Lecture 12: Effective Population Size and Gene Flow October 2, 2015

Last Time Interactions of drift and selection Effective population size Mid-semester survey

Today Historical importance of drift: shifting balance or noise? Introduction to population structure

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 Sewall Wright Beebe and Rowe 2004 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 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 Isolation by Distance Simulation (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 randomly-mating, differentiated subpopulations are merged: Wahlund Effect ONLY if merged population is not randomly mating as a whole!

Wahlund Effect Hartl and Clark 1997 Trapped mice will always be homozygous even though HE = 0.5

What happens if you remove the cats and the mice begin randomly mating?

F-Coefficients Quantification of the structure of genetic variation in populations: population structure Partition variation to the Total Population (T), Subpopulations (S), and Individuals (I) T S

F-Coefficients and Deviations from Expected Heterozygosity Recall the fixation index from inbreeding lectures and lab: Rearranging: Within a subpopulation: FIS: deviation from H-W proportions in subpopulation

F-Coefficients and Deviations from Expected Heterozygosity HI is essentially observed heterozygosity, HO FIS: deviation from H-W proportions in subpopulation FST: genetic differention over subpopulations FIT: deviation from H-W proportions in the total population

F-Coefficients Combine different sources of reduction in expected heterozygosity into one equation: Overall deviation from H-W expectations Deviation due to subpopulation differentiation Deviation due to inbreeding within populations

F-Coefficients and IBD View F-statistics as probability of Identity by Descent for different samples Probability of IBD within an individual Overall probability of IBD Probability of IBD for 2 alleles in a subpopulation

F-Coefficients T S FIT: Probability of IBD in whole population FST: Probability of IBD within subpopulation (population structure) FIS: Probability of IBD within individuals (inbreeding) T S

F-Statistics Can Measure Departures from Expected Heterozygosity Due to Wahlund Effect where HT is the average expected heterozygosity in the total population HS is the average expected heterozygosity in subpopulations HI is observed heterozygosity within a subpopulation