1. Lecture 9: Introduction to Genetic Drift February 14, 2014

2. Announcements uExam to be returned Monday uMid-term course evaluation uClass participation uOffice hours

3. Last Time uOverdominance and Underdominance uOverview of advanced topics in selection uIntroduction to Genetic Drift

4. Today uFirst in-class simulation of population genetics processes: drift uFisher-Wright model of genetic drift

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

6. Genetic Drift uRelaxing another assumption: infinite populations uGenetic drift is a consequence of having small populations uDefinition: chance changes in allele frequency that result from the sampling of gametes from generation to generation in a finite population uAssume (for now) Hardy-Weinberg conditions  Random mating  No selection, mutation, or gene flow

7. 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

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

9. Simple Model of Genetic Drift uMany independent subpopulations uSubpopulations are of constant size uRandom mating within subpopulations N=16

10. Key Points about Genetic Drift uEffects within subpopulations vs effects in overall population (combining subpopulations) uAverage outcome of drift within subpopulations depends on initial allele frequencies uDrift affects the efficiency of selection uDrift is one of the primary driving forces in evolution

11. Effects of Drift Simulation of 4 subpopulations with 20 individuals, 2 alleles uRandom changes through time uFixation or loss of alleles uLittle change in mean frequency uIncreased variance among subpopulations

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

13. Drift Strongest in Small Populations

14. Effects of Drift uBuri (1956) followed change in eye color allele (bw 75 ) uCodominant, neutral u107 populations u16 flies per subpopulation uFollowed for 19 generations http://www.cas.vanderbilt.edu/bsci111b/drosophila/flies-eyes-phenotypes.jpg

15. Modeling Drift as a Markov Chain uLike the m & m simulation, but analytical rather than empirical uSimulate large number of populations with two diploid individuals, p=0.5 uSimulate transition to next generation based on binomial sampling probability (see text and lab manual)

16. Modeled versus Observed Drift in Buri’s Flies

17. Effects of Drift Across Subpopulations uFrequency of eye color allele did not change much uVariance among subpopulations increased markedly

18. Fixation or Loss of Alleles uOnce an allele is lost or fixed, the population does not change (what are the assumptions?) uThis is called an “absorbing state” uLong-term consequences for genetic diversity 44

19. 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 A 2 N=20 q 0 =0.5 N=20

20. Effects of Drift on Heterozygosity uCan think of genetic drift as random selection of alleles from a group of FINITE populations uExample: One locus and two alleles in a forest of 20 trees determines color of fruit uProbability of homozygotes in next generation? Prior Inbreeding

21. Drift and Heterozygosity uHeterozygosity declines over time in subpopulations uChange is inversely proportional to population size uExpressing previous equation in terms of heterozygosity: uRemembering: p and q are stable through time across subpopulations, so 2pq is the same on both sides of equation: cancels

22. Diffusion Approximation

23. Time for an Allele to Become Fixed uUsing 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: uTime to fixation is linear function of population size and inversely associated with allele frequency

24. Time for a New Mutant to Become Fixed uAssume new mutant occurs at frequency of 1/2N uln(1-p) ≈ -p for small p u1-p ≈ 1 for small p uExpected time to fixation for a new mutant is 4 times the population size!

25. Effects of Drift uWithin subpopulations  Changes allele frequencies  Degrades diversity  Reduces variance of allele frequencies (makes frequencies more unequal)  Does not cause deviations from HWE uAmong 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)