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

Transcription

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 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 Parent 1 Parent 2 m m m m heads tails m m m m m m m m m m m m m m m 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 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

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

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 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? p( 1 p) Var p = 2N

14 Drift Strongest in Small Populations

15 Effects of Drift Buri (1956) followed change in eye color allele (bw 75 ) Codominant, neutral 107 populations 16 flies per subpopulation Followed for 19 generations

16 Modeling Drift as a Markov Chain P( Y = y) n = s y f y n 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)

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 44 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

20 Probability of Fixation of an allele within a subpopulation Depends upon Initial Allele Frequency u ( q) = q where u(q) is probability of a subpopulation to be fixed for allele A 2 0 q 0 =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? P 1 1 2N = IBD 2N 2 N 2 1 2N 1 2N = t+ 1 t f = Prior Inbreeding + 1 f

22 Drift and Heterozygosity Expressing previous equation in terms of heterozygosity: f = 1 2N N t+ 1 f t 1 + = 1 1 2N 1 f t 1 ( f ) t Remembering: H t 1 f = 1 = 1 H 2N t H 2pq Heterozygosity declines over time in subpopulations Change is inversely proportional to population size 0 p and q are stable across subpopulations, so 2pq cancels

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: T ( p) = 4N(1 p)ln(1 p p) Time to fixation is linear function of population size and inversely associated with allele frequency

25 Time for a New Mutant to Become Fixed T ( p) = 4N(1 p)ln(1 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) 4N Expected time to fixation for a new mutant is 4 times the population size!

26 Within subpopulations Changes allele frequencies Degrades diversity Effects of Drift 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)