MIT OpenCourseWare http://ocw.mit.edu 6.047 / 6.878 Computational Biology: Genomes, Networks, EvolutionFall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.6.047 LECTURE 11, MOLECULAR EVOLUTION/COALESCENCE/SELECTION/KAKS OCTOBER 09, 2008 1. Introduction Evolution is the shaping of phenotypic and genotypic variation by natural selec-tion. The relative importance of selection and mutation has been a long standing question in population genetics. And, we’d like to understand the relative impor-tance of each of these forces. In particular, we’d like to know which genes are undergoing active selection. neutrality tests are a key tool for addressing this ques-tion. There are many different evolutionary forces that might cause deviations from neutrality such as differential mutation rates, recombination, population structure, drift in addition selection and others. Therefore, it is easier to develop test of neu-trality rather than directly searching for signatures of selection. From a historical perspective, most of these ideas were developed theoretically in the last century. And only in the last few decades that we were able to gather data to directly test these theories. 1983 is the first time that we have molecular polymorphism data. First, we need to understand the neutral model, focusing on inheritance alone. Historically, this area of study dates back to Darwin’s time. Scientists in the 1860s believed in blending inheritance which stated that each organ was determined by a different gemmule. In this model, children inherit a blending of their parents’ corresponding gemmules, so if mom had a “yellow” gemmule and dad had a “blue” gemmule, then baby would inherit a “greenish” gemmule. As Darwin’s critics pointed out, this model predicts that everyone’s gemmules blend and blend until all gemmules are a drab shade of gray, losing all genetic diversity. Specifically, Fleeming Jenkins in 1867 showed that the total genetic variation will be halved assuming this mode of inheritance. However, Mendel had developed a theory particulate inheritance around the same time but was not widely recognized. Only in the beginning of 20th cen-tury, researchers appreciated the importance of his results. Mendel’s more accurate model, developed as a result of his famous study of pea plants, states that each trait is determined by two corresponding alleles, which together determine a per-son’s phenotype. Offspring receive one allele from each parent, selecte d randomly from the parent’s two copies. The allele model is quite close to what actually happ e ns when gametes pair during meiosis, and correctly predicts the observed phenomena of dominance and recessivity. These ideas are summarized as the Law of Segregation and the Law of Independent Assortment. 12 CAN CENIK, MATTHEW INCE, QU ZHANG 2. Hardy-Weinberg Law A natural question to ask was how genetic variation changes under the particulate theory of inheritance. The Hardy-Weinberg Law (1908) answers this question in an ideal population. This model assumes infinite population size, completely random mating, and an absence of selection, mutation, or migration. Considering two versions A and a of an allele, let u0, v0, and w0 be the respective frequencies of genotypes AA, Aa, and aa, respectively. Then the frequency of A is p = u0 + v0/2, and the frequency of a is q = w0 + v0/2. A Punnett square predicts that after a single generation, we observe frequencies u = p2 , v = 2pq, and w = q2, and that these frequencies remain fixed over successive generations. Because q = 1 − p, our entire model is characterized by a single parameter p. In practice, several of the Hardy-Weinberg Law’s assumptions are hardly ever met but it still provides a general framework for thinking about genetic variation. Consider slide 3 page 2 as an example of the application of the HW Law, and let us denote recessive allele causing sickle-cell anemia by s. We observe that many more pe ople have genotype Ss than is expected under the HW equilibrium. This discrepancy is indeed due to selection, because people with one copy of s possess immunity to the dreaded tropical disease malaria. We next study two different approaches to neutral theory: the prospective ap-proach of classic population genetics, and the retrospective approach focusing on the coalescent. 3. Prospective method 3.1. Neutral Theory History. In the 1960s, people thought that all mutations differ in their fitness, so selection would rule out bad mutations and fix good mu-tations, with variation kept by balancing selection. So when Neutral Theory was first proposed by Motoo Kimura, a Japanese population geneticist, it was shocking and controversial at the time. Having a background in physics, Kimura incorpo-rated diffusion approximations to the field of population genetics, focusing on finite populations. The main premise of Neutral Theory is that most of the mutations are neutral or nearly neutral, and the change in allelic frequencies is a result of random genetic drift in finite populations (Slide 6, Page 2). All the mutations will eventually become extinct or fixed by this process unless directly opposed by other evolutionary forces. Hence, the genetic variation seen in a population are generally caused by mutations which are on their way to fixation/extinction (Slide 1, Page 3). As a consequence, if one knows the rate of mutations and how quickly they fix in the population, one could have a good idea of how the allelic distribution in the population should be. 3.2. Ewens Sampling Formula. In 1972, Warren Ewens proposed the famous Ewens Sampling Formula, which is based on diffusion theory and introduced the infinite alleles model. The infinite alleles model claims that there are an infinite number of state s into which an allele can mutate, so each mutation generates a unique allele. Ewens used the concept of identity by descent (IBD) as opposed to identity by kind. IBD is a concept that is defined with respect to the allele in the ancestor. Imagine that you and your sibling received the same copy of chr7 from your mother. In this particular chromosome even if there