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Populations: Equilibrium and Inbreeding Evolution Biology 4974/5974 D.F. Tomback Biology 4974/5974 Evolution Population genetics: equilibrium and inbreeding Smith & Smith 1998 Ecology and Field Biology, 6th ed., Benjamin Cummings Figures are from M.W. Strickberger (2000) Evolution, 3rd ed., Jones and Bartlett, unless indicated otherwise. Smith& Smith 1998 Learning goals Understand the following: • • • • • • • • How natural selection sorts among individuals but populations are the unit that evolves over time. How to calculate allele frequencies given genotype information. The conditions required for Hardy-Weinberg equilibrium. The implications of equilibrium for evolution. Whether most populations meet H-W conditions. The definitions of inbreeding. How inbreeding violates H-W conditions. How inbreeding affects populations genetically and in fitness. Definitions Population: “….a group of organisms belonging to one species (conspecific) occupying a more or less well-defined geographical region and exhibiting reproductive continuity from generation to generation.” Mendelian population: A group of sexually interbreeding or potentially interbreeding individuals. Deme: Local population, within which individuals are most likely to mate with one another. Gene pool: The sum total of genes represented by a population. It includes all the different kinds of genes in the genome of the species, plus all the different alleles for each gene, at their represented frequencies. Gene frequencies: The proportion of the different alleles of a gene in a population. (Total diploid individuals x 2 = total “slots” for a given gene; total haploid individuals x 1 = total “slots” for a given gene.) 1 Populations: Equilibrium and Inbreeding Evolution Biology 4974/5974 D.F. Tomback Individual vs. population in evolution See p. 365-6 • Variation among individuals comes from multiple genetic sources. • Natural selection is based on the differential survival and reproduction of individuals in relation to prevailing conditions. • Populations respond to selection, with changes in allele frequencies over time. • Other genetic mechanisms change gene frequencies in populations over time, including mutation, gene flow, and genetic drift. • Individuals cannot evolve but populations and species evolve over time. Calculating gene frequencies for diploid populations Two methods: • Based on total gene counts within a gene pool. • Based on genotype frequencies. Example (see right): Gene with two alleles, T and t, T dominant. Possible genotypes: TT Tt tt (T=tasting phenylthiocarbamide) Hardy-Weinberg Equilibrium Genetic definition of evolution: “Genetic changes in populations through time that lead to differences among them.”—Strickberger’s Evolution. “Changes in allele frequencies over time.” –Price (1996) The Hardy-Weinberg equilibrium is the fundamental principle of population genetics (“founding theorem,” p. 376). • In 1908, G.H. Hardy and W. Weinberg independently determined that for a population where mating is random, allele frequencies do not change over time. • If genes are not linked and natural selection, genetic drift, mutation, and gene flow, are not affecting a particular gene locus, then the allele frequencies at that gene will not change. Hardy-Weinberg equilibrium demonstrates which conditions are necessary so gene frequencies do not change--that is, conditions for no evolution at a gene locus. 2 Populations: Equilibrium and Inbreeding Evolution Biology 4974/5974 D.F. Tomback Hardy-Weinberg Equilbrium In sexually-reproducing populations, under conditions of stability, the frequencies of genes remain constant from generation to generation. Stability no evolution “Frequencies of genes” refers to relative proportions of all alleles for any gene. Frequency of T = 0.60 = p Frequency of t = 0.40 = q p + q =1 Thus, under conditions of “stability,” the values for p and q should stay the same generation after generation. No evolution is occurring at this gene if p and q remain the same over time. Hardy-Weinberg Equilbrium Equilibrium genotype using the binomial expansion for a one gene, two allele system: • T = 0.60 = p; t = 0.40 = q • (p + q)2 = p2 + 2pq + q2 = 1 • p2 (TT) + 2pq(Tt) + q2(tt) = 1 • (0.60)2 (TT) + 2(0.60)(0.40) (Tt) + (0.40)2(tt) = 1 • Equilibrium genotype frequencies are: 0.36 TT, 0.48 Tt, 0.16 tt Fig. 18.10 Hardy-Weinberg Equilibrium assumptions For allele frequencies to remain stable from generation to generation, these conditions must be met. These conditions result in “random mating.” Fig. 18.9 3 Populations: Equilibrium and Inbreeding Evolution Biology 4974/5974 D.F. Tomback Conditions for stable gene frequencies from Fig. 18.9 • Parents represent a random sample of gene frequencies in the population. • Genes segregate normally into gametes… • Parents are equally fertile… • The gametes are equally fertile… • The population is very large… • Mating between parents is random…. • Gene frequencies are the same in both male and female parents. • All genotypes have equal reproductive ability. Interpretation of these assumptions • • • • • Population is large enough so chance does not alter gene frequencies. Mutations must not occur, or the rate of forward and back mutations are equal. Allele frequencies are not altered by gene immigration or emigration. Mating is random with respect to that gene. All genotypes have equal survival value; all genotypes leave the same number of offspring. How realistic is each assumption?! What does this tell us? Most populations experience some change in gene frequencies over time at some gene loci. • This varies with the gene locus. • Most populations are evolving at one or more genes. • However, only a relatively small number of genes violate the Hardy-Weinberg Equilibrium conditions—many are neutral, assuming a population is large enough and mutation is rare. • In population genetics, genes are assumed to be in H-W equilibrium. • If not, then natural selection or linkage disequilibrium or another process become the hypotheses for testing. 4 Populations: Equilibrium and Inbreeding Evolution Biology 4974/5974 D.F. Tomback Inbreeding Hardy-Weinberg Equilibrium condition requires that mating be random. If mating is random, the population is panmictic. • But, random mating is the exception and not the rule. • Most populations experience some degree of inbreeding: mating between relatives. • Whether inbreeding occurs and how much depends on dispersal patterns in populations and population size. • If individuals do not move far from where they were born, hatched, or germinated, they have a good chance of encountering relatives when they breed. • Also, the smaller the population, the greater the chance for inbreeding. Inbreeding definition Relatives are defined as individuals who carry genes that are identical by descent--that is, the same allele from a common ancestor. The inbreeding coefficient F expresses the probability that offspring inherit two gene copies that are identical by descent. Here, F = 1/8. Fig. 18.EB2 Relatives and inbreeding A population is inbred if the probability that offspring inherit two gene copies that are identical by descent is greater than would be expected under random mating. The Inbreeding Coefficient F ranges from 0 to 1 in value: • 0 = random mating. No genes identical by descent. • 1.0 = complete inbreeding (e.g., selfing). All genes identical by descent. • When F > 0, the population is inbred. • F also indicates the proportion of heterozygosity reduced each generation by inbreeding relative to a randomly breeding population. 5 Populations: Equilibrium and Inbreeding Evolution Biology 4974/5974 D.F. Tomback Effect on gene vs. genotype frequencies Inbreeding does not change allele frequencies but it does change genotype frequencies. The frequency of homozygotes increases and the frequency of heterozygotes decreases. • Random mating: p2 + 2pq + q2 = 1 • Inbreeding: (p2 + Fpq) + (2pq – 2Fpq) + (q2 + Fpq) = 1 • TT genotype frequency is now p2 + Fpq • Tt genotype frequency is now 2pq - 2Fpq • tt genotype frequency is now q2 + Fpq The allele frequencies p and q remain the same despite continous inbreeding. However, the genotype frequencies shift each generation, depending on the magnitude of F. Inbreeding As inbreeding continues, F increases over time and the frequency of heterozygotes decreases. • The rate of increase of F and rate of loss of heterozygosity is faster the smaller the population. • The closer the relatives mating, the faster the increase in F. Fig. EB18 2.2 Fig. EB18 2.3 The consequences of inbreeding Inbreeding increases the probability that lethal and deleterious recessive alleles are exposed in homozygous genotypes. Heterozygotes are actually considered the most fit for many traits. Case history: Song Sparrows on Mandarte Island, BC. Keller et al. 1994. Selection against inbred Song Sparrows during a natural population bottleneck. Nature 372:356-7. • All birds on Mandarte Island were color-banded and of known pedigree. • Population crash in 1988; only 11% (n = 12) of population survived. • The mean F of the dead birds was 0.0312. • The mean F of the survivors was 0.0065. So what did this study show about the relationship between survival and inbreeding for Song Sparrows on this island? 6 Populations: Equilibrium and Inbreeding Evolution Biology 4974/5974 D.F. Tomback Comparison of survival among Song Sparrows Case history: Greater Prairie Chicken The Greater Prairie Chicken (Tympanuchus cupido) has a lek mating system, where males establish small territories and display to attract females. • The Illinois population has been declining drastically with conversion of prairie to cropland. • Numbers in Illinois dwindled from 25,000 in 1933 to 50 birds in 1994 (Westemeier et al. 1998). Freeman and Herron 2004 Greater Prairie Chicken The remaining birds occurred in two remnant populations in Jasper and Marion County. • Grassland restoration increased the population in the 1960’s and 1970’s, but the population dropped to only 5 or 6 males in the 1990’s. • The few prairie chickens remaining were isolated in small populations within farmland. • These had little or no gene flow. The populations were suffering from genetic drift, inbreeding, and a general loss of heterozygosity. Freeman and Herron 2004 7 Populations: Equilibrium and Inbreeding Evolution Biology 4974/5974 D.F. Tomback Greater Prairie Chicken Loss of genetic variation and inbreeding was reflected in • Declining hatching success • Low allelic variation. Researchers began trapping Greater Prairie Chickens in other states and moving them to Jasper County in the 1990’s. Hatching success improved immediately. WHY? Freeman and Herron 2004 Study questions • Define: gene frequencies, gene pool, evolution from the genetic perspective, and inbreeding. • Calculate gene frequencies based on a) genotype frequencies and b) numerical counts? Try this problem: AA(0.49) + Aa (0.42) + aa(0.09) = 1.0 and 98AA + 84Aa + 18aa = 200 individuals • If a population meets Hardy-Weinberg conditions for a given gene, what happens to allele frequencies over time? • What is the binomial expansion for a one gene, two allele system to determine genotype frequencies? • What are the main assumptions of Hardy-Weinberg Equilibrium? How realistic are they? Study questions, continued • How is F defined as a probability? • What are the effects of inbreeding on gene frequencies vs. genotype frequencies? • What effect does population size have on rate of loss of heterozygosity? • Why is inbreeding generally bad? • What did the study of Song Sparrow survival tell us about the effects of inbreeding? • Why did hatching success improve in the Greater Prairie Chicken after new individuals were introduced into the population? 8