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1 2 3 4 5 6 7 8 Phenotypic value units of pigment Figure 9.5 Phenotypic distributions for a trait determined by two loci with either complete dominance or epistasis. a Due to dominance, the majority of phenotypes are 9 units of pigment and no individuals display phenotypes with 3 or 7 units of pigment. In this example of two diallelic loci, the frequency of heterozygotes is at a maximum because all allele frequencies are V2. In general, total phenotypic variation in the population can be...
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and response to selection calculated for Fig. 9.10, the realized heritability is then This tells us that 40 of the variance in trait values in the parental population was caused by additive genetic variation based on the definition of heritability. Why was there a response to selection Why did increase in value compared to The phenotypic value in the selected group of parents was greater than the rest of the parental population partly due to the alleles that they possessed in their multi-locus...
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that depends on the effective population size Ne and the mutation rate see equation 5.39 . In this view of neutral mutations, polymorphism results from either a high rate of input of mutations even if drift is strong, a long dwell time for each mutation due to a large effective population size even if mutations are infrequent, or intermediate levels of mutation and genetic drift. The neutral theory prediction for polymorphism can be readily compared with polymorphism expected under positive...
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Figure 9.11 Parent-offspring regressions used to estimate heritability h2 under the assumption of strict additivity a or complete dominance b . The resemblance or covariance between the mid-parent phenotypic value and the mean progeny phenotypic value is greater on average with additivity slope 1.0 than with dominance slope 0.667 . The slope of the regression line is equal to the heritability since it measures resemblance of parents and offspring. The mid-parent phenotypic value is the average...
Interact box The textbook website
Throughout this book you will encounter Interact boxes. These boxes contain opportunities for you to interact directly with the material in the text using computer simulations designed to demonstrate fundamental concepts of population genetics. Each box will contain step-by-step instructions for you to follow in order to carry out a simulation. By following the instructions you will get started with the simulation. However, always feel free to use your own imagination and intuition. After...
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for two lineages where t is time in generations. Notice that the constant in the exponential expression equivalent to the a in equation 3.67 Therefore, the exponential distribution approximates the probability of non-coalescence at each time t. To determine the chances that a coalescence event occurred at or before some time, call it TC lt twhere TC is the time to coalescence and t is time scaled in units of 2N generations, the cumulative exponential distribution is used. The cumulative...
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aMates by self-fertilization. bMates by outcrossing. of n sequences is n n - 1 2 and so dividing the sum of dj by this number gives the average number of differences per pair of sequences. The average number of pairwise differences can also be divided by the number of nucleotide sites examined L to express 1 per nucleotide site. Figure 8.11 shows an example computation of 1 for a hypothetical sample of four DNA sequences. In larger samples that may include multiple identical DNA sequences, the...
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between the environments when there is only VG . Environmental variation only VE Fig. 9.6b means that the four genotypes have identical phenotypes but the phenotype changes between the two environments the four genotype lines are not drawn exactly on top of each other so each can be seen . A combination of both genotypic VG and environmental VE variation in phenotype means that the genotypes have different phenotypes and the phenotypes also change between environments Fig. 9.6c . Notice that...
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Figure 3.23 Haploid a and diploid b reproduction in the context of coalescent events. In a haploid population, the probability of coalescence is dashed lines whereas the probability that two lineages do not have a common ancestor in the previous generation is 1 - solid lines . In a diploid population, the two gene or allele copies in one individual in the present time have one ancestor in the female population Nf and one ancestor in the male population Nm . Coalescent events in the diploid...
Problem box Applying the binomial formula
Two independent laboratory populations of the fruit fly Drosophila melanogaster were observed for two generations. The populations each had a size of N 24 individuals with an equal number of males and females. In the first generation, both populations were founded with fA p 0.5. In the second generation, one population showed fA p 0.458 and the other fA p 0.521. What are the chances of observing these allele frequencies after one generation of genetic drift Shifting our perspective, we can use...
Fundamentals of natural selection
Translating Darwin's ideas into a model. Natural selection as differential population growth. Natural selection with clonal reproduction. Natural selection with sexual reproduction and its assumptions. simple population growth model. If a population is assumed to have no upper limit in its size, the number of individuals one generation in the future Nt 1 is a product of the number of individuals present now Nt multiplied by the finite rate of increase of the population X pronounced lambda to...
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to estimate in practice because 0 cannot be estimated in the ancestral species as it does not exist any longer. However, the main point of this model is not to provide a practical test of the molecular clock. Instead, the model shows how R t gt 1 is not necessarily strong evidence to reject a constant rate of substitution. One cause of R t gt 1 is that the Poisson process accurately describes the substitution process but that substitution rates are not constant. Alternatively, the Poisson...
Problem box Estimating Ne from observed heterozygosity over time
Use the data provided in Table 3.5 to estimate N'e over four generations for each of the 10 replicate populations. Heterozygosity in the first generation was 0.5 in all populations since initial allele frequencies were p q 0.5. Does the average estimate of N'e better match what is expected for a fluctuating population of 100-10-50-100 There are an array of methods that have been employed to estimate effective population size from genetic data using various estimators of the variance and...
Interact box Genetic drift simulated with a Markov chain model
PopGene.S2 can be used to simulate genetic drift with a Markov chain. Launch PopGene.S2 and click on the Drift menu and then select Markov Process. This simulation module requires that you enter parameter values one at a time, since values of some parameters affect the values that other parameters can take. Step 1 Start by entering 2 under Population size in the upper left corner of the simulation window. This means that there are two diploid individuals or four alleles in each population. Then...
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In this table, the total frequency is just the frequency of each parental mating pair taken from the parental mating frequency table. We now need to partition this total frequency of each parental mating into the frequencies of the three progeny genotypes produced. Let's look at an example. Parents with AA and Aa genotypes will produce progeny with two genotypes half AA and half Aa you can use a Punnett square to show this is true . Therefore, the AA x Aa parental matings, which have a total...
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Figure 6.4 The change in genotype and allele frequencies caused by viability selection against the aa genotype exhibiting the recessive phenotype. The top panel shows the change in genotype frequencies over time and the bottom panel shows the frequency of the dominant allele A over time. The colored, dashed line in the bottom panel corresponds to the allele frequencies in the top panel. Because of changes in genotype frequency caused by natural selection, the frequency of the dominant allele...
Mendels model of particulate genetics
Mendel's breeding experiments. Independent assortment of alleles. Independent segregation of loci. Some common genetic terminology. In the nineteenth century there were several theories of heredity, including inheritance of acquired characteristics and blending inheritance. Jean-Baptiste Lamarck is most commonly associated with the discredited hypothesis of inheritance of acquired characteristics although it is important to recognize his efforts in seeking general causal explanations of...
Impacts of inbreeding on genotype and allele frequencies
Let's develop an example to understand the impact of inbreeding on genotype and allele frequencies in a population. Under complete positive assortative mating or selfing, individuals mate with another individual possessing an identical genotype. Figure 2.12 diagrams the process of positive genotypic assortative mating for a diallelic locus, following the frequencies of each genotype through time. Initially, the frequency of the heterozygote is H but this frequency will be halved each...
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Initial allele frequency Figure 3.14 Average time that an allele segregates, takes to reach fixation, or takes to reach loss depending on its initial frequency when under the influence of genetic drift alone. Alleles remain segregating persist for an average of 2.8N generations when their initial frequency is 1 2. Fixation or loss takes up to an average of 4N generations when alleles are initially very rare or nearly fixed, respectively. Since these are...
Hi Hs Ht Heterozygosity Fst
Figure 4.9 The distribution of FST values for 1000 replicate neutral loci in a finite island model of 200 subpopulations where each subpopulation contains 10 individuals and the rate of gene flow is 10 of each subpopulation m 0.10 . In the distribution, 95 of the replicate loci show FST values between 0.1459 and 0.2002 whereas the average of all 1000 replicate loci is 0.1586 based on the average of HT and HS then used to calculate FST . Replicate loci exhibit a range of Fst values since allele...
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allele frequencies since it is easier to summarize a diallelic locus in a population as two allele frequencies rather than three genotype frequencies. But remember that genotype frequencies are affected by genetic drift too, and genotype frequencies can always be obtained by multiplication given allele frequencies under the assumption of random mating. Up to this point, the beakers of micro-centrifuge tubes and computer simulations only considered cases of alleles at equal initial frequencies p...
The fixation index and heterozygosity
The fixation index F measures deviation from Hardy-Weinberg expected heterozygote frequencies. Examples of mating systems and F in wild populations. Observed and expected heterozygosity. The mating patterns of actual organisms frequently do not exhibit the random mating assumed by Hardy-Weinberg. In fact, many species exhibit mating systems that create predictable deviations from Hardy-Weinberg expected genotype frequencies. The term assortative mating is used to describe non-random mating....
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positions of each pedigree fAB and at the same time through the parents in the right positions of each pedigree fBD , giving fACfBD as the probability that the genotype is identical by descent. Alternatively, two alleles could be identical by descent through the parents in the left and right positions of each pedigree fAC and through the two parents in the right and left positions of each pedigree fBD , giving fAD fBC as the probability that the genotype is identical by descent. Since both...
The Mendelian basis of quantitative trait variation
10.1 The connection between particulate inheritance and quantitative trait variation Establishing a scale for genotypic values. Phenotypic values as population averages. Why we can neglect environmental variation This chapter will develop the concepts needed to understand the detailed connections between quantitative trait variation and particulate inheritance. Although the components of quantitative trait variation were described in Chapter 9 as population-level phenomena, the variance is...
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expected frequency of each of the three genotypic values within the M1 M1 marker-locus genotype is then the product of the genotype frequency and the corresponding genotypic value. The portion of the mean genotypic value for the entire F2 population due to those individuals with an M1 M1 marker genotype, call it GMpm , is the sum of the genotype-frequency-weighted genotypic values for each 0TL genotype associated with an M1 M1 marker genotype
Are these genotype frequencies consistent with inheritance due to one locus
Figure 2.10 Corn cobs demonstrating yellow and purple seeds that are either wrinkled or smooth. For a color version of this image see Plate 2.10. Figure 2.10 Corn cobs demonstrating yellow and purple seeds that are either wrinkled or smooth. For a color version of this image see Plate 2.10. Caenorhabditis elegans, are hermaphrodites that can mate with themselves. There are also cases of disassortative mating, where individuals with unlike genotypes have a higher probability of mating. A classic...
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Most coalescent events for a sample of lineages occur in the recent past with only a few lineages having long times to coalescence. The effective population size Ne can be defined for lineage branching models by reference to the probability of two randomly sampled gene copies descending from the same ancestral copy. This probability decreases as the effective size of populations grows larger. The coalescent model leads to definitions of the inbreeding effective population size that are...
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Figure 2.12 The impact of complete positive genotypic assortative mating like genotypes mate or self-fertilization on genotype frequencies. The initial genotype frequencies are represented by D, H, and R. When either of the homozygotes mates with an individual with the same genotype, all progeny bear their parent's homozygous genotype. When two heterozygote individuals mate, the expected genotype frequencies among the progeny are one half heterozygous genotypes and one quarter of each...
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Figure 2.3 Mendel self-pollinated indicated by curved arrows the F2 progeny produced by the cross shown in Figure 2.2. Of the F2 progeny that had a yellow phenotype three-quarters of the total , one-third produced all progeny with a yellow phenotype and two-thirds produced progeny with a 3 1 ratio of yellow and green progeny or three-quarters yellow progeny . Individuals are represented by diamonds since pea plants are hermaphrodites. Figure 2.3 Mendel self-pollinated indicated by curved arrows...