barcode reader vb.net source code Types of equilibria: stable, unstable, and neutral. in Software

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Types of equilibria: stable, unstable, and neutral.
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Graphical analysis of mutational equilibrium. The graph of the mutational q equation shows that when the population is perturbed from the equilibrium point (q 0.167), it returns to that equilibrium point. At q values above equilibrium, change is negative, tending to return the population to equilibrium. At q values below equilibrium, change is positive, also tending to return the population to equilibrium.
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Tamarin: Principles of Genetics, Seventh Edition
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IV. Quantitative and Evolutionary Genetics
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20. Population Genetics: Process that Change Allelic Frequencies
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Migration
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the order of 10 5, and equation 20.3 shows that change will be very slow with values of this magnitude. For example, if 10 5, 10 6, and p q 0.5, q (0.5 10 5 ) (0.5 10 6 ) 4.5 10 6, or 0.0000045. It usually takes thousands of generations to get near equilibrium, which is approached asymptotically. As you can see from the low values of mutation rates, it would usually be nearly impossible to detect perturbations to the Hardy-Weinberg equilibrium by mutation in any one generation. The mutation rate can, however, determine the eventual allelic frequencies at equilibrium if no other factors act to perturb the gradual changes that mutation rates cause. Mutation can also affect nal allelic frequencies when it restores alleles that natural selection is removing, a situation we will discuss at the end of the chapter. More important, mutation provides the alternative alleles that natural selection acts upon.
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Migration is similar to mutation in the sense that it adds or removes alleles and thereby changes allelic frequencies. Human populations are frequently affected by migration. Assume two populations, natives and migrants, both containing alleles A and a at the A locus, but at different frequencies ( p N and qN versus p M and qM ), as shown in gure 20.3. Assume that a group of migrants joins the native population and that this group of migrants makes up a fraction m (e.g., 0.2) of the new conglomerate population. Thus, the old residents, or natives, will make up a proportionate fraction (1 m; e.g., 0.8) of the combined population. The conglomerate a-allele frequency, qc, will be the weighted average of the allelic frequencies of the natives and migrants (the allelic frequencies weighted multiplied by their proportions): qc qc mqM qN (1 m(qM m)qN qN)
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(20.8) (20.9)
Diagrammatic view of migration. A group of migrants enters a native population, making up a proportion, m, of the nal conglomerate population.
The change in allelic frequency, a, from before to after the migration event is q qc qN [qN q m(qM m(qM qN)] qN) qN
(20.10) (20.11)
^ We then nd the equilibrium value, q (at q 0). Remembering that, in a product series, any multiplier with the value of zero makes the whole expression zero, q will be zero when either
0 or qM
0; qM
rium. Allelic frequencies in a population under the in uence of migration will not change if either the size of the migrant group drops to zero (m, the proportion of the conglomerate made up of migrants, drops to zero) or the allelic frequencies in the migrant and resident groups become identical. This migration model can be used to determine the degree to which alleles from one population have entered another population. It can analyze the allele interactions in any two populations. We can, for example, analyze the amount of admixture of alleles from Mongol populations with eastern European populations to explain the relatively high levels of blood type B in eastern European populations (if we make the relatively unrealistic assumption that each of these groups is homogeneous). The calculations are also based on a change happening all in one generation, which did not happen. Blood type and other loci can be used to determine allelic frequencies in western European, eastern European, and Mongol populations. We can rearrange equation 20.9 to solve for m, the proportion of migrants: m qc qM qN qN (20.12)
The conclusions we can draw from this model are intuitive. Migration can upset the Hardy-Weinberg equilib-
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