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Lecture 10: Introduction to Genetic Drift
September 28, 2012
Announcements
Exam to be returned Monday
Mid-term course evaluation
Class participation
Office hours
Last Time
Transposable Elements
Dominance and types of selection
Why do lethal recessives stick around?
Equilibrium under selection
Stable equilibrium: overdominance
Unstable equilibrium: underdominance
Today
Introduction to genetic drift
First in-class simulation of
population genetics processes
Fisher-Wright model of
genetic drift
How will the frequency of a recessive lethal
allele change through time in an infinite
population?
What will be the equilibrium allele frequency?
What Controls Genetic Diversity Within
Populations?
4 major evolutionary forces
Mutation
Drift
+
-
Diversity
+/Selection
+
Migration
Genetic Drift
 Relaxing another assumption: infinite populations
 Genetic drift is a consequence of having small
populations
 Definition: chance changes in allele frequency that
result from the sampling of gametes from generation to
generation in a finite population
 Assume (for now) Hardy-Weinberg conditions
 Random mating
 No selection, mutation, or gene flow
Drift Simulation
Parent 1
m
m
Parent 2
m
heads
m
 Pick 1 blue and 3 other m&m’s so
that all 4 have different colors
 Form two diploid ‘genotypes’ as
you wish
 Flip a coin to make 2 offspring
tails
 Draw allele from Parent 1: if
‘heads’ get another m&m with the
same color as the left ‘allele’, if
‘tails’ get one with the color of the
right ‘allele’
m
m
m
m
m
m
m
m
m
m
m
m
 ‘Mate’ offspring and repeat for
3 more generations
m
m
m
m
 Report frequency of blue ‘allele’
in last generation
 Draw allele from Parent 2 in the
same way
Genetic Drift
A sampling problem: some alleles lost by random
chance due to sampling "error" during reproduction
Simple Model of Genetic Drift
 Many independent subpopulations
 Subpopulations are of constant size
 Random mating within subpopulations
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Key Points about Genetic Drift
Effects within subpopulations vs effects in
overall population (combining subpopulations)
Average outcome of drift within subpopulations
depends on initial allele frequencies
Drift affects the efficiency of selection
Drift is one of the primary driving forces in
evolution
Effects of Drift
Simulation of 4 subpopulations with 20 individuals, 2 alleles
 Random
changes
through time
 Fixation or loss
of alleles
 Little change
in mean
frequency
 Increased
variance among
subpopulations
How Does Drift Affect the Variance of Allele
Frequencies Within Subpopulations?
Varp 
p (1  p )
2N
Drift Strongest in Small Populations
Effects of Drift
http://www.cas.vanderbilt.edu/bsci111b/drosophila/flies-eyes-phenotypes.jpg
 Buri (1956) followed
change in eye color
allele (bw75)
 Codominant, neutral
 107 populations
 16 flies per
subpopulation
 Followed for 19
generations
Modeling Drift as a Markov Chain
 n  y n y
P(Y  y)   s f ,
 y
 Like the m & m
simulation, but
analytical rather
than empirical
 Simulate large
number of
populations with two
diploid individuals,
p=0.5
 Simulate transition
to next generation
based on binomial
sampling probability
(see text and lab
manual)
Modeled versus
Observed Drift in
Buri’s Flies
Effects of Drift Across Subpopulations
 Frequency of eye color
allele did not change
much
 Variance among
subpopulations
increased markedly
Fixation or Loss of Alleles
 Once an allele is lost
or fixed, the population
does not change (what
are the assumptions?)
 This is called an
“absorbing state”
 Long-term
consequences for
genetic diversity
44
Probability of Fixation of an allele within a
subpopulation Depends upon Initial Allele Frequency
u(q)  q0
q0=0.5
N=20
where u(q) is probability of a subpopulation to be fixed for allele A2
N=20
Effects of Drift on Heterozygosity
 Can think of genetic drift as random selection of alleles from a
group of FINITE populations
 Example: One locus and two alleles in a forest of 20 trees
determines color of fruit
 Probability of homozygotes in next generation?
Prior Inbreeding
2
PIBD
1
 1 
 2N 
 
2N
 2N 
1 
1 
f t 1 
 1 
 ft
2N  2N 
Drift and Heterozygosity
 Expressing previous equation in terms of heterozygosity:
1 
1 
f t 1 
 1 
 ft
2N  2N 
H
 Remembering: 1  f 
2 pq
t
1 

H t  1 
 H0
 2N 
1 

1  f t 1  1 
1  f t
 2N 
p and q are stable across
subpopulations, so 2pq
cancels
 Heterozygosity declines over time in subpopulations
 Change is inversely proportional to population size
Diffusion Approximation
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
Time for a New Mutant to Become Fixed
4 N (1  p) ln( 1  p)
T ( p)  
p
 Assume new mutant occurs at frequency of 1/2N
 ln(1-p) ≈ -p for small p
 1-p ≈ 1 for small p
T ( p)  4 N
 Expected time to fixation for a new mutant is 4
times the population size!
Effects of Drift
 Within subpopulations
 Changes allele frequencies
 Degrades diversity
 Reduces variance of allele frequencies (makes frequencies more
unequal)
 Does not cause deviations from HWE
 Among subpopulations (if there are many)
 Does NOT change allele frequencies
 Does NOT degrade diversity
 Increases variance in allele frequencies
 Causes a deficiency of heterozygotes compared to HardyWeinberg expectations (if the existence of subpopulations is
ignored = Wahlund Effect)