Transcript ppt

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
Beebe and Rowe 2004
Sewall Wright
 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?
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
(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 randomlymating, 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:
HO
F  1
HE
 Rearranging:
HO = H E (1- F)
 Within a subpopulation:
H I  H S (1  FIS )
 FIS: deviation from H-W proportions in subpopulation
F-Coefficients and Deviations from Expected
Heterozygosity
H I  H S (1  FIS )
HI is essentially observed
heterozygosity, HO
 FIS: deviation from H-W proportions in subpopulation
H S  H T (1  FST )
 FST: genetic differention over subpopulations
H I  HT (1  FIT )
 FIT: deviation from H-W proportions in the total population
F-Coefficients
 Combine different sources of reduction in expected
heterozygosity into one equation:
1  FIT  (1  FST )(1  FIS )
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
1  FIT  (1  FST )(1  FIS )
Overall
probability
of IBD
Probability of IBD
for 2 alleles in a
subpopulation
Probability of IBD
within an
individual
F-Coefficients
H I  HT (1  FIT ) F : Probability of IBD in whole population
F : Probability of IBD within subpopulation
H S  H T (1  FST ) (population structure)
: Probability of IBD within individuals
H I  H S (1  FIS ) F(inbreeding)
IT
ST
IS
T
S
F-Statistics Can Measure Departures from Expected
Heterozygosity Due to Wahlund Effect
where
HT  H S
FST 
HT
HT is the average expected
heterozygosity in the total population
HS  HI
FIS 
HS
HS is the average expected
heterozygosity in
subpopulations
HT  H I
FIT 
HT
HI is observed
heterozygosity within a
subpopulation