Lecture 12: Effective Population Size and
Gene Flow
February 21, 2014
Midterm Survey Results
Not TOOO painful
More in-class problems
Better integration with lab
Improve lab lectures and orientation
Improve lab environment
Mixed results on “active learning” activities
in lecture
Reading and discussing current papers:
next year for grad students
Last Time
Interactions of drift and selection
Effective population size
Today
Effective population size calculations
Historical importance of drift: shifting
balance or noise?
Population structure
Factors Reducing Effective Population Size
Unequal number of breeding males and females
Unequal reproductive success
Changes in population size through time
Bottlenecks
Founder Effects
Effective Population Size: Effects of
Different Numbers of Males and Females
See Hedrick (2011) page
213 for derivation
Table courtesy of K. Ritland
Elephant Seals
 Practice extreme polygyny: one
male has a harem with many
females
 Examined reproductive success
of males using paternity analysis
on Falkland Islands
 Results:
 7 harems with 334 females
 32 mating males detected
 What is Ne?
 What if sneaky males were
unsuccessful?
 Assumptions?
Fabiani et al. 2004: Behavioural
Ecology 6: 961
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
1 1 1
1
1
1 
  

 ...  
N e t  N1 N 2 N 3
Nt 
Ne 
t
1
N
i
See Hedrick (2011) page
219 for derivation
Example: Effect of Varying Population Size Through
Time: Golden Lion Tamarins (Leontopithecus rosalia)
 Native to coastal Brazilian
Rainforests
 Estimated Population Censuses:
http://nationalzoo.si.edu
 1940: 10,000
 1970: 200
 2000: 2,000
 What is current effective
population size?
http://en.wikipedia.org
Ne 
t
1
N
i
How will genetic diversity be affected in
populations that have experienced
bottlenecks and/or founder effects?
Time for an Allele to Become Fixed
 Using the Diffusion Approximation to model drift
 Assume ‘random walk’ of allele frequencies behaves like
directional diffusion: heat through a metal rod
 Yields simple and intuitive equation for predicting time to
fixation:
4 N (1  p) ln(1  p)
T ( p)  
p
 Time to fixation is linear function of population size and
inversely associated with allele frequency
Drift and Heterozygosity
 Expressing previous equation in terms of heterozygosity:
1 
1 
f t 1 
 1 
 ft
2N  2N 
1 

1  f t 1  1 
1  f t
 2N 
H p and q are stable through time
 Remembering: 1  f 
across subpopulations, so 2pq is
2 pq
t
1 

H t  1 
 H0
 2N 
the same on both sides of
equation: cancels
 Heterozygosity declines over time in subpopulations
 Change is inversely proportional to population size
Genetic Implications of Bottlenecks and
Founder Effects
 Effective population size is drastically reduced
 Effect persists for a very long time
 Low-frequency alleles go extinct quickly and take a long time to
become fixed
4 N e (1  q) ln(1  q)
T (q)  
T(q) @ 4Ne
q
For small q
 Reduced heterozygosity
1 t
H t  (1 
) H0
2 Ne
Populations Recovering 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
 Founder effect also causes enhanced genetic distance from
source population
 Calculated using Bottleneck program
(http://www1.montpellier.inra.fr/URLB/bottleneck/bottleneck.html)
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!