Lecture 9: Introduction to Genetic Drift

February 14, 2014

Announcements

Exam to be returned Monday

Mid-term course evaluation

Class participation

Office hours

Last Time Overdominance and

Underdominance

Overview of advanced topics in selection

Introduction to Genetic Drift

TodayFirst in-class simulation of

population genetics processes: drift

Fisher-Wright model of genetic drift

What Controls Genetic Diversity Within Populations?

4 major evolutionary forces

Diversity

Mutation+

Drift-

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 Pick 1 red 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 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’

Draw allele from Parent 2 in the same way

‘Mate’ offspring and repeat for 3 more generations

Report frequency of red ‘allele’ in last generation

m m

Parent 1

m m

Parent 2

m

m m m m

m m m m

m m m m

m m

heads tails

m

Genetic DriftA 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

N=16 N=16N=16

N=16N=16

N=16 N=16

N=16N=16N=16

N=16N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16N=16N=16 N=16N=16 N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16 N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

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 DriftSimulation 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?

N

ppVar p 2

)1(

Drift Strongest in Small Populations

Effects of Drift

Buri (1956) followed change in eye color allele (bw75)

Codominant, neutral

107 populations

16 flies per subpopulation

Followed for 19 generations

http://www.cas.vanderbilt.edu/bsci111b/drosophila/flies-eyes-phenotypes.jpg

Modeling Drift as a Markov Chain 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)

,)( yny fsy

nyYP

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

0)( qqu where u(q) is probability of a subpopulation to be fixed for allele A2

N=20q0=0.5N=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?

NNNPIBD 2

1

2

12

2

tt f

NNf

2

11

2

11

Prior Inbreeding

Drift and Heterozygosity

Heterozygosity declines over time in subpopulations

Change is inversely proportional to population size

02

11 H

NH

t

t

Expressing previous equation in terms of heterozygosity:

tt fN

f

1

2

111 1

Remembering:

pq

Hf

21

tt fNN

f

2

11

2

11

p and q are stable through time across subpopulations, so 2pq is the same on both sides of equation: cancels

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:

p

ppNpT

)1ln()1(4)(

Time to fixation is linear function of population size and inversely associated with allele frequency

Time for a New Mutant to Become Fixed

Assume new mutant occurs at frequency of 1/2N

ln(1-p) ≈ -p for small p

1-p ≈ 1 for small p

p

ppNpT

)1ln()1(4)(

Expected time to fixation for a new mutant is 4 times the population size!

NpT 4)(

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 Hardy-Weinberg expectations (if the existence of subpopulations is ignored = Wahlund Effect)