## Gene genealogies and the coalescent model

Modeling the branching of lineages to predict the time to the most recent common ancestor. At this point in the chapter we need an interlude in the discussion of genetic drift and effective population size to develop a new approach based around lineage branching or gene genealogy. Initially, it is necessary to introduce some basic terminology and concepts used in this approach. Although it may not be evident at first, the lineage-branching approach to population genetics has a great deal in...

## The diffusion approximation of genetic drift

The Markov chain model has discrete allelic states and time advances from the initial conditions in individual, discrete generations, as is the case in actual biological populations. This discrete step process can be approximated using mathematical expressions where time and allele frequency are continuous variables. This class of model is based on the processes of molecular diffusion and so is termed the diffusion approximation of genetic drift (often called the diffusion equation) first...

## Box Protein locus or allozyme genotyping

Determining the genotypes of individuals at enzymatic protein loci is a rapid technique to estimate genotype frequencies in populations. Protein analysis was the primary molecular genotyping technique for several decades before DNA-based techniques became widely available. Alleles at loci that code for proteins with enzymatic function can be ascertained in a multi-step process. First, fresh tissue samples are ground up under conditions that preserve the function of proteins. Next, these protein...

## Parameters and parameter estimates

While developing the expectations of population genetics in this book, we will most often be working with idealized quantities. For example, allele frequency in a population is a fundamental quantity. For a genetic locus with two alleles, A and a, it is common to say that p equals the frequency of the A allele and q equals the frequency of the a allele. In mathematics, parameter is another term for an idealized quantity like an allele frequency. It is assumed that parameters have an exact...

## Genetic populations

Genetic versus geographic organization of populations. Isolation by distance and divergence of populations. Direct and indirect measures of gene flow. The expectation that genotypes will be present in Hardy-Weinberg frequencies, covered in detail in Chapter 2, depends on the assumption of random mating throughout a population. Implicit is the view that a population is a single entity where processes such as mating and movement of individuals are uniform throughout, a condition often called...

## D d ttxt Jxt dxdx

We can also substitute the flux in allele frequency from equation 3.27 (using x to represent p and 1 - x to represent q) With only random sampling error acting to change allele frequency, (M(x)dt 0), this rearranges to the diffusion equation for genetic drift (x,t) dXI x(1 - x) (x,t)l (3.39) The diffusion equation predicts the probability distribution of allele frequencies in many populations over time and some examples are given in Fig. 3.13. Compare Fig. 3.13 with Fig. 3.10 and it is apparent...

## Interact box Continentisland model of gene flow

PopGene.S2 contains a module to simulate the continent-island model of gene flow. In PopGene. S2 click on the Gene Flow and Subdivision menu and then select Continent-Island model of migration. The simulation window allows you to set allele frequencies in the island and continent, the rate at which island alleles are replaced by continent alleles (or the migration rate) and the number of generations to simulate. Enter the parameters of pC 0.9, pI 0.1, m 0.1, and 100 generations to run. Before...

## Breeding effective population size Nb

The number of individuals found in a genetic neighborhood defined by the variance in gamete dispersal. Deme The largest area or collection of individuals where mating is (on average) random. Genetic neighborhood An area or subunit of a population within which mating is random. Isolation by distance Decrease in the probability of mating and dispersal of gametes as physical distance increases. In a classic study, Schaal (1980) estimated the breeding effective population size in Texas bluebonnets...

## Interact box Build your own coalescent genealogies

Building a few coalescent trees can help you to understand how the exponential distribution is put into practice to estimate coalescence times as well as give you a better sense the random nature of the coalescence process. You can use a Microsoft Excel spreadsheet at the textbook website that has been constructed to calculate the quantities necessary to build a coalescent genealogy. The spreadsheet contains the cumulative exponential distributions for a time interval passing without...

## Growing or shrinking populations

TreeToy is a java applet that simulates genealogies for neutral alleles in populations that are growing in size through time. The lineages experience mutations with a rate that depends on 0 4Ne (called Theta0 in the simulation for 0 at time zero since Ne changes over time). The simulation displays the genealogy along with the mismatch distribution and the frequency histogram of each of the haplotypes in the population. The simulation requires values for the number of lineages in the genealogy...

## Parallelism between drift and inbreeding

Autozygosity due to sampling in a finite gamete population. The relationship between the fixation index (F) and heterozygosity (H). Decline in heterozygosity over time due to genetic drift. Heterozygosity in island and mainland populations. The chapter up to this point has focused on population size and genetic drift. This section will demonstrate that finite population size can also be thought of as a form of inbreeding. In large populations with random mating, chance biparental inbreeding is...

## Interact box Genetic drift

Genetic drift can be simulated with either Populus or PopGene.S2. Try using Populus and following the instructions here. Under the Model menu, select Mendelian Genetics and then Genetic Drift. Make sure the Monte Carlo tab is selected. The simulation dialog has entry fields for Population Size (N) and Number of Loci (or replicates). Number of generations shown in the graphs can be specified as 3N or a fixed number of generations (Other ) with radio buttons (the program will automatically set...

## Interact box xtest

The program PopGene.S2 (refer to the link for Interact box 2.1 to obtain PopGene.S2 if necessary) can be used to carry out a x2 test for one locus with two alleles under the null hypothesis of Hardy-Weinberg genotype frequencies. Launch PopGene.S2 and select Chi-square test under the Allele and Genotype Frequencies menu. Input the observed genotype frequencies in Table 2.4 to confirm the calculations and x2 value. Test the null hypothesis of Hardy-Weinberg genotype frequencies for these data...

## Problem box answer

Each of the values in the transition matrix is obtained using the binomial formula. The chance that a population at fixation or loss transitions to an allele frequency different than 1 or 0, respectively, is always 0. The chance of transitioning from one to four A alleles is identical to the chance of transitioning from three to no a alleles, since the number of A alleles is four minus the number of a alleles. Using this symmetry permits two columns to be filled out after performing...

## Info

Selection steadily changed oil content to about 22 in the high line and to 0 in the low line. Response to selection was similarly linear for protein content, starting at 10.9 and reaching 32.1 in the high line and 4.2 in the low line. The Illinois Long-Term Selection experiment shows that response to selection is relatively steady and linear over a long period of time. (Slight fluctuations in the mean phenotype over time may be explained by some variation in the selection differential each...

## Gametic disequilibrium under both recombination and natural selection

To simulate the combined action of recombination and natural selection on gametic disequilibrium, try the program Populus, which can be obtained by following the link on the text website. In the Java version of Populus, use the Natural Selection menu to select the Two-Locus Selection simulation. Set pAB pab 0.5 and pAb paB 0.0 as a case where there is maximum gametic disequilibrium initially. Use fitness values of wAaBb 1, all others 0.5 and wAAbb waaBB 1, all others 0.5 to generate strong...

## Jrd

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...

## 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...

## 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...

## Mendels model of particulate genetics

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...

## N

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

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...

## Are these genotype frequencies consistent with inheritance due to one locus with three alleles or two loci each with

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...