1. Lecture 10: Introduction to Genetic Drift
September 28, 2012

2. Announcements
Exam to be returned Monday
Mid-term course evaluation
Class participation
Office hours

3. Last Time Transposable Elements Dominance and types of selection
Why do lethal recessives stick around?
Equilibrium under selection
Stable equilibrium: overdominance
Unstable equilibrium: underdominance

4. Today Introduction to genetic drift
First in-class simulation of population genetics processes
Fisher-Wright model of genetic drift

5. What will be the equilibrium allele frequency?
How will the frequency of a recessive lethal allele change through time in an infinite population?
What will be the equilibrium allele frequency?

6. What Controls Genetic Diversity Within Populations?
4 major evolutionary forces
Mutation +
Drift -
Diversity
Selection
+/-
Migration +

7. 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

8. Drift Simulation
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
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 blue ‘allele’ in last generation
Parent 1
Parent 2 m m m m
tails
heads m m m m m m

9. Genetic Drift
A sampling problem: some alleles lost by random chance due to sampling "error" during reproduction

10. Simple Model of Genetic Drift
Many independent subpopulations
Subpopulations are of constant size
Random mating within subpopulations
N=16

11. 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

12. Effects of Drift Random changes through time
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

13. How Does Drift Affect the Variance of Allele Frequencies Within Subpopulations?

14. Drift Strongest in Small Populations

15. Effects of Drift
Buri (1956) followed change in eye color allele (bw75)
Codominant, neutral
107 populations
16 flies per subpopulation
Followed for 19 generations

16. 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)

17. Modeled versus Observed Drift in Buri’s Flies

18. Effects of Drift Across Subpopulations
Frequency of eye color allele did not change much
Variance among subpopulations increased markedly

19. 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

20. where u(q) is probability of a subpopulation to be fixed for allele A2
Probability of Fixation of an allele within a subpopulation Depends upon Initial Allele Frequency
where u(q) is probability of a subpopulation to be fixed for allele A2
q0=0.5
N=20
N=20

21. 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

22. Drift and Heterozygosity
Expressing previous equation in terms of heterozygosity:
Remembering:
p and q are stable across subpopulations, so 2pq cancels
Heterozygosity declines over time in subpopulations
Change is inversely proportional to population size

23. Diffusion Approximation

24. 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:
Time to fixation is linear function of population size and inversely associated with allele frequency

25. 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
Expected time to fixation for a new mutant is 4 times the population size!

26. 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)