Forces Determining Amount of Genetic Diversity

The following are major factors or forces that determine the amount of diversityin a population. They also determine the rate and pattern of evolutionary basesubstitution.

factor (parameter)(1) mutation (rate)(2) natural selection (kind and strength)(3) random drift (effective population size)

Mutation

• Mutation is the ultimate source of genetic variation and differences betweenspecies.

• All other things being equal, the higher the mutation rate the greater thegenetic variance in the population and the larger the differences betweenspecies.

• u = mutation rate = probability that a particular base pair will undergomutation

• u is very low, on the order of 10-8 to 10-9 per base pair or10-4 to 10-6 per gene.

We are interested in the total number of mutations that enter the gene pool inone generation.

In a diploid organism, if there are N individuals in the population, 2N gametesmust be produced each generation.

The total mutation rate in the population is the rate per base pair (or gene) pergamete times the number of copies of the gene in the population. The number ofcopies is the number of individuals (population size) N times 2 for a diploidorganism.

M = 2Nu

M = 2Nu

Mutations per gene = Number of gametes × mutations per gene per gamete

dimensional analysis:

mutations = gametes × mutations genes genes × gametes

M is usually very large:

If N is 105, the population will contain on the average of 2 new mutations in eachgene in each generation. Clearly most of these must be eliminated, otherwisegenetic variation will accumulate until species identity is lost.

If use DNA sequences to identify mutations, u is in mutations per bp per gameteor mutations per site per gamete.

If N = 105 and u = 10-9 and there are 3 X 109 bp per human genome, will have3 X 106 new mutations in gene pool in each generation.

3 X 106 new mutations 3 X 106 new and old mutations

Random genetic drift.

• Nondirectional force.• Acts equally to increase or decrease frequencies.• Eliminates or fixes new mutations.• Happens because different individuals have different numbers of offspring

by chance.• The probability that an allele will be fixed by drift is equal to its frequency.

Why drift happens

• Not all individuals in a population produce the same number of offspring.• Not all genes leave the same number of offspring.• Some of difference due to selection, some to pure dumb luck.

E.g. Mutation happens in one of the 6 million primary oocytes in your germ linewhen you were a fetus. Only a few hundred survive and ovulate. But you onlyhave two children. Probability that a child will have the mutation is about 2/6million or 1/3 million.

E.g. Three bdelloid rotifers belonging to same clone dry up and blow around.Each one lands in a tiny pothole just after a rain and starts to reproduce. Eachone produces 5,000 offspring. A deer comes along and drinks the other potholedry, so that bdelloid has no offspring. Any allele of any gene carried by it onlyleaves no offspring.

Eleplhant drinks all

Bad things can happen even to good genes. (S--- happens.)

Drift leads to fixation or loss of alleles

Even in the absence of selection, allele frequencies are not constant: they undergorandom walks. If the frequency of an allele drifts to 0, it is lost; if it drifts to 1, itis fixed and all other alleles of that gene are lost.

Probability of fixation of an allele is equal to its frequency:

P(fix neutral allele of frequency x) = x

• Section 18 divided into 18a, b, c. 18a and b on web.• Another homework assignment, on population and evolutionary genetics,will be posted soon, hopefully on Friday.

Probability of fixation of an allele is equal to its frequency:

P(fix neutral allele of frequency x) = x

Random drift is much more likely to eliminate a new mutation than to fix it.

New mutation: x = 1/2N P(fix new mutation) = 1/2NP(lose new mutation) = 1 - 1/2N

e.g. N = 5,000 P(fix) = 1/10,000 = 0.0001 P(loss) = 0.9999

New mutation begins with frequency very close to 0 and very likely to hit 0 andbe lost. Conversely, it is very far from 1 and very unlikely to get there.

Proof that random drift actually occurs has been obtained repeatedly inlaboratory experiments. Done with very small population size to make it go fast.

Fig. 17.30 and adjacent text describe an experiment in Drosophila. Read it.

The strength of random drift depends on the population size; works faster insmaller populations.

E.g. Haploid population with N = 5 or 10.

• What is important is the effective population size Ne.• N e depends on N but also on the sex ratio and other factors that determine

the variance in offspring number.• In nearly all cases, Ne < N. Often Ne << N.

e.g. elk harems

In diploids the important number is 2Ne because each individual has 2 genomes.

Play with a simple model of drift to understand it

Go to bottom of web site, then go either to URL for simulation or, better,download stuff and do manual simulation. Best is to do both.

Another program available on web is PopG program which tracks changes ingene frequencies under mutation, drift, and/or selection. We will use it later.

Combined effects of mutation and drift: neutral modelDrift always happens.Mutation always happens. So add mutation to simulation:

This model is realistic: it fits many real situations in which most geneticdiversity is due to neutral alleles. Some people think that it fits the majority ofmolecular data.

H ≈ 4Neu

1 + 4Neu ≈ 4Neu = θ Haploids and asexuals: substitute 2Neu

Animal mitochondrial genes: substitute Nfu

π ≈ 4Neu

1 + 4Neu ≈ 4Neu = θ but now u is in mutations per site per gamete,sometimes symbolized by µ

Intuitive explanation for these equations:Higher mutation rate: more mutations pumped into the population.Larger Ne: drift is slower so mutations tend to linger in population longer.

Directional selectionIf mutation and drift were all that happened, there would be no adaptation oforganisms to different habitats.

Differences in Ne and u can’t explain synonymous > nonsynonymous or introns> exons, because all these are in same genome in same organism and have sameNe and u.

Directional selection is a directional force that tends to increase frequencies ofadvantageous alleles and decrease frequencies of detrimental alleles.

By itself, directional selection will fix advantageous alleles and eliminatedetrimental alleles.

Directional selection is the basis for most cases of Darwinian adaptive evolution,because it results in a phenotypic change that increases the fitness of theorganism.

Drosophila experimental results usually not as neat as those cases we use inclass.

Did three-factor cross in genetics lab course.All mutant genotypes (e.g. white eye) present in fewer than the expectednumbers.All visible mutants, all at least slightly detrimental.

If they were not detrimental, they would be more common in nature.If they were advantageous, they would have become the wild type.

Adaptive Melanism in Lava Flow Mice

Hopi Hoekstra (now at Harvard), Michael Nachman (EEB), et al.

See Hopi’s web site:http://www-biology.ucsd.edu/faculty/hoekstra.htmlFollow the link to Projects.

Melanism seen in mice, lizards, and snakes living on desert lava flows.Earlier work showed that melanism reduces owl predation on mice on dark lavarock, and dark mice have reduced fitness on light rock.

Rock pocket mouse Chaeootdipus intermedius living in Arizona, New Mexico, andnorthern SonoraHair color matches rock color.

Due to natural selection, acting over < 500,000 years. Requires strong selection.

This is short-term evolution, within a species.

Mouse populations on lava are not completely isolated from mouse populationson light rock in adjacent desert. Therefore selection must be very strong tocounteract effects of migration.

Melanism in Pinacate population in Arizona is due to a single point mutation inthe melanocolrtin-1 receptor gene (Mc1r) that is responsible for melanism.

Melanism in New Mexico populations due to different gene. ≥ 2 independentorigins of adaptive melanism in pocket mice.

Selection intensity is measured by relative fitness or by selection coefficient s of mutantallele:

offspring number (relative fitness) mutant 0 50 100wild type 100 50 0

s -1 ---------------- 0 ---------------- 1lethal detrimental neutral advantageous lethalmutant wild typle

The majority of mutants have selection coefficients with smallabsolute values: |s| < 0.1.

Combined Effects of Selection and Drift

Probability of fixation of a new mutant allele with selection coefficient s in populationwith effective size Ne is given by Kimura’s equation:

F = (1 – e-2Nes/N)/ (1 – e-4Nes)Solving equation for various values of N, Ne, and s leads to the following conclusions:

• Even detrimental mutations can be fixed by drift.• Even advantageous mutations can be lost by drift.• Relative strength of selection and drift depends on the product Ne|s|:

Ne|s| >> 1 selection dominates Ne|s| << 1 drift dominates (mutation is effectively neutral)

If Ne|s| >> 1, then either Ne is very large so drift works very slowly, or |s| is very largeso selection is very strong (or both).

If Ne|s| << 1, then either Ne is very small so drift is strong, or |s| is very small soselection is very weak (or both).

Analogy: selection is signal, drift is noise.

Balancing Selection

Balancing selection is any kind of selection that maintains two or more allelesin a population.

Sickle-cell anemiaSickle-cell gene has been maintained in fairly high frequency even though it isdetrimental.Heterozygotes are more resistant to malaria than homozygous normal.Heterozygotes have selective advantage where malaria is endemic.

effects ofanemia malaria

HbA HbA none severeHbA HbS mild less severeHbS HbS severe ?

Example of overdominance = heterozygotes are more fit than eitherhomozygote.

There are a number of other kinds of balancing selection.e.g. different alleles are adapted to different habitats.

Deer mice in western U.S. live from sea level to 14,000 feet.Polymorphic for two variants of α-globin protein, one more efficient at bindingoxygen at high altitude and the other at low altitude.

Only a few cases of balancing selection have been clearly demonstrated.Probably less important than directional selection, but this is still being debated.

Balancing selection delays the fixation or loss of alleles, which increasesheterozygosity.

Combined Effects of Mutation, Drift, and Selection: Simple Modelsof Extreme Cases

Each dot represents a gene.Time goes left to right.Each vertical column of dots represents the genes in one generation.

Directional selection reduces genetic variability relative to neutralcase by accelerating the fixation or loss of mutations.

Balancing selection increases genetic variability relative to neutralcase.

Directional Selection Mutations stay in population average H or πneutral ≈ 4Ne generations ≈ 4Neudetrimental pushed to loss < 4Ne generations < 4Neuadvantageous pushed to fixation < 4Ne generations < 4Neubalanced maintained > 4Ne generations > 4Neu

Balancing selection is not very common. Therefore if we look at a largesegment of DNA, we will find that H < 4Neu.

A few genes have H > 4Neu showing balancing selection.

Analogy:Gene pool is bathtub with water molecules as alleles.Mutation is faucet.Drift is drain.Directional selection is pump.Balancing selection is 2 (or more) rubber duckies which can’t fit out the drainor pump.

Evidence for directional and balancing selection from populationgenetics of Drolsophila Adh

Directional selection:

(1) There is more polymorphism in introns than in exons.

(2) In the exons, there is much more polymorphism in DNA sequence than inamino acid sequence.

(4) The left end of exon 4 is an exception. The F/S site is polymorphic, andregions close to it on both sides have a higher polymorphism than other exons.The F/S difference is maintained by balancing selection. This selection also tendsto maintain heterozygosity for mutations closely linked to F or S. Further away,recombination tends to separate new mutations from F or S and directionalselection acts to reduce polymorphism.

Explaining patterns/phenomena:

Different species have different diversities

Could be due to differences in u, Ne, or s.

Why are cheetahs so uniform?

• No reason to believe mutation rate different from other animals.• Some markers probably nearly neutral so probably not due to very strong selection.• Probably mainly small N and Ne; lingering effects of population bottleneck.

Different genomes have different diversities.

Hominids: mitochondrial gene diversity > nuclear gene diversity

2Nfum > 4Neun where Nf = number of females we know 2Nf < 4Ne

therefore um > un

Mitochondria have different DNA polymerase, less effective repair systems, and moreexposure to mutagens.

Different genes or regions of genome have different diversity.

E.g. fibrinopeptides > α-globin

• All nuclear genes in same species, so difference not due to Ne or to u.• Is due to selection; fibrinopeptides work with a wide range of amino acid sequences so new

mutations are only slightly detrimental; globin mutations more detrimental.

Why are conserved sequences lower in variation than others?

• Not low u, which is same on average for all segments of a genome.• Not N and Ne, which are same for all genes in an organism.• Conserved sequences have arge negative s: on average, larger proportion of

mutations are detrimental, fewer are neutral.

Why are VNTRs so useful for forensic work?

• N e is same for VNTRs and other genes.• Most nearly neutral, so high variation partly due to lack of directional selection.• Mutation rate u is high (due to replication slippage and changes in repeat numbers,

not to single-base mutations)

smaller N

smaller Ne and Ne|s|

less effectiveselection

reduced fitness

One Implication for Conservation

Endangered species have small N. This means small Ne and Ne|s|, whichmeans less effective selection, which includes more accumulation ofdetrimental mutations, leading to reduced fitness and further reduction inN.

Vicious circle: