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

Transcription

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

2 Last Time Interactions of drift and selection Effective population size

3 Today Effective population size calculations Historical importance of drift: shifting balance or noise? Population structure

4 Factors Reducing Effective Population Size Unequal number of breeding males and females Unequal reproductive success Changes in population size through time Bottlenecks Founder Effects

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

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

7 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 N e 1 N = = 1 t t 1 N i 1 N + 1 N + 1 N e N t 1 See Hedrick (2011) page 219 for derivation

8 Example: Effect of Varying Population Size Through Time: Golden Lion Tamarins (Leontopithecus rosalia) Native to coastal Brazilian Rainforests Estimated Population Censuses: : 10, : : 2,000 What is current effective population size? Ne = t 1 N i

9 Genetic Implications of Bottlenecks and Founder Effects Effective population size is drastically reduced Effect persists for a very long time Reduced allelic diversity 4N (1 q)ln(1 q) T( q) = e T(p)! 4N q e Reduced heterozygosity For small q H t = 1 t ( 1 ) H 2N e 0

10 Populations Resulting 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 Also causes enhanced genetic distance from source population Calculated using Bottleneck program (Cornuet and Luikart 1996)

11 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) Controversy raged until advent of molecular markers showed diversity was quite high Neutral theory revived controversy almost immediately

12 Genotype Space and Fitness Surfaces All combinations of alleles at a locus is genotype space Each combination has an associated fitness A 1 A 2 A 3 A 4 A 5 A 1 A 1 A 1 A 1 A 2 A 1 A 3 A 1 A 4 A 1 A 5 A 2 A 1 A 2 A 2 A 2 A 2 A 3 A 2 A 4 A 2 A 5 A 3 A 1 A 3 A 2 A 3 A 3 A 3 A 3 A 4 A 3 A 5 A 4 A 1 A 4 A 2 A 4 A 3 A 4 A 4 A 4 A 4 A 5 A 5 A 1 A 5 A 2 A 5 A 3 A 5 A 4 A 5 A 5 A 5

13 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

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

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

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

17 Can the shifting balance theory apply to real species? How can you have demes with a widespread, abundant species?

18 What Controls Genetic Diversity Within Populations? 4 major evolutionary forces Mutation + - Drift +/- Diversity + Selection Migration

19 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

20 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, twoallele locuus Random mating within neighborhood Run for 200 generations

21 Wahlund Effect H E depends on how you define populations Separate Subpopulations: H E = 2pq = 2(1)(0) = 2(0)(1) = 0 Merged Subpopulations: H E = 2pq = 2(0.5)(0.5) = 0.5 H E ALWAYS exceeds H O when randomlymating, differentiated subpopulations are merged: Wahlund Effect ONLY if merged population is not randomly mating as a whole!

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

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

24 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) S T

25 F-Coefficients and Deviations from Expected Heterozygosity Recall the fixation index from inbreeding lectures and lab: F Rearranging: H O = =1 H H O E H ( 1 F ) E IS Within a subpopulation: H I = H S ( 1 FIS ) F IS : deviation from H-W proportions in subpopulation

26 F-Coefficients and Deviations from Expected Heterozygosity H I = H S ( 1 FIS ) F IS : deviation from H-W proportions in subpopulation H S = H T ( 1 FST ) F ST : genetic differention over subpopulations H I = H 1 F T ( IT F IT : deviation from H-W proportions in the total population )

27 F-Coefficients Combine different sources of reduction in expected heterozygosity into one equation: 1 F = (1 F )(1 F IT ST IS ) Overall deviation from H-W expectations Deviation due to subpopulation differentiation Deviation due to inbreeding within populations