 in textbook). - in fact, it cannot do the opposite, i.e., result in a net reduction in fitness. - what happens when selection does not cause the fixation of the allele, i.e., the case of balancing selection? - let us now reconsider the case of overdominance. Genotype: Fitness (w): A1A1 A1A2 A2A2 w11 w12 w22 1-s 1 1-t - the equilibrium allele frequencies are: A = phat = t/(s + t) a = qhat = s/(s + t). - suppose the fitnesses are Genotype: Fitness (w): A1A1 A1A2 A2A2 0.90 1 0.90 - here s and t are both = 0.10. - the equilibrium frequency of A1 = A2 = 0.50. - we can plot mean population fitness (wbar) as a function of the frequency of the A1 allele. - two important conclusions can be drawn. - first, natural selection results in a maximization of mean population fitness at some intermediate frequency of the two alleles. - if the frequencies are perturbed from this point, then overdominant selection will return them to this equilibrium point. - second, the population never realizes its highest possible fitness (i.e., that of the heterozygote = 1) but is maintained at a reduced level because of the maintenance of the polymorphism. - this is a type of genetic load incurred by the population. - it is called the segregational load because less fit homozygotes always produced by matings between the most fit heterozygote. - we will return to the issue of genetic load later in class. - the concept of mean population fitness has been at the center of an important controversy in evolutionary biology. - this took place between Sewall Wright and Ronald Fisher and concerned Wright’s shifting balance theory. - central to this theory is the concept of an adaptive landscape – a multi-dimensional representation of mean population fitness as a function of allele frequencies at multiple loci. - according to Wright, this surface was covered by many peaks separated by valleys of reduced fitness. - under this model, natural selection would act to push populations up to local adaptive peaks but not necessarily the highest “global” peak. - once at a local peak, the population would be stuck – its ability to move across a saddle of lower fitness to reach a higher adaptive peak would be thwarted by selection. - to circumvent this problem, Wright argued that random genetic drift could act to move populations off local peaks, across valleys, and on to higher adaptive peaks. - for this process to occur, however, natural populations must be small (so the effects of drift are large) and experience little gene flow. - in contrast, Fisher viewed natural populations as extremely large and not subdivided to any significant degree. - according to Fisher, Wright’s model simply wouldn’t work because of the inability of random genetic drift to knock populations off local peaks. - this controversy persists today as theoreticians continue to explore the feasibility of Wright’s model. - a nice example where a population can get “stuck” on a lower peak when an adjacent peak of higher fitnesses is present involves sickle-cell hemoglobin. - in a class last week, this was discussed as a nice example of overdominance. - however, the situation is more complicated because an other allele occurs at this locus – HbC. - here are the fitnesses of genotypes including HbC: Genotype Fitness Phenotype AA AS SS AC SC CC 0.9 1 0.2 0.9 0.7 1.3 malarial susceptible malarial resistant severe anemia malarial susceptible anemia malarial resistant - the highest mean population fitness would be realized by a population fixed for the C allele. - why doesn’t this happen? - because the C allele cannot invade a population at the stable equilibrium point for the A and S alleles because it would have to traverse a valley of reduced fitness (i.e., the AC and SC heterozygotes). - natural selection will act to oppose any movement off the local AS peak. - the population could get onto the higher CC peak if inbreeding results in the production of CC homozygotes in a small isolated population, or if random drift happened to cause a higher frequency of the C allele. Mutation - mutation is the process that fuels evolution. - without a continuous influx of mutations into natural populations, genetic variability will eventually be lost and the population will become monomorphic. - as a process causing evolutionary change at individual loci within natural populations, however, mutation is very inefficient. - consider a simple case in which we have two alleles at a locus A and a, with frequencies of 0.5 each. - suppose that the A allele mutates to a at a rate of u = 1 x 10-5. A u a - this is a typical estimate for a protein coding gene for a new allele causing an amino acid replacement. - in each generation, the frequency of a is increased by u x p (and conversely the frequency of A is reduced by u x p). - denoting the change in frequency of a in one generation as q: q = u x p = u(1-q) = 0.000005. - the frequency of q has thus increased in one generation to 0.500005. - at this rate it would take about 70,000 to get the frequency to 0.75, and another 70,000 years to get the frequency to 0.875. - thus, the rate of change due to mutation pressure is exceedingly small. - despite this fact, mutation rates are sufficient to generate large pools of genetic variation in natural populations. - this is because there are many loci capable of mutating and there are typically many individuals in a population in which these new mutations can occur. Migration/gene flow - gene flow can be defined as the movement of gametes or individuals among populations. - unlike selection, drift, and mutation that occur within single populations, gene flow by definition refers to a process that occurs among populations - gene flow, if unopposed by other factors (i.e., selection, drift, or mutation) will lead to the homogenization of different populations of a species. - this means that allele frequency differences that existed among the populations will be eliminated by gene flow. - gene flow is thus the most important process determining what determining population structure. How rapidly does gene flow occur? - the magnitude of gene flow is determined by m. m = the proportion of genes entering a population in individuals immigrating from other populations - consider the simplest case of a single population receiving migrants from another population. - let p1 be the frequency of an allele in the recipient population 1 and p2 be the frequency of the allele in the “donor” population 2. - let m = the proportion of gene copies in population 1 that originate from population 2. - thus a fraction 1-m of genes are non-immigrant alleles. p1’ = p1(1-m) + p2m = p1 - p1m + p2m p = p1’ - p1 = m(p2 - p1) - this tells us that the relative change in frequency in population 1 is determined by the allele frequency difference between population 1 and population 2 and by the level of gene flow. an example: let p1 = 0.25, p2 = 0.75, and m = 0.001, then p = 0.0005. if p1 = 0.25, p2 = 0.75, and m = 0.1, then p = 0.05. - these rates of change approach those that we saw for selection. - gene flow can thus be a very potent force in causing microevolution. - however, given the above two examples allele frequency differences among populations would be rapidly eliminated. - if unopposed by selection, gene flow will always result in the elimination of genetic differences between populations.