Course outline HWE: What happens when Hardy- Weinberg assumptions are met Inheritance: Multiple alleles in a population; Transmission of alleles in a family Unit 1: HWE and Inheritance Evolution: When violations in H-W assumptions cause changes in the genetic composition of a population Population Structure: When violations in H-W assumptions cause changes in the distribution of alleles within/across populations Unit 2: Evolution and Pop. Structure (a.k.a. violations in H-W assumptions)

Course outline Evolution: When violations in H-W assumptions cause changes in the genetic composition of a population Population Structure: When violations in H-W assumptions cause changes in the distribution of alleles within/across populations Unit 2: Evolution and Pop. Structure (a.k.a. violations in H-W assumptions) Wed. 2/4: genetic drift Mon. 2/9: natural selection Wed. 2/11: mutation Mon. 2/16: migration Wed. 2/18: assortative mating Mon. 2/23: inbreeding

Genetic Drift Feb. 4, 2015 HUGEN 2022: Population Genetics J. Shaffer Dept. Human Genetics University of Pittsburgh

Objectives After this lecture you will need to be able to: 1.explain the qualitative effects of genetic drift on a population founder effects bottleneck effects rare disease alleles 2.use Binomial distribution to calculate probabilities of having i alleles in the next generation 3.calculate: effective population size probability of allele going to fixation at some point in the future approximate number of generations until allele fixation

The big picture: Evolution Definition: –change in the genetic composition (allele frequencies) of a population across successive generations Evolution vs. Hardy-Weinberg –the H-W Law tells us that if the assumptions are met, genotype and allele frequencies do NOT change from one generation to the next –for evolution to occur, H-W assumptions must be violated –Which processes drive evolution? mutation natural selection random changes in allele frequency (due to population size) –genetic drift

Hardy-Weinberg assumptions diploid organism sexual reproduction nonoverlapping generations random mating large population size equal allele frequencies in the sexes no migration no mutation no selection

Definition of Drift Random changes in allele frequency by chance in finite populations. Key points: Particularly important for small populations. Due to the random sampling of gametes.

Why does drift happen? Cause: random sampling of alleles “law of large numbers” predicts random sampling of alleles will have a small effect in large populations however… in small populations, random sampling of alleles can greatly affect allele frequencies in the next generation

Why does drift happen? Simple Scenario: Population of N = 4 individuals (8 alleles) 4 A alleles and 4 a alleles P(A) = 0.5P(a) = 0.5 HWE says that in the next generation we will have: P(AA) = p 2 P(Aa) = 2pq P(aa) = q 2 P(AA) = 0.25 P(Aa) = 0.5P(aa) = 0.25

Why does drift happen? Simple Scenario: Population of N = 4 individuals (8 alleles) 4 A alleles and 4 a alleles P(A) = 0.5P(a) = 0.5 HWE says that in the next generation we will have: P(AA) = p 2 P(Aa) = 2pq P(aa) = q 2 P(AA) = 0.25 P(Aa) = 0.5P(aa) = 0.25 P(A) = 0.5 P(a) = 0.5

Why does drift happen? Simple Scenario: Population of N = 4 individuals (8 alleles) 4 A alleles and 4 a alleles P(A) = 0.5P(a) = 0.5 HWE says that in the next generation we will have: P(AA) = p 2 P(Aa) = 2pq P(aa) = q 2 P(AA) = 0.25 P(Aa) = 0.5P(aa) = 0.25 P(A) = 0.5 P(a) = 0.5 Will that really happen? What about allele frequencies in the third generation?

Why does drift happen? generation 0 A A A A a a a a each allele uniquely labeled P(A) = 0.5

Why does drift happen? generation 0 A A A A a a a a each allele uniquely labeled random sampling (with replacement) used my TI-83 calculator to randomly pick alleles 1-8 P(A) = 0.5

Why does drift happen? generation 0 A A A A a a a a generation 1 A A A a A A a a each allele uniquely labeled random sampling (with replacement) used my TI-83 calculator to randomly pick alleles 1-8 P(A) = 0.5 P(A) = 0.625

Why does drift happen? generation 0 A A A A a a a a generation 1 A A A a A A a a generation 2 a A A A A A A a each allele uniquely labeled random sampling (with replacement) used my TI-83 calculator to randomly pick alleles P(A) = 0.5 P(A) = P(A) = 0.75

Why does drift happen? generation 0 A A A A a a a a generation 1 A A A a A A a a generation 2 a A A A A A A a generation 3 A a a A A A a A each allele uniquely labeled random sampling (with replacement) used my TI-83 calculator to randomly pick alleles P(A) = 0.5 P(A) = P(A) = P(A) = 0.625

Wright-Fisher model assumes two alleles: P(A)=pP(a)=q assumes non-overlapping generations Binomial Distribution: probability of exactly i A alleles in the next generation whereN = population size x! = x (x-1) (x-2) ….. 1 0! =1 (2N)! (2N – i)! i! = p i q 2N-i

Wright-Fisher model assumes two alleles: P(A)=pP(a)=q assumes non-overlapping generations Binomial Distribution: probability of exactly i A alleles in the next generation whereN = population size x! = x (x-1) (x-2) ….. 1 0! =1 (2N)! (2N – i)! i! = p i q 2N-i NOTE: formula is for the A allele, with P(A)=p

Example: Two-Allele Model for Drift Start with 2N = 8, 4A and 4a alleles ~27% chance that the allele frequency stays the same 8! 4! 4! P (i A alleles in next generation ) What is the probability that the next generation has exactly i = 4 A alleles? P (4 A alleles in next generation ) = p = 0.5 q = (2N)! (2N – i)! i! = p i q 2N-i ~73% chance that the allele frequency changes! (in one generation) Example =

What happens in long term? generation 0 A A A A a a a a generation 1 A A A a A A a a generation 2 a A A A A A A a generation 3 A a a A A A a A random sampling (with replacement) P(A) = 0.5 P(A) = P(A) = P(A) = 0.625

What happens in long term? generation 0 A A A A a a a a generation 1 A A A a A A a a generation 2 a A A A A A A a generation 3 A a a A A A a A random sampling (with replacement) P(A) = 0.5 P(A) = P(A) = P(A) = A a 4 6 some alleles are lost

What happens in long term? generation 0 A A A A a a a a generation 1 A A A a A A a a generation 2 a A A A A A A a generation 3 A a a A A A a A random sampling (with replacement) P(A) = 0.5 P(A) = P(A) = P(A) = A a 4 6 some alleles are lost A a 3 5

What happens in long term? generation 0 A A A A a a a a generation 1 A A A a A A a a generation 2 a A A A A A A a generation 3 A a a A A A a A random sampling (with replacement) P(A) = 0.5 P(A) = P(A) = P(A) = A a 4 6 some alleles are lost A a 3 5 (none lost this gen.)

What happens in long term? generation 3 A a a A A A a A P(A) = some alleles are lost (none lost this gen.)

What happens in long term? generation 3 A a a A A A a A P(A) = generation 4 a a A A A A A A P(A) = 0.75 some alleles are lost (none lost this gen.) A 2

What happens in long term? generation 3 A a a A A A a A P(A) = generation 4 a a A A A A A A P(A) = 0.75 some alleles are lost (none lost this gen.) A 2 generation 5 A A A a A A A A P(A) = a 8

What happens in long term? generation 3 A a a A A A a A P(A) = generation 4 a a A A A A A A P(A) = 0.75 some alleles are lost (none lost this gen.) A 2 generation 5 A A A a A A A A P(A) = a 8 generation 6 A A A A P(A) = 1.0 a 7

What happens in long term? generation 6 A A A A P(A) = 1.0

What happens in long term? generation 6 A A A A P(A) = 1.0 generation 7 A A A A P(A) = 1.0 allele fixation

What happens in long term? generation 6 A A A A P(A) = 1.0 generation 7 A A A A P(A) = 1.0 generation t A A A A P(A) = 1.0 allele fixation note: allele fixation is because they are all A alleles;

Genetic Drift Simulations If p 0 = 0.5 … What happens when N = 4?(i.e., 2N = 8) N=25? N=100? N=1000? if p 0 is … p 0 = 0.25? p 0 = 0.10? p 0 = 0.01?

Long-term results Eventually (at time < infinity) one allele is fixed. It can be either allele. With 2N = 8, it happens pretty fast, usually. At any given point in time, the probability that A is the allele that will become fixed in the future is the current allele frequency, p t important slide

Long-term results Eventually (at time < infinity) one allele is fixed. It can be either allele. With 2N = 8, it happens pretty fast, usually. At any given point in time, the probability that A is the allele that will become fixed in the future is the current allele frequency, p t Additional comments: if a bunch of separate populations all have the same starting allele frequency, p 0 … given drift, each population goes to fixation. We expect p 0 populations to become fixed for A and q 0 populations to become fixed for a The expected (approximate) time, t, to fixation of A due to drift is: important slide t fixation = -4N e (1-p 0 )ln(1-p 0 ) p 0 where N e is the effective population size A lot of variation around this estimate

Effective Population Size How do you think this would affect our assumptions/calculations? Example: Population of 1000 people, but only 1 male Solution: Effective population size N f females and N m males N e = More complicated formulae exist for populations that are changing in size over time. (not covered in this course) N m + N f 4 N m N f

How does drift operate in real human populations? Migration, environmental disasters/epidemics, social factors (religion) Why important for humans? Until recently (last 5000 yrs), most human populations were small - ergo, drift could occur Drift mostly comes into play when the population is genetically isolated. New small isolated populations form recently due to:

How does drift operate in real human populations? Bottleneck Founder Effect Genetic effects on a population started by a small group of individuals Large population is reduced, then re-expands As a result, alleles in the founder group become the alleles in the population Ex. If 100 alleles emigrate to the desert, THAT IS the new population

Founder effect example In a large population, q = for a recessive disease. Call the disease allele “a.” 50 individuals join a religious cult and go off and form an isolated commune. If one of those individuals carries the “a” allele, what’s the allele frequency in the new population? How might this affect the new population going forward?

Why Founder Effects are Important Because the founder effect occurs at every locus, there will be some loci with very different allele frequencies than those in the population from which the founders came. Thought experiment: - Genome consists of 1000 loci with disease alleles. - Disease allele at each locus has frequency q = Choose a new population of 100 alleles at each locus. Results of one random example of choosing this new population: of the 1000 loci of interest: loci: 0 copies of the disease allele in the new population (q = 0) - 95 loci: 1 copy of the disease allele in the new population (q =.01) - 4 loci: 2 copies of the disease allele in the new population (q =.02) - 1 locus: 3 copies of the disease allele in the new population (q =.03) Take home message: Founder effect = new population has decreased risk for many genetic diseases but greatly increased risk for few genetic diseases

What happens after the founder effect? (1)Genetic drift: What happens in the first few generations? (2)Other violations to H-W assumptions: Inbreeding Mutation Natural selection After we found a small population, what happens next? Drift eliminates alleles (randomly) Remove a few founder alleles, but increase others (more on these in upcoming lectures) Overall Result Lots of small populations have genetic variation caused by founder effects and drift. Different populations will have different “common” genetic diseases (especially recessive diseases)

Summary Genetic drift –drift simulations effect of sample size effect of starting allele frequency –allele fixation –founder effect, bottleneck effect, etc. Calculations: –binomial formula –effective population size probability of allele going to fixation at some point in the future approximate number of generations until allele fixation