Forces Determining Amount of Genetic DiversityThe 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 = 2NuM = 2NuMutations per gene = Number of gametes × mutations per gene per gametedimensional analysis:mutations = gametes × mutations genes genes × gametesM 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 mutationsRandom genetic drift.• Nondirectional force.• Acts equally to increase or decrease frequencies.• Eliminates or fixes new mutations.• Happens because different individuals have different numbers of offspringby 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 allBad things can happen even to good genes. (S--- happens.)Drift leads to fixation or loss of allelesEven 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) = xRandom 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 - 1/2Ne.g. N = 5,000 P(fix) = 1/10,000 = 0.0001 P(loss) = 0.9999New 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.• Ne depends on N but also on the sex ratio and other factors that determinethe variance in offspring number.• In nearly all cases, Ne < N. Often Ne << N.e.g. elk haremsIn diploids the important number is 2Ne because each individual has 2 genomes.Play with a simple model of drift to understand itGo 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 ≈ 4Neu1"+"4Neu ≈ 4Neu = θ Haploids and asexuals: substitute 2NeuAnimal mitochondrial genes: substitute Nfuπ ≈ 4Neu1"+"4Neu ≈ 4Neu = θ but now u is in mutations per site per gamete,sometimes symbolized by µIntuitive 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