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Mendelian Genetics in Populations II

Migration, Genetic Drift, and Nonrandom Mating

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Chance events can alter allele and genotype frequencies (Fig. 6.10a)

In the “sampling” of egg and sperm to make zygotes, there were 14 A1 and 6 A2 alleles. So the allele frequencies changed to 0.7 for A1 and 0.3 for A2

Note: these alleles are not affected by natural selection = neutral alleles

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Range of possible outcomes when 20 gametes are sampled from a population with allele frequencies of p = 0.6 and q = 0.4 (Fig. 6.11)

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Genetic drift is evolution that happens by chance

The figure on the previous slide demonstrates that:

1) Allele frequencies are more likely to change than stay the same across generations

2) Small per generation changes in allele frequency are more likely than large changes

3) If the “initial” frequency of an allele is > 0.5, it is more likely to increase in frequency that decrease in the next generation

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Computer simulations of random genetic drift

• Random sample of 20 gametes from a population with p(A1) = 0.6 and q(A2) = 0.4

• Using Populus 5.3– http://www.cbs.umn.edu/populus/Download/download.html

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Evolutionary effects of genetic drift – 1• Genetic drift results in the eventual fixation of one allele,

and the loss of all other alleles (provided no other “forces” are acting = neutral alleles)

• As one allele drifts toward fixation, the heterozygosity of the population declines

• The probability of eventual fixation of a neutral allele is equal to its current frequency in the population (Note: in a diploid population of size N, a new mutation will have a frequency of 1/2N)

• Larger populations require more time for fixation• Drift also operates on alleles that are affected by selection

(more on that later)

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Genetic drift and heterozygosity (Fig. 6.15)

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Genetic drift in experimental lab populations107 populations of size N = 16, initial allele frequencies 0.5, incomplete

dominance

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Loss of heterozygosity in a laboratory population

• Dashed line is the theoretical prediction for population size N = 16

• Solid gray line is theoretical prediction for N = 9

• The effective population size was smaller than the actual population size

• See previous slide for additional experimental details

Heterozygosity

Generation

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Population size and genetic diversity in natural populations (Fig. 6.19a,b)

Polymorphism = proportion of loci for which the frequency of the most common allele is < 0.99

Allelic richness = average number of alleles per locus

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Genetic variation in Ozark glade populations of collared lizard (Fig.

• The colors in the pie chart at left represent 7 different multilocus genotypes based on: malate dehydrogenase (MDH) genotypes, mtDNA haplotypes, and ribosomal DNA (rDNA) genotypes.

• Populations in different glades are represented by colored circles on the maps

• A solid-color circle indicates that only one multilocus genotype is present in that population.

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Founder effects and bottlenecks are special cases of genetic drift

• Founder effects occur when a new population is started with a small number of migrants from another (usually larger) population

• Bottlenecks occur when a large population is reduced to a small size

• In both cases drift is strong because of small population size, which may persist for a number of generations

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How founder effects and bottlenecks change the genetic composition of populations

• Reduce genetic variation through loss of low frequency alleles

• Increase the frequency of some very rare (probably harmful) alleles that happen to be present in founders or survivors of bottlenecks

• Lead to inbreeding, which increases the chance that recessive mutations will be homozygous

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The founder effect in an island-hopping birdthe silvereye, Zosterops lateralis (Fig. 6.13)

• Progressive founder events reduce genetic diversity as measured by the average number of alleles at six microsatellite loci

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A founder effect in a human population: achromatopsia in the Pingelapese people of the Eastern Caroline Islands

• The current population of about 3,000 people on the Pingelap Atoll are descended from 20 survivors of a typhoon in about 1775

• The frequency of achromatopsia (complete colorblindness, extreme sensitivity to light, and poor visual accuity), a homozygous recessive disorder, is about 1 in 20 (compared to less than 1 in 20,000 in most populations)

• At least one of the survivors of the typhoon carried at least one copy of the defective allele, which means that among the survivors the frequency of the defective allele was at least 2.5%

• The frequency of the defective allele has since increased to > 20% under the influence of drift

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Migration and genetic drift

• Migration of individuals (movement from one population to another) retards the rate of drift within each population

• If migration among populations is high enough, the several populations become, in effect, one larger population in which drift is slower

• In general, 2 or more migrants into a population per generation is enough gene flow to make several populations behave like one larger population

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Selection and genetic drift – 1• Genetic drift also affects the frequencies of alleles that are under

selection• Suppose the fitnesses (relative survivorships) of genotypes at a locus are

as follows:

• According to what we have learned, if A2 is a new mutation, directional selection should result in the fixation of allele A2 because A2A2 homozygotes have the highest survivorship: that is, the Pr(fix A2) ≈ 1.0

• However in a finite population of size N, it’s not so simple• If the quantity 4Ns is greater than about 2, then Pr(fix A2) ≈ 2s, which

will be much less than 1.0 for realistic selection coefficients• If the quantity 4Ns is less than about 1, then Pr(fix A2) ≈ 1/2N, which is

the probability of fixation of a new neutral mutation by drift, and will also be less than 1.0

• Either way, most beneficial mutations are lost from populations because of random genetic drift! And it’s even worse if A2 is recessive!

A1A1 A1A2 A2A2

1 1 + s 1 + 2s

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Selection and genetic drift – 2• Let’s look at some numbers:• Suppose N = 200, and s = 0.01 (i.e., a 1% selective advantage to A2

when heterozygous)• Then 4Ns = 8, which is “large”, and the probability of eventual

fixation of A2 if it is a new mutation ≈ 2s = 0.02

• On the other hand:• Suppose N = 5, and s = 0.01• Then 4Ns = 0.2, which is “small”, and the probability of eventual

fixation of A2 is ≈ 1/2N = 0.1

• In this particular example, then, our new favorable mutation, A2, is more likely to become fixed in a small population, where its initial frequency is higher, than in a large population, where its initial frequency is lower.

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The Neutral Theory of Molecular Evolution – 1

• It is important to distinguish between evolution of proteins (i.e., amino acid sequences) and evolution of nucleotide sequences

• It is reasonable to assume that much nucleotide sequence evolution is selectively neutral or nearly so: pseudogenes, introns and other non-translated regions; synonymous substitutions

• On the other hand, we might expect many amino acid substitutions to be under selection

• The long-standing argument between neutralists and selectionists is really about whether most protein evolution (= amino acid substitutions = non-synonymous nucleotide substitutions) is neutral, or is adaptive and driven by natural selection

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The Neutral Theory of Molecular Evolution – 2

• Neutralists do not claim that most mutations are neutral• However, they do argue that most of the protein variation

that we see within populations has no fitness consequences (i.e. alleles are neutral), and that most of the evolutionary change in proteins that we see between related taxa is due to drift acting on selectively neutral alleles. According to neutralists, positive selection (= adaptation) plays little or no role in evolution at the molecular level

• For neutralists, as well as selectionists, most mutations are harmful and are removed from populations by the action of natural selection

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Neutral theory predicts a molecular clock

• Let the neutral mutation rate be µ(= proportion of new mutant copies of a gene per generation, e.g., 1 in a million)

• In a diploid population of size N, there will be 2Nµ new mutations at a gene per generation

• Since these mutations are neutral, the probability of eventual fixation of any one mutation is 1/2N, and its probability of loss is 1 - (1/2N) which will be very close to 1.0 for reasonably large populations

• Most new neutral mutations will be lost by drift within a few generations, but occasionally a new mutation will increase infrequency under drift and replace previously existing alleles – this is known as an allelic substitution

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Mutation and allelic substitution over time (Fig. 6.20)

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The average rate of allelic substitution, which is the rate of neutral evolution, is equal to the

neutral mutation rate• The average number of allelic fixations per

generation is equal to the number of new mutations per generation x the probability that any one mutation eventually becomes fixed = 2Nµ x 1/2N = µ

• So, the predicted average amount of time between allelic substitutions is 1/µ generations: this is the molecular clock

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Molecular divergence among three related taxa

t

2t

ABC Tim

e since most recent com

mon ancestor

Neutral theory predicts:1. The amount of molecular difference between A and C will

be the same as the amount of difference between B and C, since the amount of evolutionary time is the same in both comparisons

2. The amount of molecular difference between A and C (or B and C) will be twice the amount of difference between A and B, since the common ancestor of A and B lived half as long ago as the common ancestor of A and C (or B and C)

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Synonymous and non-synonymous base substitutions (Fig. 6.21)

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Molecular evolution in

influenza viruses is consistent

with neural theory (Fig.

6.21c)

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A paradox and an inconsistency

• The paradox is that under neutral theory, in which allelic substitutions are due only to drift (rather than directional selection) the rate of evolution does not depend upon population size but only the mutation rate to neutral alleles

• The inconsistency is that the theory predicts a clock that “ticks” in generation time, yet much of the evidence for a molecular clock is based on “clock” time

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Nearly neutral theory – 1

• Neutralists have addressed the problem of time scale with what is known as nearly neutral theory

• The idea is that many slightly deleterious mutations will be effectively neutral, depending on population size

• In general, as we saw above, drift will govern the fate of alleles if the quantity 4Ns is “small”, where N is effective population size and s is the coefficient that describes the action of natural selection on the heterozygote

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Nearly neutral theory – 2• Imagine a species in which effective population size, N, is

500. If the selection coefficient, s, against a mutant heterozygote is 0.0005, then 4Ns = 1.0, which qualifies as “small”, and the mutation is effectively neutral

• On the other hand, the same selection coefficient in a population of 5,000 would mean that 4Ns = 10.0, which would be “large” and would mean that natual selection would act against the mutation (that is, the mutation is harmful – not neutral)

• If species with long generation times tend to have small population sizes, then the mutation rate to effectively neutral mutations will be greater in species with longer generations, and this higher mutation rate per generation will compensate for the longer generation time

• The net result is that the molecular clock will tend to tick at the same speed in clock time for all species

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Population size, generation time, and nearly neutral mutations (Fig. 22)

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Synonymous and non-synonymous substitutions and the molecular clock – 1

• Evolution of synonymous nucleotide substitutions generally supports a molecular clock (this is not controversial)

• In some cases, non-synonymous substitutions also appear to be clock-like (e.g., the influenza virus data in Fig. 6.21)

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Synonymous and non-synonymous substitutions and the molecular clock – 2

• Data from many genes indicates that the rate of evolution of synonymous substitutions is higher (often much higher) than the rate of evolution of non-synonymous substitutions (see Table 6.1 in your text)– This observation is consistent with the expectation that

most amino acid changes will be deleterious and, therefore, that the neutral mutation rate will be lower for non-synonymous substitutions (as would be predicted by both neutralists and selectionists)

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Molecular evolution in

influenza viruses is consistent

with neural theory (Fig.

6.21c)

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Evidence for molecular evolution by “positive” selection

• Neutral theory states that if we compare protein coding sequences (exons) between species, there will be more nucleotide substitutions at synonymous than non-synonymous sites (because the neutral mutation rate is lower at non-synonymous sites) : dN/dS < 1.0

• On the other hand, if much evolution involves positive selection on alleles that increase fitness, then evolution at non-synonymous sites may be faster than at synonymous sites (because positive selection will substitute alleles faster than drift): dN/dS > 1.0

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Positive selection on the BRCA1 gene in humans and chimpanzees (Fig. 6.23)Ratio of replacement to silent mutations that is greater than 1.0 on branches leading to humans and chimps is evidence for positive selection

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Molecular evolution – summary

• Neutral theory appears describe much evolution at the nucleotide level in untranslated parts of the genome and at synonymous sites

• However, for many, but not all proteins, there is evidence that evolution has been driven by positive selection on non-synonymous substitutions:– recently duplicated genes that have attained new

functions, disease-resistance loci (e.g., genes that code for antibody proteins), genes involved in interactions between egg and sperm at fertilization, genes that code for certain enzymes (e.g., alcohol dehydrogenase)

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Nonrandom mating• Most commonly, nonrandom mating takes the form of

inbreeding, or mating with relatives• Inbreeding can be “systematic”, such as by self-

fertilization in hermaphroditic plants and animals (this is the most extreme form of inbreeding)

• Inbreeding can be “accidental”, as when mating occurs between related individuals in finite, especially small, populations

• In either case, the genetic effect of inbreeding is to reduce heterozygosity below Hardy-Weinberg expectation (2pq), and to increase homozygosity

• One way of defining the inbreeding coefficient:F = (HH-W - Hobserved) / HH-W

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Inbreeding increases homozygosity – the example of selfing (Fig. 6.25a)

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Inbreeding increases homozygosity – the example of selfing (Fig. 6.25b)

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The effects of inbreeding

• Because inbreeding increases homozygosity, it makes it more likely that deleterious recessive alleles in a population will be expressed

• This increases the effectiveness of selection against harmful recessives

• However, in species that do not normally inbreed, it also leads to inbreeding depression

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Inbreeding depression in humans (Fig. 6.28)

Children of first cousins have higher mortality rates than children of unrelated parents (by about 4 percentage points)

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Inbreeding depression in great tits (Fig. 6.30)

F = 1/4 is the inbreeding coefficient of children of brother-sister matingsF= 1/16 is the inbreeding coefficient of children of 1st cousins

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Synergism between small population size, drift and inbreeding – 1

• Drift is especially strong in small populations• Drift reduces genetic variation (= increased

homozygosity)• It is possible for deleterious alleles to increase in

frequency under drift (think about bottlenecks and achromatopsia in Pingelapese islanders)

• In small populations, inbreeding (mating between relatives) is unavoidable (remember the Pingelapese who are

all descended from 20 survivors of a typhoon) This is true even if the population is mating at random

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Synergism between small population size, drift and inbreeding – 2

• So, small population size results in loss of genetic variation, chance increases in the frequency of harmful alleles, and inbreeding

• Inbreeding results in inbreeding depression, which further reduces population size, which further enhances the effect of drift, and also results in more inbreeding, which results in more inbreeding depression, which results in further reductions in population size, etc., etc., etc.

• This has been referred to as the “extinction vortex”