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Unformatted text preview: 1 from last time (1/13)... e) Overdominance: w 11 < w 12 > w 22 (i.e, het has highest fitness) Let fitnesses be w 11 = 1- s , w 12 = 1, w 22 = 1- t then, substituting in the general equation, Δ p = pq (- sp + tq )/(1- sp 2 + tq 2 ) thus, there is an "internal equilibrium" (i.e., Δ p = 0 and p ≠ 0 or 1) when sp = tq . This is an example of " balancing selection ", whereby selection acts to maintain genetic variation (i.e., an allele increases in frequency when rare). Note: overdominance is sometimes called "heterosis" or "heterozygote advantage". f) Underdominance: w 11 > w 12 < w 22 ; Let w 11 = 1 + s , w 12 = 1, w 22 = 1 + t . Again substituting in the general equation, you get Δ p = pq ( sp- tq )/(1+ sp 2 + tq 2 ). Equilibrium (again) at sp = tq . g) Stable vs. Unstable equilibrium: An equlibrium is stable if when the system is perturbed it tends to return to where it was previously. An equilibrium is unstable if when the system is perturbed it goes to some other state. For example, in the absence of mutation or migration, p = 0 and p = 1 are stable, because once an allele is lost, the system won't change. Overdominance is a stable equilibrium because if you perturb the allele frequencies away from the equilibrium they will tend to return. Underdominance is an unstable equilibrium because if you perturb the allele frequencies away from the equilibrium they will go to 0 or 1, depending on the direction of the perturbation. We can further distinguish between locally stable and globally stable equilibria. Q: If a population is on a local fitness peak, how might it evolve to get to a higher (or lower) peak? We can depict these situations in terms of a fitness function in which mean fitness is plotted against allele frequency. I will describe various types of fitness functions in which fitness is plotted against something (allele freq, phenotype, genotype, etc.); again, pay attention to context. Lecture 4.1 - Balancing Selection and the Maintenance of Genetic Variation Look around - lots of genetic variation. Why? "Classical" view is that there is a single "wild-type" allele at any locus. Most mutations are deleterious, removed by selection. Occasional beneficial mutation sweeps to fixation. Idea dates back to Morgan. 2 Alternative view, put initially put forth by Dobzhansky, is that balancing selection actively maintains genetic variation. 1. True overdominance- heterozygote is unconditionally advantageous Initial evidence came from chromosomal inversions in Drosophila, but many loci in an inversion, so not clear if any one locus is truly overdominant. - Classical example? Sickle-cell anemia. Cystic Fibrosis? (many common mutations) - Enzyme loci; different alleles may have different kinetics (e.g., optimum temperature), so het has wider "effective zone"....
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This note was uploaded on 03/01/2010 for the course PCB 4683 taught by Professor Williams,j during the Spring '08 term at University of Central Florida.
- Spring '08