Genetic drift in finite populations HWE assumes that population size is infinite approximately true if population is very large but, very large size unlikely for most species -- environmental patchiness -- social organization evolutionarily relevant population size is not simply the number of individuals Ne = effective population size = number of individualsthat contribute genes to the next generation

Effective population size, Ne affected by: -- sex ratio (breeding system) -- fluctuations in population size -- differences in fecundity due to chance Ne and sex ratio: for breeding individuals only (4N% )(N&) N% + N& Ne = Mating systems where Sex Ratio greatly skewed alter Ne -- dominance hierarchy -- resource polygyny -- leks

Ne and population fluctuations if population size fluctuates frequently, the arithmetic mean is not appropriate hare-lynx cycles Ne = 3Ni 1 n i=1 t humans in Egypt Ne: 100 150 25 150 125 Ne = 110

3 average Ne affected disproportionately by the smallest size --> population bottleneck results in the loss of genetic variation With a fluctuating population use the harmonic mean (geometric average): 1 1 1 Ne t Ni 3 i=1 t = Ne: 100 150 25 150 125 Ne ~ 70 population fluctuations characterize irruptive species -- forest insects (e.g., gypsy moth) -- seed-eating finches -- voles – hare – lynx -- coniferous trees

if Ne is small, what are the genetic consequences?? -- neutral alleles -- interaction of selection and small population size

genetic drift is sampling effect “true frequency distn” vs. “sample frequency distn” take finite samples from an infinite population ---> most will deviate slightly from the actual distribution (frequency of A1, A2) if you have a large number of samples, the average frequency over all samples will better approximate the true distribution than any single sample ~infinite number of gametes ---> finite number of adults (population) (sample)

“true” mean = 0.35 X = 0.361 + 0.105 X = 0.345 + 0.032

Random walk of allele frequency in one dimension - direction of change is random in each generation - amount of change is determined by Ne (Dq % ) 1 Ne 0 q0 1

2N = 18 2N = 100

What is the probability that an allele is fixed by drift?? If {A1, A2, A3, A4, ……, An} alleles in a population N individuals, 2N alleles -- one is fixed, others lost If each allele is unique, pr(Ai) is fixed = 1/2N (2N possible outcomes, pr(particular) = 1/2N) With x copies of an allele in the population, pr(fixation) = x/2N *common alleles are more likely to be fixed

Ht+1 = (1 - )Ht how does drift affect heterozygosity?? because alleles are fixed or lost, heterozygosity and within popn genetic variance declines What is the chance that two identical alleles from an individual unite to form a zygote? 1/2N When they do heterozygosity is lost. What is the chance that they do not unite? 1- 1/2N Ht+1 = (1 - )Ht 1 2Ne

how does drift affect heterozygosity?? because alleles are fixed or lost, heterozygosity and within popn genetic s2 decline After t generations Ht = (1 - )tH0 if 2N is large, 1/2N ~ 0, and (1 - ) ~ 1, Ht ~ H0 if 2N is small, 1/2N ~ ‘ ‘, and (1 - ) ~ 0, Ht ~ 0 1 2N 1 2N 1 2N very large

drift decreases within population genetic variance drift changes allele frequencies within a population in a random fashion drift decreases within population genetic variance net change in mean allele frequency (across all popns) due to drift is 0 drift increases among population genetic variance A2A2 A1A1 A1A2 A2A2 A1A1 A1A1 A1A2 A2A2 A1A1 A1A1 A1A2 A2A2 A1A1 A1A2 A2A2 A2A2 A2A2 A1A1 A1A2 A2A2 A1A1 A1A2 A2A2 A1A1

Drift in real populations Buri Drosophila melanogaster alleles at brown eye color locus; bw, bw75 are neutral to each other initially f(bw) = f(bw75) = 0.5 107 replicate lines, Ne = 16 (8%, 8&), each generation randomly chose 16 new individuals what happens to genetic variation???

Buri’s results by generation 19, 30 popns fix bw; 28 popns fix bw75 which allele fixed is random decrease in within popn variance (58/107 fixed for one allele) increase in among population genetic variance (s2: 0 ---> 0.16)

Genetic drift and selection Drift fixes alleles (at random) when Ne is small Directional selection fixes the favored allele When does drift overcome selection (or vice versa)??

interaction of drift and directional selection AA Aa aa initial f(A) = 0.5 wij 0.4 1 1 N=50 N=10

interaction of drift and directional selection AA Aa aa initial f(A) = 0.5 wij 0.8 1 1 N=10

interaction of drift and selection AA Aa aa initial f(A) = 0.5 wij 0.8 1 0.9 N=50

Genetic drift and selection Drift fixes alleles (at random) when Ne is small Directional selection fixes the favored allele When does drift overcome selection (+ vice versa)?? s = strength of selection = strength of genetic drift if s >> 1/4Ne, selection determines outcome if s << 1/4Ne, drift can overcome selection 1 4Ne

s = 0.01 Ne = 10 1/4Ne = 0.025 25 0.01 100 0.0025 250 0.001

Drift and Selection, con’t Population may not attain equilibrium allele frequencies predicted by selection coefficients Deleterious alleles can be fixed by drift if selection is relatively weak Slightly advantageous alleles are less likely to be fixed in small populations Implications for conservation biology: - habitat fragmentation ---> small population size - loss of heterozygosity - fixation of deleterious alleles ---> “mutational meltdown”

Founder Event Genetic drift occurs when a new population is started by a small number of individuals Usually, loss of rare or uncommon alleles (i.e., reduced polymorphism, within popn genetic s2)

Founder event Genetic drift occurs when a new population is started by a small number of individuals Usually, loss of rare or uncommon alleles (i.e., reduced polymorphism, within popn genetic s2) Loss of variation may differentially affect social organisms

Ne, the effective population size, can be affected by mating system, temporal fluctuations in population size, or differences in fecundity due to chance Genetic drift is sampling error Drift occurs in all finite populations, but its relative importance is determined by population size Genetic drift reduces genetic variation within a population by random fixation of alleles, but increases genetic variance among populations Directional selection in small populations is often less effective; deleterious alleles may occur at higher frequency and may become fixed

Genome-wide effects of drift may result in a high genetic load of deleterious alleles and consequent effect on individual and population survival (“mutational meltdown”) Founder events can produce new populations with radically different patterns of genetic variation compared to their source - loss of alleles, especially rare alleles - changes in allele frequency - changes in genetic variance depend on subsequent rates of growth