Lecture 6 Genetic drift & Mutation Sonja Kujala

Allele frequency: relative frequency of an allele on a genetic locus in a population allele frequencies change through time 2 main factors causing the change: natural selectiongenetic drift A A A A A A A a a a a a a a a a a a 2N=18

1) Mendel’s law of segregation: when a parent produces a gamete, each of its two homologous alleles are equally likely to to appear in the gamete Two main sources of RANDOMness in natural populations: 2) Demographic stochasticity: different individuals have different numbers of offspring for complex reasons other than genetics A/a A a 50%

Genetic drift RANDOM change of allele frequencies in populations of finite size generation t generation t +1 2N = 18 freq ( ) = 7/18 2N = 18 freq ( ) = 4/18 A A A A A A A a a a a a a a a a a a A A A A A A a a a a a a a a a a a a a a

Genetic drift process continues over many generations can produce large changes in allele frequencies One of the most important principles of evolutionary theory: ”many small changes may result in large evolutionary changes over sufficiently long periods of time”

Genetic drift initially 107 populations each of size 16 (8males, 8 females) each individual heterozygous for bw75/bw (brown eyes) 19 generations of random mating within populations most lineages fixed for one of the two alleles

Wright-Fisher model most common model for describing genetic drift allows to characterize the changes in allele frequencies mathematically assumes haploid population, however approximates very well a diploid population with two sexes Genetic drift Sewall Wright Ronald Fisher

Genetic drift Wright-Fisher model assumptions: discrete & non-overlapping generations constant population size random mating (=panmixia=no population structure) 2N haploid individuals = N diploid individuals gene copies are transmitted from generation t to the next generation (t+1) by random sampling (independently and with equal probability) all individuals equally fit no recurrent mutation no recombination

Simulations Genetic drift initial frequency p=0.39 2N=18 50 generations 10 replications A

DRIFT IS ”BLIND” (vs. selection) equally likely to ”favor” either allele neutral weak selection strong selection 2N=5000 Genetic drift

In some replicates allele frequency goes to zero or one = LOSS or FIXATION drift removes genetic variation from populations A fixed lost 2N=18

Genetic drift

the above argument is about average over replications (in each individual replicate, the allele frequency has likely changed) 2N=5000

Genetic drift mean of allele frequencies over replicates stays the same variance of allele frequencies over replicates grows

Genetic drift Probability transition matrix expected allele frequency in individual population In a population with 2N gene copies, in generation t there are j copies of allele A and 2N - j copies of allele a. What is the probability that in the next generation there will be exactly i copies of allele A?

= A probability transition matrix for a population of size 2N=4: Genetic drift

How fast can drift change allele frequencies? depends on the population size initial frequency p= generations 20 replications 2N=10 2N=100 EVENTUALLY THE ALLELE FREQUENCY WILL REACH EITHER ZERO OR ONE

Genetic drift What is the probability of allele frequency change from 0.50 to 0.33? in a population of 10 individuals: 0.34 in a population of 1000 individuals: 2 x Large changes in allele frequency in large populations are unlikely More likely in small populations, i.e. genetic drift works FASTER in small populations

Genetic drift

Drift removes variation Why are populations not monomorphic? What factors create/bring polymorphism into populations? MutationMigration

the only evolutionary factor that creates NEW variation Mutation point mutation (SNP) insertion, deletion (indel) inversion translocation beneficial deleteriousneutral

USUALLY can use di-allelic model: absense of mutation vs. presence of mutation A vs a nucleotide G versus nucleotide A Mutation

Different population genetic models of mutation for different types of data ISM infinite sites model IAM infinite alleles model SMM stepwise mutation model

Mutation Infinite sites model for DNA sequence data each new mutation creates a new variable site assuming that the sequence is infinitely long chance that two mutations hit the same site is essentially zero segregating sites = polymorphic sites = single nucleotide polymorphisms (SNPs)

Mutation Infinite alleles model for data categorized in terms of different allelic types i.e. is the DNA different or identical between different gene copies? (not interested how the allelic types are related to each other) each mutation produces a new allele e.g. protein electrophoresis:

Mutation Stepwise mutation model e.g. for microsatellite data assumes that mutation only occurs to adjacent states mutation may produce alleles that are already present in the population

Mutation Allele frequency change caused by mutation only? (no drift, no selection) if mutation would occur only from a to A expected frequency of A in generation t+1: = frequency of A in generation t = frequency of a in generation t (=1-p t ) = probability that a mutates to A (per generation) = MUTATION RATE

Mutation BUT mutation can act in both ways from a to A ( ) and from A to a ( ) = BACKMUTATION

Mutation Equilibrium frequency is eventually reached when rearranging to (see next slide)

Mutation

equilibrium frequency, examples Mutation

mutation rates are highly variable among species also vary across the genome typical mutation rate for point mutations in higher organisms on the order of to Baer et al Nature Reviews Genetics Hodgkinson & Eyre-Walker 2011 Nature Reviews Genetics

mutation alone is very weak force for changing allele frequencies in higher organisms mutations occurring multiple times at the same site can be safely ignored most times Mutation

fate of a single mutation? aa Aa aa

Mutation if Aa produces ONE offspring, what is the probability that it inherits allele a? (see slide 4) = probability of loss of a new allele if Aa produces ONE offspring that inherits allele A allele frequency of A is still very low after one generation

Mutation in general, the probability of loss in one generation in a family of size k is 0.5 k total probability of loss in one generation is e -1 = 0.368

Mutation & Drift Initial freq of new mutation = 1/2N Probability of fixation = 1/2N Probability of loss of the new mutant = 1-1/2N aa Aa aa

Mutation & Drift unless a population is very small, new mutations will nearly always be lost.

fixation and loss of a new mutant involve very different amounts of time expected time to fixation expected time to loss Mutation & Drift

1) Play with redlynx! 2) Watch this video and take the quiz! m/sites/ /student_vie w0/chapter20/simulation_of_ge netic_drift.html 3) define (more verbally than in these slides) the terms: mutation model, mutation rate, equilibrium frequency Homework: