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Lecture 7: Introduction to Selection January 31, 2014 Last Time Effects of inbreeding on heterozygosity and genetic diversity Estimating inbreeding coefficients from pedigrees Mixed mating systems Inbreeding equilibrium Introduction to selection Today Inbreeding and selection: inbreeding depression The basic selection model Dominance and selection Relatedness in Natural Populations Number of matings White-toothed shrew inbreeding (Crocidura russula) (Duarte et al. 2003, Evol. 57:638-645) Breeding pairs defend territory Some female offspring disperse away from parents 12 microsatellite loci used to calculate relatedness in population and determine parentage 17% of matings from inbreeding Offspring Heterozygosity How much inbreeding occurs? Relatedness Parental Relatedness What will be the long-term effects of inbreeding on this shrew population? Inbreeding and allele frequency Inbreeding alone does not alter allele frequencies Yet in real populations, frequencies DO change when inbreeding occurs What causes allele frequency change? Natural Selection Non-random and differential reproduction of genotypes Preserve favorable variants Exclude nonfavorable variants Primary driving force behind adaptive evolution of quantitative traits Fitness Very specific meaning in evolutionary biology: Relative competitive ability of a given genotype Usually quantified as the average number of surviving progeny of one genotype compared to a competing genotype, or the relative contribution of one genotype to the next generation Heritable variation is the primary focus Extremely difficult to measure in practice. Often look at fitness components Consider only survival, assume fecundity is equal Inbreeding, Heterozygosity, and Fitness Inbreeding reduces heterozygosity on genome-wide scale Heterozygosity of individual can be index of extent of inbreeding Multilocus Heterozygosity: Proportion of loci for which individual is heterozygous Often shows relationship with fitness Simulated Number of heterozygous loci Deng and Fu 1998 Genetics 148:1333 Observed Correlation Between Heterozygosity and Fitness Reed and Frankham 2003 Cons Biol 17:230 Inbreeding Depression Reduced fitness of inbred individuals compared to outcrossed individuals terrierman.com/inbredthinking.htm notexactlyrocketscience.wordpress.com Negative correlation between fitness and inbreeding coefficient observed in wide variety of organisms Inbreeding depression often more prevalent under stressful conditions Lynch and Walsh 1998 www.myrmecos.net/ wikipedia Mechanisms of Inbreeding Depression Two major hypotheses: Partial Dominance and Overdominance Partial Dominance (really a misnomer) Inbreeding depression is due to exposure of recessive deleterious alleles Overdominance Inherent advantage of heterozygosity Enhanced fitness of heterozygote due to pleiotropy (one gene affects multiple traits): differentiation of allele functions Bypass homeostasis/regulation What about long-term effects on the shrew? Fecundity (measured by number of offspring weaned) was not affected by relatedness between mating pairs or heterozygosity of individuals No evidence of inbreeding depression in this species Why not? How do we quantify the effects of natural selection on allele frequencies over time? Can we predict and model evolution? Relative Fitness of Diploids Consider a population of newborns with variable survival among three genotypes: N A1A1 A1A2 A2A2 100 100 100 Survival 80 56 40 New parameter: ω, relative fitness (assuming equal fecundity of genotypes in this case) Define ω=1 for best performer; others are ratios relative to best performer: N11s N 22 s 80 40 Where N is number of A A offspring surviving after selection in N11 100 N 22 100 11 1 22 0.5 current generation N Ms 80 N Ms 80 And N is the best-performing genotype 100 100 NM NM 11s M 1 1 Average Fitness Use genotype frequencies to calculate weighted fitness for entire population ω A1A1 A1A2 A2A2 1 0.7 0.5 ω = D(ω11) + H(ω12) + R(ω22) ω = (100/300)(1) + (100/300)(0.7) + (100/300)(0.5) = 0.733 When fitness varies among genotypes, average fitness of the population is less than 1 Frequency After Selection D’ = D(ω11)/ω = (0.33)(1)/0.733 = 0.45 H’ = H(ω12)/ω = (0.33)(0.7)/0.733 = 0.32 R’ = R(ω22)/ω = (0.33)(0.5)/0.733 = 0.23 Selection causes increase in more fit genotype and reduction in less fit genotypes Allele Frequency Change: q = (N22 + N12/2)/N = (100 + 100/2)/300 = 0.5 q’ = (40+56/2)/176 = 0.39 Δq = q’ – q = 0.39 – 0.5 = -0.11 Over time, what will happen to p and q in this population? What is Δp in the previous example? Starting from Allele Frequencies A1A1 A1A2 A2A2 freq0 p2 2pq q2 ω ω11 ω12 ω22 freq1 p2 ω11/ω 2pq ω12/ω q2 ω22/ω ω = p2(ω11) + 2pq(ω12) + q2(ω22) q’ = q2ω22+pqω12 ω Change in Allele Frequencies due to Selection (i.e., evolution) q2ω22+pqω12 - qω q2ω22+pqω12 - q = q’ - q = ω ω Simplifies to: Δq =pq[q(ω22- ω12) - p(ω11 – ω12)] ω See p. 118 in your text for derivation “The single most important equation in all of population genetics and evolution!” Gillespie 2004, p. 62 Fitness effects of individual alleles Δq =pq[q(ω22 – ω12) - p(ω11- ω12)] ω Effects of substituting one allele for another Conceptually, compare fitness of homozygote to heterozygote Rate of change inversely proportional to mean fitness of population: allele frequencies don’t change much in a fit population! Marginal fitness: the effects of an individual allele on fitness (the average fitness genotypes containing that allele) Incorporating Selection and Dominance Selection Coefficient (s) Measure of the relative fitness of one homozygote compared to another. ω11 = 1 and ω22 = 1-s s ranges 0 to 1 in most cases (more fit allele always A1 by convention) Heterozygous Effect (level of dominance) (h) Measure of the fitness of the heterozygote relative to the selective difference between homozygotes ω12 = 1 - hs Heterozygous Effect A1A1 Relative Fitness (ω) Relative Fitness (hs) ω11 1 h = 0, A1 dominant, A2 recessive h = 1, A2 dominant, A1 recessive 0 < h < 1, incomplete dominance h = 0.5, additivity h < 0, overdominance h > 1, underdominance A1A2 A2A2 ω12 ω22 1-hs 1-s Putting it all together A1A1 Relative Fitness (ω) ω11 Relative Fitness (hs) 1 A1A2 ω12 ω22 1-hs 1-s Δq =pq[q(ω22 – ω12) - p(ω11- ω12)] Reduces to: ω Δq =-pqs[ph + q(1-h)] 1-2pqhs-q2s A2A2 Modes of Selection on Single Loci Directional – One homozygous genotype has the highest fitness Purifying selection AND Darwinian/positive/adaptive selection 1 0.8 ω 0.6 0.4 0.2 0 Depends on your perspective! AAA 1A1 aa AAa 1A2 A2A2 AAA 1A1 aa AAa 1A2 A2A2 AAA 1A1 AAa1A2 A2aaA2 0 ≤ h ≤ 1 1 Overdominance – Heterozygous genotype has the highest fitness (balancing selection) 0.8 ω Underdominance – The heterozygous h>1, (1-hs) < (1 – s) < 1 for s > 0 0.4 0.2 0 h<0, 1-hs > 1 genotypes has the lowest fitness (diversifying selection) 0.6 1 0.8 ω 0.6 0.4 0.2 0 Directional Selection Δq =-pqs[ph + q(1-h)] 1-2pqhs-q2s 0 ≤ h ≤ 1 q Δq 0 0.5 q 1 h=0.5, s=0.1 Time Lethal Recessives A1A1 Relative Fitness (ω) ω11 Relative Fitness (hs) 1 A1A2 A2A2 ω12 ω22 1-hs 1-s For completely recessive case, h=0 What is s for lethal alleles? 1 0.8 0.6 ω 0.4 0.2 0 A1 1 1A AAA11A 1 A22 A AAA111A 2 AA22 AAA222A 2