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

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

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

4. 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)

5. 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

6. 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

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

8. 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

9. 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?

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

11. 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

12. 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

13. 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!

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

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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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