Lecture 12: Effective Population Size and Gene Flow October 5, 2012

Last Time uInteractions of drift and selection uEffective population size

Today uEffective population size calculations uHistorical importance of drift: shifting balance or noise? uPopulation structure

Factors Reducing Effective Population Size uUnequal number of breeding males and females uUnequal reproductive success uChanges in population size through time  Bottlenecks  Founder Effects

Table courtesy of K. Ritland Effective Population Size: Effects of Different Numbers of Males and Females See Hedrick (2011) page 213 for derivation

Elephant Seals uPractice extreme polygyny: one male has a harem with many females uExamined reproductive success of males using paternity analysis on Falkland Islands uResults:  7 harems with 334 females  32 mating males detected  What is N e ?  What if sneaky males were unsuccessful?  Assumptions? Fabiani et al. 2004: Behavioural Ecology 6: 961

uSmall population size in one generation can cause drastic reduction in diversity for many future generations uEffect is approximated by harmonic mean Variation of population size in different generations See Hedrick (2011) page 219 for derivation

Example: Effect of Varying Population Size Through Time: Golden Lion Tamarins ( Leontopithecus rosalia) uNative to coastal Brazilian Rainforests uEstimated Population Censuses:  1940: 10,000  1970: 200  2000: 2,000 uWhat is current effective population size?

uEffective population size is drastically reduced uEffect persists for a very long time uReduced allelic diversity uReduced heterozygosity Genetic Implications of Bottlenecks and Founder Effects For small q

Populations Resulting from Founder Effects and Bottlenecks Have Elevated Heterozygosity uHeterozygosity recovers more quickly following bottleneck/founding event than number of alleles uRare alleles are preferentially lost, but these don’t affect heterozygosity much uBottleneck/founding event yields heterozygosity excess when taking number of alleles into account uAlso causes enhanced genetic distance from source population uCalculated using Bottleneck program (Cornuet and Luikart 1996)

Historical View on Drift uFisher  Importance of selection in determining variation  Selection should quickly homogenize populations (Classical view)  Genetic drift is noise that obscures effects of selection uWright  Focused more on processes of genetic drift and gene flow  Argued that diversity was likely to be quite high (Balance view) uControversy raged until advent of molecular markers showed diversity was quite high uNeutral theory revived controversy almost immediately

Genotype Space and Fitness Surfaces uAll combinations of alleles at a locus is genotype space uEach combination has an associated fitness A1A1 A2A2 A3A3 A4A4 A5A5 A1A1 A2A2 A3A3 A4A4 A5A5 A1A1A1A1 A1A2A1A2 A1A3A1A3 A1A4A1A4 A1A5A1A5 A1A2A1A2 A2A2A2A2 A2A3A2A3 A2A4A2A4 A2A5A2A5 A1A3A1A3 A2A3A2A3 A3A3A3A3 A3A4A3A4 A3A5A3A5 A1A4A1A4 A2A4A2A4 A3A4A3A4 A4A4A4A4 A4A5A4A5 A1A5A1A5 A2A5A2A5 A3A5A3A5 A4A5A4A5 A5A5A5A5

Fisherian View uFisher's fundamental theorem: The rate of change in fitness of a population is proportional to the genetic variation present uUltimate outcome of strong directional selection is no genetic variation uMost selection is directional uVariation should be minimal in natural populations

Wright's Shifting Balance Theory uGenetic drift within 'demes' to allow descent into fitness valleys uMass selection to climb new adaptive peak uInterdeme selection allows spread of superior demes across landscape Sewall Wright Beebe and Rowe 2004

Wright's Adaptive Landscape uRepresentation of two sets of genotypes along X and Y axis uVertical dimension is relative fitness of combined genotype

Sewall Wright Beebe and Rowe 2004 Wright's Shifting Balance Theory uGenetic drift within 'demes' to allow descent into fitness valleys uMass selection to climb new adaptive peak uInterdeme 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 Diversity Mutation + Drift - 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: 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 Separate Subpopulations: H E = 2pq = 2(1)(0) = 2(0)(1) = 0 H E depends on how you define populations H E ALWAYS exceeds H O when randomly- mating, differentiated subpopulations are merged: Wahlund Effect ONLY if merged population is not randomly mating as a whole! Merged Subpopulations: H E = 2pq = 2(0.5)(0.5) = 0.5

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

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

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

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

F-Coefficients and Deviations from Expected Heterozygosity  F IS : deviation from H-W proportions in subpopulation  F ST : genetic differention over subpopulations  F IT : deviation from H-W proportions in the total population

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