lecture 12: effective population size and gene flow
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Last Time Interactions of drift and selection Effective population size Mid-semester surveyTRANSCRIPT
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 variationSelection 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 flowArgued 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 A2 A3 A4 A5
A1A1 A1A2 A1A3 A1A4 A1A5
A1A2 A2A2 A2A3 A2A4 A2A5
A1A3 A2A3 A3A3 A3A4 A3A5
A1A4 A2A4 A3A4 A4A4 A4A5
A1A5 A2A5 A3A5 A4A5 A5A5
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
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
Sewall WrightBeebe and Rowe 2004
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
(from Hamilton 2009 text)
Wahlund Effect
Separate Subpopulations:
HE = 2pq = 2(1)(0) = 2(0)(1) = 0
HE depends on how you define populations
HE ALWAYS exceeds HO when randomly-mating, differentiated subpopulations are
merged: Wahlund Effect
ONLY if merged population is not randomly mating as a whole!
Merged Subpopulations:
HE = 2pq = 2(0.5)(0.5) = 0.5
Wahlund Effect
Trapped mice will always be homozygous even though HE = 0.5
Hartl and Clark 1997
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)
TS
F-Coefficients and Deviations from Expected Heterozygosity
FIS: deviation from H-W proportions in subpopulation
E
O
HHF 1
Recall the fixation index from inbreeding lectures and lab:
Rearranging:
)1( ISSI FHH Within a subpopulation:
F-Coefficients and Deviations from Expected Heterozygosity
)1( ISSI FHH FIS: deviation from H-W proportions in subpopulation
FST: genetic differention over subpopulations
)1( STTS FHH
FIT: deviation from H-W proportions in the total population
)1( ITTI FHH
HI is essentially observed heterozygosity, HO
F-Coefficients Combine different sources of reduction in expected
heterozygosity into one equation:
)1)(1(1 ISSTIT FFF
Deviation due to subpopulation differentiation
Overall deviation from H-W expectations
Deviation due to inbreeding within populations
F-Coefficients and IBD
View F-statistics as probability of Identity by Descent for different samples
)1)(1(1 ISSTIT FFF
Overall probability of IBD
Probability of IBD for 2 alleles in a subpopulation
Probability of IBD within an individual
F-Coefficients
TS
)1( ISSI FHH )1( STTS FHH )1( ITTI FHH FIT: Probability of IBD in whole population
FST: Probability of IBD within subpopulation (population structure)
FIS: Probability of IBD within individuals (inbreeding)
F-Statistics Can Measure Departures from Expected Heterozygosity Due to Wahlund Effect
S
ISIS H
HHF
T
ITIT H
HHF
T
STST H
HHF
where
HT is the average expected heterozygosity in the total population
HI is observed heterozygosity within a
subpopulation
HS is the average expected heterozygosity in subpopulations