Genetic Drift and Neutral Theory

Genetic Drift and Neutral Theory Lecture 4

Lecture Outline • Genetic Drift • Effective population size • Founder Effect • The Neutral Theory of Molecular Evolution

Evolution results from chance (unpredictable) and deterministic (predictable) factors • Evolution • Natural Selection • Mutation • Genetic Drift • … Deterministic nonrandom process Random processes Natural selection and genetic drift are the two most important causes of allele substitution in populations

Some evolutionary geneticists hold the opinion that genetic drift should be the “null hypothesis” used to explain an evolutionary observation unless there is positive evidence of natural selection or some other factor Motoo Kimura Sewall Wright

The Theory of Genetic Drift Genetic Drift as Sampling Error The frequency of an allele can change because one or more of its copies happen not to be included in those gametes that unite into zygotes, or may happen not to be carried by the offspring that survive to reproductive age The genes included in any generation, whether in newly formed zygotes or in offspring that survive to reproduce, are a sample of the genes carried by the previous generation. Any sample is subject to random variation or sampling error 50% 46% 50% 54%

The Theory of Genetic Drift Coalescence Looking backwards in time all gene copies in the population ultimately are descended from a single ancestral copy, because given long enough, all other original gene lineages become extinct The genealogy of the genes in the present population is said to coalesce back to a single common ancestor • By chance: • A population will eventually become monomorphic for one allele or the other • The probability that one allele will be fixed, rather than other alleles, equal the initial frequency of that allele The frequency of heterozygotes declines as one of the allele frequencies shift closer to 1

The Theory of Genetic Drift Random Fluctuation in Allele Frequencies Metapopulation 2N Deme p q Neutral alleles time?

The Theory of Genetic Drift Random Fluctuation in Allele Frequencies Metapopulation 2N Deme p q p' pt … Neutral alleles time When the frequency changes from p= ½ to p' in the following generation it will change to some other value p'' either higher or lower with equal probability Since no stabilizing force returns the allele frequency towards ½, p will eventually drift either to 0 or 1: the allele is either lost or fixed

The Theory of Genetic Drift Random Fluctuation in Allele Frequencies What happens to genetic variation at a locus in a deme?

The Theory of Genetic Drift Random Fluctuation in Allele Frequencies The allele frequency describes a random walk, analogous to a New Year’s Eve reveler staggering along a very long train platform with a railroad track on either side: if he is so drunk that he does not compensate steps towards one side with steps towards the other, he will eventually fall off the edge of the platform onto one of the two tracks

The Theory of Genetic Drift Random Fluctuation in Allele Frequencies How does population size affect this process?

The Theory of Genetic Drift Random Fluctuation in Allele Frequencies If an allele has just arisen by mutation what would be its likelihood of reaching fixation?

The Theory of Genetic Drift Random Fluctuation in Allele Frequencies What happens to the allele frequency in the metapopulation?

The Theory of Genetic Drift Random Fluctuation in Allele Frequencies What happens to the frequency of heterozygotes in each deme? and in the metapopulation?

The Theory of Genetic Drift Random Fluctuation in Allele Frequencies Some demes reach p=0 pr p=1 and can no longer change. Among those in which fixation of one or the other allele has not yet occurred, the allele frequencies continue to spread out, with all frequencies between 0 and 1 eventually becoming equally likely p q pt … time Demes that initially are genetically identical evolve by chance to have different genetic constitutions

The Theory of Genetic Drift Random Fluctuation in Allele Frequencies • Small Populations • Larger oscillations • Alleles are more rapidly fixed (7) or lost (5) • Large Populations • Smaller oscillations • Alleles less rapidly fixed (0) or lost (0) The variance in allele frequency among the demes continues to increase from generation to generation

Evolution by Genetic Drift • Allele frequencies fluctuate at random within a population and eventually one or another becomes fixed • Genetic variation at a locus declines and is eventually lost • An allele’s probability of fixation equals its frequency at that time and is not affected by its previous history • Populations with the same initial allele frequency (p) diverge and a proportion p of the population is expected to become fixed for that allele • If an allele has just arisen by mutation its likelihood of reaching fixation is 1/2N: it is more likely to be fixed in a small population than in a large population • In a diploid population, the average time to fixation of a newly arisen neutral allele that does become fix is 4N generations: evolution by genetic drift proceeds faster in small than in large populations • Among a number of initially identical demes in a metapopulation, the average allele frequency does not change but the frequency of heterozygotes declines to 0 in each deme and in the metapopulation as a whole

Evolution by Genetic Drift Effective Population Size The effective size (Ne) of an actual population is the number of individuals in a population in which every adult contribute the same number of genes to the next generation in which the rate of genetic drift would be the same as in the actual population

Evolution by Genetic Drift Effective Population Size • The effective population size Ne can be smaller than the census size N for several reasons: • Variation in the number of progeny produced by each of the sexes • Unequal sex-ratio • Natural selection changes variation in progeny number • Inbreeding • Fluctuations in population size

Evolution by Genetic Drift Founder Effect Bottleneck Restrictions in size through which populations may pass Founder Effect Random genetic drift that ensues the establishment of a new population by a small number of colonists What would one expect from the formation of new populations by just a few individuals?

Evolution by Genetic Drift Founder Effect Bottleneck Restrictions in size through which populations may pass Founder Effect Random genetic drift that ensues the establishment of a new population by a small number of colonists Polydactylia Ellis-van Creveld Amish of Pennsylvania

Evolution by Genetic Drift Founder Effect 1. If the colony rapidly grows: allele frequencies will not be greatly altered from those in the source population although some rare alleles will not have been carried by the founders 2. If the colony remains small: genetic drift will alter allele frequencies and erode genetic variation 3. If the colony persists and grows: new mutations eventually restore heterozygosity to higher levels

The Neutral Theory of Molecular Evolution • Random genetic drift: • Has played an important role in the evolution of phenotypic features of organisms? • Has played an important role in the evolution of DNA and protein sequences! • The Neutral Theory of Molecular Evolution holds that: • 1.1 A minority of mutations are advantageous and fixed by natural selection • 1.2 Many mutations are disadvantageous and eliminated by natural selection • 1.3 The great majority of those mutations that are fixed are effectively neutral with respect to fitness and are fixed by genetic drift

The Neutral Theory of Molecular Evolution 2. Most genetic variation at the molecular level is selectively neutral and lacks adaptive significance 3. Evolutionary substitutions at the molecular level proceed at a roughly constant rate so that the degree of sequence difference between species can serve as a molecular clock

The Neutral Theory of Molecular Evolution Principles of Neutral Theory uT Constant mutation rate per gamete per generation Assume that initially due to the great number of mutable sites, every mutation constitutes a new DNA sequence u0 neutral mutation rate u0=f0uT where f0 is the fraction of mutations that effectively neutral Effectively Neutral the mutant allele is so similar to other alleles in its effect on fitness that changes in its frequency are governed by genetic drift alone, not by natural selection

The Neutral Theory of Molecular Evolution Principles of Neutral Theory When will u0 be equal to uT? When will u0 significantly smaller than uT?

The Neutral Theory of Molecular Evolution Principles of Neutral Theory • u0 depends on the gene’s function: • u0<<uT • Functional Constraints • Transcribed DNA: • If many of the amino acids in the protein it encodes cannot be altered without seriously affecting an important function. Second bp in codons • u0≈uT • No Functional Constraints • Transcribed DNA: • If the protein can function well despite any of many amino acid changes. Third bp position in codons • Not transcribed DNA: • introns and pseudo-genes

The Neutral Theory of Molecular Evolution Principles of Neutral Theory What is the number of neutral mutations that arise in any generation and will someday be fixed?

The Neutral Theory of Molecular Evolution Principles of Neutral Theory The number of neutral mutations that arise in any generation and will someday be fixed is: u0 2Ne (1/2Ne) = u0 How do you think this could be useful?

The Neutral Theory of Molecular Evolution Principles of Neutral Theory The number of neutral mutations that arise in any generation and will someday be fixed is: u0 2Ne (1/2Ne) = u0 The rate of fixation of mutations is theoretically constant, and equals the neutral mutation rate. This is the theoretical basis of the molecular clock The time required for fixation is longer in larger populations. More neutral mutations

The Neutral Theory of Molecular Evolution Principles of Neutral Theory If we know the number of differences D between the sequences of two species how can we estimate the time of divergence?

The Neutral Theory of Molecular Evolution Principles of Neutral Theory The number of base pair differences between two species is D=2 u0t (because there are 2 lineages) therefore the number of generations since divergence is: t = D/2u0 How is this estimate inaccurate?

The Neutral Theory of Molecular Evolution Principles of Neutral Theory The number of base pair differences between two species is D=2 u0t (because there are 2 lineages) therefore the number of generations since divergence is: t = D/2u0 Over a sufficiently long time some sites experience repeated base substitutions. Thus the observed number of differences between species will be less than the number of substitutions that have transpired . As the time since divergence becomes greater, the number of differences begins to plateau

The Neutral Theory of Molecular Evolution Principles of Neutral Theory How does the level of heterozygosity compare is small and large populations?

The Neutral Theory of Molecular Evolution Principles of Neutral Theory Although the identity of the several of many alleles present in the population changes over time, the level of variation reaches an equilibrium when the rate at which alleles arise by mutation is balanced by the rate at which they are lost by genetic drift The equilibrium level of variation, represented by the frequency of heterozygotes (H) is: Is higher in a large population than in a small one

The Neutral Theory of Molecular Evolution Evidence Evidence shows that most, although not all, DNA sequence evolution has been neutral: Substitutions occur most frequently at third-base positions in codons Rates of substitution are higher in introns than coding regions of the same gene and even higher in pseudogenes than their functional counterparts Some genes evolve much more slowly than others. The genes that evolve most slowly are those constrained by their precise function

Gene Flow and Genetic Drift A measure of the variation in allele frequency among populations is FST The rate at which populations drift toward fixation of one allele or another is inversely proportional to the effective population size Ne. However, the drift toward fixation is counteracted by gene flow from other populations at rate m These factors strike a balance at which the fixation index FST is: Even if there is only one migrant per generation FST=0.2, that is, little gene flow keeps all the demes fairly similar in allele frequency and heterozygosity remains high

Gene Flow and Genetic Drift Gene trees and population history The genealogical history of genes in populations is the basis of Coalescent Theory The smaller the effective size of a population the existing gene copies in a small population must stem from a more recent common ancestor than the gene copies in a large population

Gene Flow and Genetic Drift The Origin of Modern Homo Sapiens The gene tree for human mitochondrial DNA supports the “out-of-Africa” hypothesis according to which the world’s human population outside of Africa is descended from a relatively small population that spread from Africa recently replacing Eurasian populations of archaic Homo sapiens without interbreeding with them Non-African and African diverged 40,000 to 143,000 years ago. The world’s human population is descended from an effective breeding population of 4,600-11,200 people This evidence supports the “out-of-Africa” hypothesis

Gene Flow and Genetic Drift The Origin of Modern Homo Sapiens

Lecture Ideas • Genetic drift • Finite populations • Null hypothesis • Sampling error • Loss of heterozygosity • Population size • Speed of fixation • Effective population size • Founder’s effect • Mutations counteract genetic drift • At specific loci • Migration counteracts drift • All loci

Genetic Drift and Neutral Theory