Lecture 6: Finite Populations, Drift PDF

Biology 206: Evolutionary Genetics Lecture 6 Finite Populations, Drift Readings: E&Z Ch.6 –6.4, 6.5  H-W Assumptions: 1) There is no selection (all individuals have equal probabilities of survival and reproduction) 2) There is no mutation (genes do not c...

Biology 206: Evolutionary Genetics Lecture 6 Finite Populations, Drift Readings: E&Z Ch.6 –6.4, 6.5  H-W Assumptions: 1) There is no selection (all individuals have equal probabilities of survival and reproduction) 2) There is no mutation (genes do not change from one allelic state to another) 3) There is no migration (genes are not added from outside the population) 4) There are no chance events (population is infinitely large) 5) There is random mating  Chance events (finite population) Gene pool with frequency of A (p) = 0.6; a (q) = 0.4 Randomly pair egg and sperm to make zygotes. If population is finite in size, will not get allele frequencies in their exact proportions Small  Genetic drift results from random sampling E&Z Fig 6.5 Sampling error is higher with smaller sample Sampling error is purely random Genetic drift = during mating, alleles are “sampled” to form progeny  Population bottlenecks causes genetic drift narrowing then pop rebounce A genetic bottleneck results in a non-representative set of alleles for subsequent populations, even after the population size rebounds E&Z Fig 6.8 E.g.: Northern elephant seals slaughtered by hunters in 1980’s. Population decimated. Researchers sequenced mitochondrial DNA and found almost no genetic variation (only 2 polymorphic sites in a section of mitochondria that is usually highly variable). Estimated the population dwindled to ~30 animals, before rebounding (now at ~124,000) Sencice population size not meaningfull if its alwaysbeenthat size  Founder effect causes genetic drift E&Z Fig 6.10 The founder effect is a type of genetic bottleneck resulting from a small number of individuals colonizing a new, isolated habitat. Allele frequencies among colonists not representative of source population  Founder effect causes a change in allele frequencies, with long-lasting effects dominant disorder E.g.: porphyria variegate: inherited error in haem synthesis (vampire disease?) common among white S. Africans of Afrikaaner descent (1/250). rare in rest of world, incl. Europe and surrounding Africa (1/100,000). Dutch Afrikaaners arrived in S. Africa in 1652 as colonial settlers. In 1688, Holland sent a ship of women “for marriage”. 50% of current population have 20 names traceable to the early ships. Founder mutation for PV happened to be among these settlers >8000 cases of PV traceable to one married couple (Gerrit Jansz & Ariaantje Jacobs) See also Z&E pp 190-191 for another interesting example (Pitcairn/Norfolk Islands: Mutiny on the Bounty)  How does population size affect genetic drift? likely to pilose react grab A. Large populations will experience more drift experted B. Small populations will experience more drift C. Drift will be the same in small and large populations because it is a random process D. I have no idea  Genetic drift causes evolution (defined as a change in allele frequencies) https://keholsinger.shinyapps.io/Genetic-Drift/  bigger jumps bigger randomness Smo 9 Allele frequency performs a pop "random walk” (ie. it drifts) Alleles are lost more rapidly in small populations The changes are less predictable in small populations E&Z Fig 6.6 likely hood of loosing allele Is based on its frequency  Rare alleles are more likely to be lost in a population bottleneck Probability of loss of allele in a bottleneck E&Z Fig 6.7 (one round of sampling): ample 6 !!"## = 1 − ! $% Drift over time: The probability of eventual fixation of an allele affected only by drift = p (its allele frequency) Note that with two alleles we can interchangeably talk about loss of one allele, or fixation of the other allele: p+q=1 q=1-p  Properties of genetic drift The direction of change in allele frequency can not be predicted. results in loss of genetic variation genetic drift One allele will eventually be fixed, the other eliminated: genetic drift tends to remove genetic variation (because if a population only has one allele it is not variable). The probability that a particular allele will eventually be fixed (or lost) is proportional to its frequency in the population  Let’s go back to Hardy-Weinberg frequencies Allele frequencies sum to 1, and genotype frequencies sum to 1 For every set of allele frequencies, there is a set of expected genotype frequencies p=0.1, q=0.9 AA Aa aa p2 2pq q2 0.01 0.18 0.81  Let’s go back to Hardy-Weinberg frequencies Allele frequencies sum to 1, and genotype frequencies sum to 1 For every set of allele frequencies, there is a set of expected genotype frequencies p=0.7, q=0.3 AA Aa aa p2 2pq q2 0.49 0.42 0.09  Using heterozygosity to measure genetic variation For every set of allele frequencies, there is a set of expected genotype frequencies Notes: Rare alleles are primarily found in heterozygotes (when q is very small, q2 is even smaller) When a mutation arises, it is rare, and almost always in the heterozygous form He = 2pq = “expected heterozygosity” 29 9 1 The amount of heterozygosity is 5 maximized when the allele frequencies are intermediate 2pq has a maximum value of 0.5 0.5 when p = q = 0.5 1ft tends removes allele  Do we find HWE in nature? Won’t there always be some drift, mutation, migration, selection, or non-random mating? It is actually a very robust and useful expression One generation of random mating returns you to HWE, and mating is mostly random with respect to genotype at most loci in the genome  Do we find HWE in nature? Human genome project: 10,000 SNPS from European and African populations For every SNP, plot the allele frequency against the frequency of the 3 genotypes. Each SNP is represented by 3 different coloured points for the three genotypes. The solid lines show the mean genotype frequency calculated using a regression. The dashed line shows the predicted genotype frequency from Hardy Weinberg equilibrium. Using heterozygosity to measure genetic variation For a locus with two alleles, the expected heterozygosity (HE) is 2pq. It has a maximum value of 0.5 when p=q=0.5 The amount of heterozygosity is maximized when the allele frequencies are intermediate. Aa (2pq) He  For simplicity, we will start all alleles at a frequency of 0.5 The line represents the history of allele Frequency of A allele frequency change in one population. With small populations you can see that the allele frequency tends to go towards 0 (lost) or 1 (fixed). What does this mean for Heterozygosity?  How does heterozygosity change in response to drift? A. As allele frequency goes to 1 (or 0), heterozygosity will increase B. As allele frequency goes to 1 (or 0), heterozygosity will decrease p2 2 2Pa C. Heterozygosity will be lowest at the start of the simulation when p=0.5 D. Heterozygosity will not change during the simulation, because p+q=1  For simplicity, we will start all alleles at a frequency of 0.5 The line represents the history of allele Frequency of A allele frequency change in one population. With small populations you can see that the allele frequency tends to go towards 0 (lost) or 1 (fixed). What does this mean for Heterozygosity? What is the value of heterozygosity when p=0.5? What is the value of heterozygosity when p=0.75? What is the value of heterozygosity when p=1?  Average heterozygosity Frequency of A allele even in large pop it will decline drift removes variation  Similar figure Demonstration of genetic drift in D. melanogaster E&Z Fig 6.4 Experiment by Buri in 1965 107 populations (ea. 8M + 8F) eye colour (bw75/bw) starting frea 0.5 choose 16 flies start: p=q every gen to start the next Maintained at N= 16 for 19 gen @ gen 19: bw75 lost in 30 pops, fixed in 28  Similar figure Demonstration of genetic drift in D. melanogaster E&Z Fig 6.4 Experiment by Buri in 1965 107 populations (ea. 8M + 8F) eye colour (bw75/bw) start: p=q Maintained at N= 16 for 19 gen @ gen 19: bw75 lost in 30 pops, fixed in 28  Similar figure Demonstration of genetic drift in D. melanogaster E&Z Fig 6.4 Experiment by Buri in 1965 107 populations (ea. 8M + 8F) eye colour (bw75/bw) start: p=q Maintained at N= 16 for 19 gen @ gen 19: bw75 lost in 30 pops, fixed in 28 2pq 30pop lost redeye allele  Drift reduces genetic diversity The reduction in heterozygosity over time is closely related to the size of the population: Average heterozygosity depends on sample size  Main features of genetic drift A loss of genetic variation results within populations (because one allele will eventually be lost or fixed) Genetic divergence results between populations (populations become more different by chance) Drift causes evolution (i.e., allele frequencies change), but not adaptive evolution  Key points 1. Genetic drift involves generation-to-generation fluctuations of allele frequencies in finite populations 2. Drift reduces genetic variation and heterozygosity (alleles are lost) 3. Reduction in genetic variation (and heterozygosity) happens more rapidly in small populations. 4. Rare alleles are more likely to be lost, common alleles are more likely to be fixed 5. Drift causes isolated populations to become different from each other, because by chance different alleles fixed/lost.