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Lecture 12: Effective Population Size and Gene Flow February 21, 2014 Midterm Survey Results Not TOOO painful More in-class problems Better integration with lab Improve lab lectures and orientation Improve lab environment Mixed results on “active learning” activities in lecture Reading and discussing current papers: next year for grad students Last Time Interactions of drift and selection Effective population size Today Effective population size calculations Historical importance of drift: shifting balance or noise? Population structure Factors Reducing Effective Population Size Unequal number of breeding males and females Unequal reproductive success Changes in population size through time Bottlenecks Founder Effects Effective Population Size: Effects of Different Numbers of Males and Females See Hedrick (2011) page 213 for derivation Table courtesy of K. Ritland Elephant Seals Practice extreme polygyny: one male has a harem with many females Examined reproductive success of males using paternity analysis on Falkland Islands Results: 7 harems with 334 females 32 mating males detected What is Ne? What if sneaky males were unsuccessful? Assumptions? Fabiani et al. 2004: Behavioural Ecology 6: 961 Variation of population size in different generations Small population size in one generation can cause drastic reduction in diversity for many future generations Effect is approximated by harmonic mean 1 1 1 1 1 1 ... N e t N1 N 2 N 3 Nt Ne t 1 N i See Hedrick (2011) page 219 for derivation Example: Effect of Varying Population Size Through Time: Golden Lion Tamarins (Leontopithecus rosalia) Native to coastal Brazilian Rainforests Estimated Population Censuses: http://nationalzoo.si.edu 1940: 10,000 1970: 200 2000: 2,000 What is current effective population size? http://en.wikipedia.org Ne t 1 N i How will genetic diversity be affected in populations that have experienced bottlenecks and/or founder effects? Time for an Allele to Become Fixed Using the Diffusion Approximation to model drift Assume ‘random walk’ of allele frequencies behaves like directional diffusion: heat through a metal rod Yields simple and intuitive equation for predicting time to fixation: 4 N (1 p) ln(1 p) T ( p) p Time to fixation is linear function of population size and inversely associated with allele frequency Drift and Heterozygosity Expressing previous equation in terms of heterozygosity: 1 1 f t 1 1 ft 2N 2N 1 1 f t 1 1 1 f t 2N H p and q are stable through time Remembering: 1 f across subpopulations, so 2pq is 2 pq t 1 H t 1 H0 2N the same on both sides of equation: cancels Heterozygosity declines over time in subpopulations Change is inversely proportional to population size Genetic Implications of Bottlenecks and Founder Effects Effective population size is drastically reduced Effect persists for a very long time Low-frequency alleles go extinct quickly and take a long time to become fixed 4 N e (1 q) ln(1 q) T (q) T(q) @ 4Ne q For small q Reduced heterozygosity 1 t H t (1 ) H0 2 Ne Populations Recovering from Founder Effects and Bottlenecks Have Elevated Heterozygosity Heterozygosity recovers more quickly following bottleneck/founding event than number of alleles Rare alleles are preferentially lost, but these don’t affect heterozygosity much Bottleneck/founding event yields heterozygosity excess when taking number of alleles into account Founder effect also causes enhanced genetic distance from source population Calculated using Bottleneck program (http://www1.montpellier.inra.fr/URLB/bottleneck/bottleneck.html) Historical View on Drift Fisher Importance of selection in determining variation Selection should quickly homogenize populations (Classical view) Genetic drift is noise that obscures effects of selection Wright Focused more on processes of genetic drift and gene flow Argued that diversity was likely to be quite high (Balance view) Genotype Space and Fitness Surfaces All combinations of alleles at a locus is genotype space Each combination has an associated fitness A1 A2 A3 A4 A5 A1 A1A1 A1A2 A1A3 A1A4 A1A5 A2 A1A2 A2A2 A2A3 A2A4 A2A5 A3 A1A3 A2A3 A3A3 A3A4 A3A5 A4 A1A4 A2A4 A3A4 A4A4 A4A5 A1A5 A2A5 A3A5 A4A5 A5A5 A5 Fisherian View Fisher's fundamental theorem: The rate of change in fitness of a population is proportional to the genetic variation present Ultimate outcome of strong directional selection is no genetic variation Most selection is directional Variation should be minimal in natural populations Wright's Adaptive Landscape Representation of two sets of alleles along X and Y axis Vertical dimension is relative fitness of combined genotype Wright's Shifting Balance Theory Beebe and Rowe 2004 Sewall Wright Genetic drift within 'demes' to allow descent into fitness valleys Mass selection to climb new adaptive peak Interdeme selection allows spread of superior demes across landscape Can the shifting balance theory apply to real species? How can you have demes with a widespread, abundant species? What Controls Genetic Diversity Within Populations? 4 major evolutionary forces Mutation Drift + - Diversity +/Selection + Migration Migration is a homogenizing force Differentiation is inversely proportional to gene flow Use differentiation of the populations to estimate historic gene flow Gene flow important determinant of effective population size Estimation of gene flow important in ecology, evolution, conservation biology, and forensics Isolation by Distance Simulation Random Mating: Neighborhood = 99 x 99 (from Hamilton 2009 text) Isolation by Distance: Neighborhood = 3x3 Each square is a diploid with color determined by codominant, two-allele locuus Random mating within “neighborhood” Run for 200 generations Wahlund Effect HE depends on how you define populations Separate Subpopulations: HE = 2pq = 2(1)(0) = 2(0)(1) = 0 Merged Subpopulations: HE = 2pq = 2(0.5)(0.5) = 0.5 HE ALWAYS exceeds HO when randomlymating, differentiated subpopulations are merged: Wahlund Effect ONLY if merged population is not randomly mating as a whole!