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Meiotic drive at single locus with two alleles, A and a. Figure 13.3. Meiotic drive at single locus with two alleles, A and a. To see if meiotic drive is an evolutionary force, we calculate the change in allele frequency as Ap p'- p GAa (k - 1) (13.9) Equation 13.9 tells us that meiotic drive is an evolutionary force that will change allele frequencies whenever GAa > 0 and k 2. The first condition relates to a specific individual-level genotype frequency (G Aa > 0) and reflects...

Basic Premises Of Population Genetics

Microevolutionary mechanisms work upon genetic variability, so it is not surprising that the fundamental premises that underlie population genetic theory and practice all deal with various properties of deoxyribonucleic acid (DNA), the molecule that encodes genetic information in most organisms. A few organisms use ribonucleic acid (RNA) as their genetic material, and the same properties apply to RNA in those cases. Indeed, the theory of microevolutionary change stems from just three premises...

P

Adaptive surface for one-locus, two-allele model with fitness of AA 1, Aa 0.5, and aa 0.9. The surface represents a plot of w under the assumption of random mating against p, the frequency of the A allele. A line at p 0.444 indicates the minimum value of w. Arrows indicate the direction of evolution induced by natural selection on either side of this minimum value. which violates equation 11.22. This inability of natural selection to allow a climb downward in a fitness surface...

Box 31 The Correlation Of Uniting Gametes

In order to show that X is the covariance among uniting gametes, we must first define a random variable to assign to the gametes. In our simple genetic model, the gametes bear only one of two possible alleles, A and a. Let x be a random variable that indicates the allele borne by a male gamete such that x 1 if the male gamete bears an A allele and x 0 if the male gamete bears an a allele. Similarly, let y be a random variable that indicates the allele borne by a female gamete such that y 1 if...

Balance Of Gene Flow And Drift

Recall from Chapter 4 that to measure the impact of genetic drift upon identity by descent, we started with equation 4.3 where N is replaced by the inbreeding effective size for nonideal populations. To examine the balance between drift and mutation, we modified the above equation to yield equation 5.4 Because gene flow and mutation behave in an analogous manner with respect to genetic variation within a local deme, a similar modification of equation 4.3 can be used to address the following...

Gene Trees Versus Allele or Haplotype trees

With mutation in the model, a distinction can now be made between gene trees and haplotype trees. Gene trees are genealogies of genes. They describe how different copies at a homologous DNA region are related by ordering coalescent events. Figure 5.12a shows a simple gene tree for a sample of six copies of an homologous DNA region. This figure is a repeat of the gene tree shown in Figure 5.9, but now we allow some of the DNA replication events to have experienced mutation. Looking back through...

Founder And Bottleneck Effects

As shown in the previous section, genetic drift causes its most dramatic and rapid changes in small populations. However, even a population that is large most of the time but has an occasional generation of very small size can experience pronounced evolutionary changes due to drift in the generation of small size. If the population size grows rapidly after a generation of small size, the increased population size tends to decrease the force of subsequent drift, thereby freezing in the drift...

Ww

Where W Y,i zi vi is the average fitness of AA across all habitats as weighted by zygotic inputs. Note that equation 14.7 depends only upon the arithmetic means of fitnesses across habitats and not the harmonic means. Indeed, there is really no difference at all between equations 14.7 and 11.5 because all fitnesses assigned to genotypes in Chapter 11 were arithmetic averages across all individuals bearing that genotype that is, fitness is a geno-typic value which explicitly averages over all...

Zr2113

Recall from Chapter 8 that the genotypic deviation of a phenotype is the genotypic value minus the overall population mean. Hence, the terms Wj w in the numerator of equation 11.3 are the genotypic deviations for the phenotype of fitness. Recall also from Chapter 8 (equation 8.8) that the conditional frequency of an A-bearing gamete being found in genotype AA is zAA p and in genotype Aa is 1 2zAa p. Hence, equation 11.3 can be expressed as The portion of equation 11.4 in the brackets is the...

Interaction Of Natural Selection With Genetic Drift

Genetic drift induces random changes in allele frequency, so the second term in equation 12.2 when applied to drift is expected to vary in sign at random from generation to generation. Hence, unlike gene flow, there is no consistent enhancement or retardation of the effects of selection with genetic drift. To R. A. Fisher, this meant that genetic drift would play little role in shaping adaptive outcomes unless the population size is extremely small or, as we will see below, in dealing with the...

Fundamental Theorem Of Natural Selection Unmeasured Genotypes

Equation 11.5 is the fundamental equation describing natural selection for a measured genotype at a single locus. Given that many adaptive traits are polygenic but with the underlying loci being unknown, Fisher (1930) elucidated many properties of natural selection using the theory of the quantitative genetics of unmeasured genotypes (Chapter 9). His central result is summarized in an equation that is the unmeasured genotype analogue of the measured genotype equation 11.5. Fisher called this...

Effective Population Size

As seen above, finite population size has many important evolutionary consequences increasing the average amount of identity by descent, increasing the variance of allele frequencies through time and across populations, and causing the loss or fixation of alleles. As also shown by the above examples and simulations, the rate at which these effects occur is roughly inversely proportional to population size. In an idealized population, we can derive a precise quantitative relationship between...

Multiple Patterns in Nested Clade Analysis

No single test statistic discriminates between recurrent gene flow, past fragmentation, and past range expansion in the nested-clade analysis. Rather, it is a pattern formed from several statistics that allows discrimination. Also, as indicated in the above discussion, many different patterns can sometimes lead to the same biological conclusion. Finally, as pointed out with the impala example (Figure 7.6), sometimes the pattern associated with significant clade and nested-clade distances is an...

Some Lessons from the Past Inversion Trees and Networks

The concept of a haplotype tree is not a new one in population genetics but actually goes back to the very origins of the balanced school. Recall that this school arose from the work of Sturtevant and Dobzhansky on cytogenetic variation observable in the polytene chromosomes of Drosophila. As mentioned previously, polytene chromosomes in Drosophila provide many bands or landmarks in the Drosophila genome (see Figure 5.2), so these polytene chromosomes provided the first high-resolution genetic...

Hardyweinberg Model

One of the simplest models of population genetics is the Hardy-Weinberg model, named after two individuals who independently developed this model in 1908 (Hardy 1908 Weinberg 1908). Although this model makes several simplifying assumptions that are unrealistic, it has still proven to be useful in describing many population genetic attributes and will serve as a useful base model in the development of more realistic models of microevolution. Hardy was an English mathematician, and his...

Genetic Impact of Gene Flow

We have already seen that allele frequencies are altered when gene flow occurs between genetically distinct populations. Gene flow therefore can be an evolutionary force. In this section, we will see that gene flow causes evolution in a nonrandom, predictable fashion. To show this, we will return to our simple model of symmetrical gene flow given in Figure 6.1. Starting with the initial populations prior to gene flow, their genetic distinctiveness is measured by the difference in their allele...

Integrating Haplotype Tree Inferences Across Loci Or Dna Regions

No single locus or DNA region can capture the totality of a species' population structure and evolutionary history. Therefore, ideally many loci or gene regions should be examined. Moreover, Templeton (1998c, 2004a) examined several examples where the nested-clade analysis was applied to data sets for which much prior information existed about the organisms' recent evolutionary history. These examples reveal that the nested-clade inference key works well, but sometimes mistakes are made, mostly...

Theory Of Hemoglobin Genotype

Protein electrophoresis of genotypic variation associated with A and S alleles at hemoglobin ,6-chain locus in humans. The buffer environment is such that the hemoglobin molecule is disassociated into its component a and , chains and the , chains have a charge difference depending upon the animo acid they have at the sixth position of the amino acid chain. tetramer consisting of two a-globin chains and two ,-globin chains. Under the appropriate buffer conditions, the hemoglobin...

Example Of Hardyweinberg

As an illustration of the application of this model, consider a human population of Pueblo Indians scored for genetic variation at the autosomal blood group locus MN (Figure 2.3). This locus has two common alleles in most human populations, the M allele and the N allele. Genetic variation at this locus determines your MN blood group type, with a very simple genotype-to-phenotype mapping MM genotypes have blood group M, MN genotypes have blood group MN, and NN genotypes have blood group N....

Interaction Of Natural Selection With Mutation

Mutation is the source of new allelic variation and directly changes allele frequencies by converting a copy of one allele (thereby decreasing its frequency) into another type of allele (thereby increasing its frequency). Because mutation rates are generally very small, mutation by itself seems to be a minor cause of change in allele frequencies. But Equation 12.3 has already warned us that seemingly minor forces can have major evolutionary implications when combined with natural selection, as...

Box 53 Neighborjoining Method Of Tree Estimation

Step 1 in neighbor joining is the calculation of the net molecule genetic distance of each haplotype from all other haplotypes in the sample. Letting dik be the molecule genetic distance between haplotype i and haplotype k, the net molecule genetic distance for haplotype i is where n is the number of haplotypes in the sample. The net distances are used to evaluate violations of the molecular clock model. For example, suppose one haplotype lineage experienced a much higher rate of accumulation...

Sickle Cell Anemia As Example Of Natural Selection

One of the textbook classics of natural selection, selection at the human j -Hb locus that codes for the j chain of adult hemoglobin, illustrates the fact that selection is not survival of the fittest and the importance of understanding natural selection in terms of average excesses. Although this story is usually told starting in Africa, we will start the story thousands of kilometers away, in Southeast Asia. The people living in the coastal areas of Southeast Asia and the islands that now...

Coalescence with Mutation

The basic coalescent model given above ignores mutation. Now we want to include both genetic drift and mutation as potential evolutionary forces. Consider first a sample of just two genes. By adding mutation, the two gene lineages could coalesce, mutate, or do neither in any given generation. As before, the probability that these two genes coalesce in the previous generation is 1 (xNef), and the probability that they do not coalesce in the previous generation is 1 - 1 (xNef). Assuming an...

Pleiotropy and Epistasis

A gene can have both pleiotropic and epistatic effects, For example, we have already seen that the genetic variation at the ApoE locus affects many phenotypes and displays many epistatic interactions. The complexity of this genetic architecture centered on ApoE is greatly augmented by the fact that the epistatic interactions displayed by ApoE differ greatly for the various pleiotropic phenotypes. Thus, we have already seen strong epistasis between ApoE and LDLR for the phenotype of total serum...

Adaptation As Polygenic Process

One way humans adapted to malaria in wet, tropical Africa was through the A S polymorphism at the j-Hb locus, an adaptation that confers malarial resistance to only about 20 of the population. In general, many loci can contribute to how an individual responds to its environment in determining the phenotype of fitness. As a consequence, adaptation to a new environment is usually a polygenic process, with genetic variation at many loci responding to natural selection. This is certainly the case...

W

Y y(y 1)(y 2) (1) (A2.11) Note that a, b, and n are the parameters of this probability distribution. The random variable can take on any integer value between zero and the minimum of n and a, inclusively. The mean and variance of the hypergeometric are Binomial Distribution. If the size of the population being sampled (N) is much larger than the sample size (n) (formally, the limit as N n to), the hypergeometric distribution converges to the form f (x p, n) (nx)pxqn x (A2.13) where the random...

Disassortative Mating

Disassortative mating is the preferential mating of individuals with dissimilar phenotypes. This means that there is a negative correlation between the phenotypes of mating individuals. For example, the major histocompatibility complex (MHC), mentioned in Chapter 1, is found not only in humans but in mice as well. In mice, genetic variation in MHC induces odor differences. There is disassortative mating at this gene complex in mice that is due to olfactory discrimination of potential mates...

Assortative Mating

System-of-mating inbreeding (f) represents a deviation from random mating in which the biological relatedness among individuals affects their probability of becoming mates. Individuals can also have their probability of mating influenced by the traits or phenotypes displayed by potential mates. One such deviation from random mating based on individual phenotype is called assortative mating. Under assortative mating, individuals with similar phenotypes are more likely to mate than expected under...

Fundamental Equation Of Natural Selection Measured Genotypes

We will first explore the consequences of natural selection through a simple extension of the one-locus, two-allele model introduced in Chapter 2. As before, we need to go through a complete generation transition, ending up in the next generation at a comparable point to the starting generation. In the models used in Chapter 2 we went from parental genotypes to gametes via Mendelian probabilities, then to offspring genotypes through the mechanisms of uniting gametes (population structure). To...

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Molecule and the greater the chance of two or more hits at any one nucleotide site (Tem-pleton et al. 1992). This observation implies that there is information about evolutionary history not only in the total number of mutational events but also in how homoplasy is allocated among the inferred branches. For example, we saw that there are four equally parsimonious ways of breaking the loop shown in Figure 5.17a. However, consider breaking the loop between the two haplotypes at the top with the...

Pxy i

Although inbreeding as measured by f alters the genotype frequencies from Hardy-Weinberg (equations 3.2), it does not cause any change in allele frequency. The frequency of the A allele in the final generation in Table 3.1 is p' 1 x (p2 + pqf) +1 2 2pq(1 - f) p2 + pqf + pq(1 - f) p2 + pqf + pq - pqf p2 + pq p(p + q) p Because the allele frequencies are not changing over time in Table 3.1, inbreeding as measured by f is not an evolutionary force by itself at the single-locus level (that is,...

Haplotypes

Haplotypes are defined by the genetic state of many polymorphic sites within a single DNA molecule. Haplotypes are usually defined for relatively small genetic regions, and many of these regions have low rates of or even no recombination. Haplotypes in such DNA regions therefore retain their historical configuration of nucleotide sites for many generations or even throughout their entire evolutionary existence in time. The persistence of their original evolutionary state through time serves as...

Wahlund Effect And Fstatistics

We have just seen how yet another inbreeding coefficient based upon the concept of identity by descent enters into the population genetic literature, but this time as a measure of how the balance of drift and gene flow influences identity by descent and coalescent times within and between demes in a subdivided species. We also saw in Chapter 4 that genetic drift influences many genetic parameters besides identity by descent, including the variance of allele frequencies across isolated replicate...

E P p2 f1 p p2r n ai 2pXa111 pnX a2 1 dp

F 1 Jo T(X + 1)r(n - X + 2) It turns out that the estimator that minimizes the expected squared-error loss is the Pitman estimator in this case. We can also test hypotheses with the posterior distribution. For example, to test the hypothesis that p is < 0.25, we can find the probability tail from 0-0.25 of the posterior distribution. For the three posterior distributions shown in Figure A2.2, these tail probabilities are 0.115, 0.127, and 0.009, so only in the last case (the one with the...

Inbreeding

In its most basic sense, inbreeding is mating between biological relatives. Two individuals are related if among the ancestors of the first individual are one or more ancestors of the second individual. Because of shared common ancestors, the two individuals could share genes at a locus that are identical copies of a single ancestral gene (via premise 1 DNA can replicate). Such identical copies due to shared ancestry are said to be identical by descent. In contrast, the same allele can arise...

Esh

Evolutionary tree of inversion types found on third chromosome of individuals sampled from race A and race B now considered species, as explained in the text of D. pseudoobscura as estimated through maximum parsimony by Sturtevant and Dobzhansky 1936 with subsequent addition inversion data. Each line in the tree represents a single inversion mutation, with the exception of the dashed line connecting hypothetical A to the banding patterns found in the closely related species, D....