Forces Determining Amount of Genetic Diversity The following are major factors or forces that determine the amount of diversity in a population. They also determine the rate and pattern of evolutionary base substitution. 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 between species. All other things being equal, the higher the mutation rate the greater the genetic variance in the population and the larger the differences between species. u = mutation rate = probability that a particular base pair will undergo mutation u is very low, on the order of 10-8 to 10-9 per base pair or 10-4 to 10-6 per gene. We are interested in the total number of mutations that enter the gene pool in one generation. In a diploid organism, if there are N individuals in the population, 2N gametes must be produced each generation. The total mutation rate in the population is the rate per base pair (or gene) per gamete times the number of copies of the gene in the population. The number of copies is the number of individuals (population size) N times 2 for a diploid organism. 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 10 5, the population will contain on the average of 2 new mutations in each gene in each generation. Clearly most of these must be eliminated, otherwise genetic variation will accumulate until species identity is lost. If use DNA sequences to identify mutations, u is in mutations per bp per gamete or mutations per site per gamete. If N = 10 5 and u = 10-9 and there are 3 X 10 9 bp per human genome, will have 3 X 10 6 new mutations in gene pool in each generation. 3 X 10 6 new mutations 3 X 10 6 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 line when you were a fetus. Only a few hundred survive and ovulate. But you only have two children. Probability that a child will have the mutation is about 2/6 million 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. Each one produces 5,000 offspring. A deer comes along and drinks the other pothole dry, so that bdelloid has no offspring. Any allele of any gene carried by it only leaves 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 undergo random walks. If the frequency of an allele drifts to 0, it is lost; if it drifts to 1, it is 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) = 1/2N P(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 and be lost. Conversely, it is very far from 1 and very unlikely to get there. Proof that random drift actually occurs has been obtained repeatedly in laboratory 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 in smaller 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 in gene frequencies under mutation, drift, and/or selection. We will use it later.
Combined effects of mutation and drift: neutral model Drift always happens. Mutation always happens. So add mutation to simulation: This model is realistic: it fits many real situations in which most genetic diversity is due to neutral alleles. Some people think that it fits the majority of molecular data. H π 4N e u 1 + 4N e u 4N eu = θ Haploids and asexuals: substitute 2Neu Animal mitochondrial genes: substitute N f u 4N e u 1 + 4N e u 4N eu = 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 N e : drift is slower so mutations tend to linger in population longer.
Directional selection If mutation and drift were all that happened, there would be no adaptation of organisms to different habitats. Differences in N e and u can t explain synonymous > nonsynonymous or introns > exons, because all these are in same genome in same organism and have same N e and u. Directional selection is a directional force that tends to increase frequencies of advantageous alleles and decrease frequencies of detrimental alleles. By itself, directional selection will fix advantageous alleles and eliminate detrimental 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 the organism.
Drosophila experimental results usually not as neat as those cases we use in class. Did three-factor cross in genetics lab course. All mutant genotypes (e.g. white eye) present in fewer than the expected numbers. 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.html Follow 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 lava rock, and dark mice have reduced fitness on light rock. Rock pocket mouse Chaeootdipus intermedius living in Arizona, New Mexico, and northern Sonora Hair 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 populations on light rock in adjacent desert. Therefore selection must be very strong to counteract effects of migration. Melanism in Pinacate population in Arizona is due to a single point mutation in the melanocolrtin-1 receptor gene (Mc1r) that is responsible for melanism. Melanism in New Mexico populations due to different gene. 2 independent origins of adaptive melanism in pocket mice.
Selection intensity is measured by relative fitness or by selection coefficient s of mutant allele: offspring number (relative fitness) mutant 0 50 100 wild type 100 50 0 s -1 ---------------- 0 ---------------- 1 lethal detrimental neutral advantageous lethal mutant wild typle The majority of mutants have selection coefficients with small absolute values: s < 0.1.
Combined Effects of Selection and Drift Probability of fixation of a new mutant allele with selection coefficient s in population with effective size N e is given by Kimura s equation: F = (1 e -2N e s/n )/ (1 e -4N e s ) Solving equation for various values of N, N e, 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 N e s : N e s >> 1 selection dominates N e s << 1 drift dominates (mutation is effectively neutral) If N e s >> 1, then either N e is very large so drift works very slowly, or s is very large so selection is very strong (or both). If N e s << 1, then either N e is very small so drift is strong, or s is very small so selection 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 alleles in a population. Sickle-cell anemia Sickle-cell gene has been maintained in fairly high frequency even though it is detrimental. Heterozygotes are more resistant to malaria than homozygous normal. Heterozygotes have selective advantage where malaria is endemic. effects of anemia malaria Hb A Hb A none severe Hb A Hb S mild less severe Hb S Hb S severe? Example of overdominance = heterozygotes are more fit than either homozygote.
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 binding oxygen 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 increases heterozygosity.
Combined Effects of Mutation, Drift, and Selection: Simple Models of 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 neutral case by accelerating the fixation or loss of mutations. Balancing selection increases genetic variability relative to neutral case.
Directional Selection Mutations stay in population average H or π neutral 4Ne generations 4N e u detrimental pushed to loss < 4N e generations < 4N e u advantageous pushed to fixation < 4N e generations < 4N e u balanced maintained > 4N e generations > 4N e u Balancing selection is not very common. Therefore if we look at a large segment of DNA, we will find that H < 4N e u. A few genes have H > 4N e u 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 drain or pump.
Evidence for directional and balancing selection from population genetics 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 in amino acid sequence. (4) The left end of exon 4 is an exception. The F/S site is polymorphic, and regions 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 tends to maintain heterozygosity for mutations closely linked to F or S. Further away, recombination tends to separate new mutations from F or S and directional selection acts to reduce polymorphism.
Explaining patterns/phenomena: Different species have different diversities Could be due to differences in u, N e, 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 2N f u m > 4N e u n where N f = number of females we know 2N f < 4N e therefore u m > u n Mitochondria have different DNA polymerase, less effective repair systems, and more exposure 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 N e 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 N e, 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)
One Implication for Conservation Endangered species have small N. This means small Ne and Ne s, which means less effective selection, which includes more accumulation of detrimental mutations, leading to reduced fitness and further reduction in N. Vicious circle: smaller N reduced fitness smaller N e and N e s less effective selection