homology - implies common ancestry. If you go back far enough, get to one single copy from which all current copies descend (premise 1).

Transcription

1 Drift in Large Populations -- the Neutral Theory Recall that the impact of drift as an evolutionary force is proportional to 1/(2N) for a diploid system. This has caused many people to think that drift is only important in very small populations or if there had been a small population size (i.e., bottleneck/founder event) in a population s recent past. But drift can be important in large populations as well. Two major cases: 1. New mutations. Whenever a mutation first occurs, is is very rare and subject to drift no matter how large the total population is. Theory has shown that even for a mutation that doubles fitness, their most likely fate is to be lost due to drift within the first 10 generations after the mutation occurred. Hence, genetic drift is a major determininant of what mutations become frequent enough to be subjected to effective natural selection. 2. Neutral alleles. Wright brought drift to the forefront as an evolutionary force, but he was concerned with how it interacted with natural selection. He was not interested in alleles that have no selective significance at all. But in the 1960's, two important molecular biology breakthroughs contributed significantly to our understanding of genetic variation and the importance of drift. 1) amino acid sequencing ---> led to idea of a molecular clock 2) protein electrophoresis ---> found lots of functionally equivalent (neutral) genetic variation 1) Amino acid sequencing: - allowed homologous comparisons between taxa so we could see the fate of gene products over lo homology - implies common ancestry. If you go back far enough, get to one single copy from which all current copies descend (premise 1). EX) α-chain of hemoglobin: Mouse Chicken Newt Carp Shark Human Mouse Chicken Newt Carp 85 Notice that the values within each column are all approximately constant, which would indicate, for example, that humans, mice, chickens, newts, and carps are all approximately equidistantly related to sharks. That is, even though humans are phenotypically very much unlike sharks and carps are more similar to sharks, humans and carps are evolutionarily equidistant from sharks. We can see this better with the following diagram: The distance along any given line from the shark to any other taxon is the same. This linear distance reflect time since divergence. It would indicate that although phenotypic evolution appears to proceed at different rates (carp and sharks are phenotypically similar; humans and sharks are much less so), molecular evolution accumulates more or less constantly through time. ---> Molecular Clock? Molecular Clock (See King and Jukes, Science) Human Mouse Chicken Newt Carp Shark

2 Evolutionists, under the prevailing paradigm of natural selection as the primary evolutionary force, thought that changes in species (phenotypic and molecular) should reflect the influence of changes in environment or niche space. Yet here was evidence that, at the molecular level, that only time since divergence seemed important. Molecular evolution appeared to accumulate at a constant rate. NOTE: We now know that it is not terribly clock-like, but rather an artifact of the data. For example, suppose the distance from the shark to the common ancestor of humans and chickens is X and the distances from that common ancestor the human and chicken are Y and Z, respectively. One can see that X is relatively much longer than either Y or Z. That is, there could be a relatively significant difference in the distances between Y and Z (i.e., Y not equal to Z) but when each is added to the much larger X, one can no longer see any significant difference between the two resulting values. They appear relatively the same. Today, we are able to much more reliably measure and compare these values and can see the accumulation of molecular divergence is seldom constant when tested (i.e., does not result in equal distances). The artifact was the result of poor data and less than optimal analytical techniques but the findings were of tremendous importance to the formulation of scientific thought at the time (even to this day). Although not strictly clock-like in it behavior, the accumulation of molecular divergence is expected and provides a useful albeit rough measure of timing evolutonary events. 2) Protein electrophoresis: - for the first time we could survey large numbers of individuals in natural populations for many loci, whether or not those loci were variable or not. ---> led to the first accurate picture of the true level of variation in amino acids Found that roughly 1/3rd of these loci were polymorphic. This was in direct conflict with Morgan s Classical School that predicted there was little polymorphism in natural populations. Such evidence of wide spread polymorphism would, at first, seem to support Dobzhansky s Balanced School which proposed that natural selection maintained high levels of genetic variation in natural populations. In actuality, proponents of the Classical School, rather than converting to the Balanced School, interpreted the electrophoretic data as evidence that while much variation exists in natural populations, most of it is functionally equivalent (i.e., neutral with respect to natural selection). They went from the idea of a wildtype allele to sets of functionally equivalent alleles. They acknowledged the presence of variation but not that it was maintained by natural selection. MOTOO KIMURA (1968 paper) - put forth a model that explained both the observation of high levels of genetic variation and that molecular evolution accumulated at a constant rate (molecular clock) ---> NEUTRAL MODEL Neutral alleles, operating under the influence of drift alone, could explain both high levels of variation and the molecular clock. Given 2N neutral genes (that is two per locus for each of N individuals). We can see the different types of genes (called alleles) at the molecular level (via sequencing, restriction enzymes, etc.), but they are all functionally equivalent with respect to natural selection. Genes NOTE: These are not the same as alleles, per se. Alleles refer to different types of genes. refer to the individual copies. Therefore, in ten individuals there are necessarily 20 genes that We know that eventually drift always fixes one gene (and therefore one allelic type) and loses all the others, but which gene gets fixed? Under neutrality, all genes are equally likely to be fixed with a probability of fixation = 1/2N.

3 * Remember from the lecture on drift that the probability of fixation of an allele (type of gene) is its frequency in the population. Therefore, if there are five individuals (10 genes), three of which are A alleles and seven are a alleles, then the prob(fix) of any single gene is 1/10 but the prob(fix) of each allele is 1/3 and 1/7, respectively. The rate of production of new alleles per generation (assumed neutral) = (# genes)(mutation rate) = 2Nµ Large populations have a much smaller probability of fixation but a greater rate of mutant production than do small populations. These two effects balance one another out so that the overall rate of molecular evolution (the rate at which new alleles are produced and then go to fixation) = (1/2N)(2Nµ) = µ There is no effect of the population size on the rate of neutral evolution by drift! That is, the rate of neutral molecular evolution proceeds at the same rate regardless of the population size (or anything else except the mutation rate). Therefore, if the neutral mutation rate is relatively constant (an inherent property as opposed to natural selection, for example), then the rate of molecular evolution is independent of what is going on in the environment. This explains why we see an apparent molecular clock, that is if the alleles are neutral (functionally equivalent). of the model NOTE: In reality, not all alleles can be completely neutral. Natural selection is a factor for some them. For this reason, molecular evolution doesn t proceed at exactly the rate of mutation and molecular clock isn t exactly clock like. Nonetheless, if most alleles are neutral, Kimura s does explain the observation of a molecular clock quite nicely. This can also explain why there is so much polymorphism in natural populations. Any variation that exists in a population is subject to the influence of drift alone (since they are neutral). Since the rate of fixation, or the rate at which one allele replaces all others (the opposite of polymorphism), is the mutation rate, and since mutation rates tend to be quite low overall, it takes a long time for any one allele to replace the others. When we look at a population at nearly any point in time, it is quite likely there will be several such alleles being jostled about by drift. So, Kimura explained the presence of much polymorphism and the observation of a rough molecular clock with his model of neutral alleles under the influence of drift. Oddly enough, given the balance between the power of drift to remove alleles (inversely proportional to population size) and the power of mutation to add them (more mutants possible in larger populations), the results are independent of population size, even though drift is the evolutionary force behind it. Each population is affected in the same way with respect to neutral genetic turn over, regardless of N. Drift is an important evolutionary force in all populations for neutral alleles, not just small ones. It is important to remember that we are talking about the rate of neutral molecular evolution. That is, the rate at which one functionally equivalent allele replaces another over time. Kimura showed that such fixed differences between populations/taxa accumulate in all populations equally at a constant rate equal to the mutation rate. That is not to say that large and small populations have the same number of mutants or the same amount of polymorphism. They do not. Remember, the accumulation of fixed differences between populations is made possible because of the balance between the power of drift (inversely related to N) and the number of mutants (proportional to N). Therefore, larger populations will have more variants because for any given mutation rate there will be more mutants and drift will be less effective in removing them. We can say that while the rate of accumulation of fixed differences between populations is constant at without reference to N, the time it takes for any single gene in any given single population to go to fixation is a function of N. In a small population, it will be a longer time between mutants but when one does occur, it has a proportionally higher probability of being fixed (although we also know that the vast majority are lost due to drift). Likewise, in a large population, mutants occur more regularly (and most are lost due to drift), but it will take longer for one to be taken to fixation by drift.m, but in any given population, things are not happening in the same ways.

4 We saw before that F t+1 = 1/(2N ef ) + [1-1/(2N ef )]F t. This is the prob(ibd) if there is no mutation. However, if there is mutation, then the only way to be truly identical by descent is to have no mutation events occurring between the generations. Given that mutation occurs at a rate = µ (mutation rate with the same prob(mut) in each replication event), the probability that no mutation occurs is 1 - µ. Since there are two independent lineages leading to any single individual, in order to be ibd mutation could not have occurred in either lineage. This probability in (1-µ) 2. We can now incorporate these new probabilities into the previous formula: F t+1 = {1/2N ef + [1-1/(2N ef )]F t }(1- ) 2 Prob(ibd) Prob(no mut) We can see that without mutation, F always increases over time (---> 1) due to drift (since N ef is in the denominator and drift will act to reduce to inbreeding effective size). However, with mutation in the model, we see that mutation destroys identity by descent. Drift increases ibd : mutation decreases ibd Over time, a population may reach an equilibrium between these two forces where the ibd is kept relatively constant by the opposing forces of drift and mutation. At such an equilibrium, the prob(ibd) is: F eq = 1/[2N ef [1/(1-µ) 2-1] + 1] Using a Taylor s Series Expansion and assume µ << 0 ---> F eq = 1/[4N ef µ + 1]. Let 4N ef µ = θ ---> F eq = 1/( + 1) ; represents this balance between drift and mutation. Therefore, assuming we could see all mutations, the prob(not ibd) = Heterozygosity = 1 - F eq = /( + 1) There are a few problems with this formulation. 1) Even with all the variation that has been found, there appears to be much too little variation to fit the neutral model s expectations. Maynard Smith pointed out that with the above equation for heterozygosity and assuming a mutation rate = 10-5 to 10-6, one would expect H = Way higher than what is typically observed. 2) If we plot the expected values of heterozygosity (prob(not ibd)) under the neutral model, we get the following curve: Any value of H eq is possible depending on the value of θ. Remembering that θ = 4N ef µ, we can see that larger populations are much less likely to be ibd (more polymorphism), as was discussed previously. Heq However, the circled region of the curve shows the range of heterozygosities we tend to observe in nature. As you can see, the range of observed heterozygosities is much narrower than what is expected under the neutral model. Finally, it is interesting to point out that these observed values lie on the most sensitive part of the curve where even a very small change in θ

5 the value of θ results in a very significant change in the observed heterozygosity. Although Kimura s work has been widely influential and is still quite controversial, for these and other reasons the ideas of a strict molecular clock or of strict neutrality are losing favor. Nonetheless, the more basic ideas of the Neutral Model are well established: - many alleles are neutral (functionally equivalent) - drift is a major player in the evolution of genes at the molecular level. Kimura s theory makes another prediction: - the level of polymorphism and the rate of fixation is proportional under neutrality (i.e., fastly evolving genes should show high levels of polymorphism, slowly evolving genes should show low levels). That is, the stronger the functional constraints (i.e., NS acting) the lower the polymorphism and the slower the rate of accumulation of molecular differences (evolution) between taxa/populations. Likewise, the less the constraint, the more polymorphism and the more rapid the rate of molecular evolution. EX) psuedogenes - a functional gene that for some reason was duplicated and only one of them is needed Drift becomes more important as the functionality decreases (neutrality increases). Leads to increased polymorphism and higher rates of molecular evolution. We now have the ability to test this predicted relationship between polymorphism and evolutionary rate in a simple direct fashion. However, before this can be presented, we must consider an alternative method of looking at genetic variation: the coalescent and the idea of gene and haplotype (allele) trees.