In a population of Garden-digging Armadillos in HW equilibrium, the C allele for

Question

In a population of Garden-digging Armadillos in HW equilibrium, the C allele for long claws is completely dominant to the c allele for clawlessness. Extensive sampling of this population showed 9% of the armadillos to be clawless.

a. What are the gene and genotypic frequencies of the C locus?

b. On closer examination, wildlife biologists discover that one in four of the clawless armadillos also has webbed feet. A third allele (cw) for webbed feet causes this condition. It is completely recessive to both the clawed (C) and clawless (c) alleles. What are the gene and genotypic frequencies in the population now?

Explanation / Answer

In genetics the allelic frequency or gene frequency is the proportion that is observed of a specific allele with respect to the set of those that can occupy a determined locus in the population. If the frequencies remain constant from one generation to the next, the population is not experiencing evolutionary change, and is said to be in gene balance. However, changes in allele frequencies in successive generations imply that evolution has occurred. The results of the gene frequency analysis are expressed in proportions, so the sum of the frequencies of the alleles studied for the locus is equal to one: p + q = 1,

Where p is the gene frequency of the dominant allele and q, that of the recessive allele.

The proportion in which the genotypes of a population are observed for a given locus is called genotypic frequency and its theoretical expectation in a population that is in equilibrium are the terms of the development of the square of a binomial. If p denotes the allelic frequency of one allele (example "A") and q as the frequency of the other allele of the same gene (example "a"), we have that the genotypic frequencies will be p2 for the "AA" genotype, 2pq for the heterozygote "Aa" and q2 for "aa", such that: (p + q) 2 = p2 + 2pq + q2

In this case it is indicated that it is a population of Armadillos excavators of orchards in equilibrium HW; the Hardy-Weinberg law states that in a sufficiently large population, in which matings occur at random and that are not subject to mutation, selection or migration, the genotype and genotype frequencies remain constant from one generation to another, once a state of equilibrium has been reached that in autosomal loci is reached after a generation.

It is said that a population is in equilibrium when the alleles of the polymorphic systems maintain their frequency in the population through the generations. To achieve genetic balance, according to the English mathematician Hardy and the German physician Weinberg, several conditions must be met:

• The population must be infinitely large and random matings (panmictics).

• There should be no selection, that is, each genotype under consideration must be able to survive as well as any other (there is no differential mortality) and each genotype must be equally efficient in the production of progeny (there is no differential reproduction).

• There must be no gene flow, that is, it must be a closed population where there is no immigration or emigration.

• There should be no mutations, except that the mutation occurs in the opposite direction with equivalent frequencies, for example, A mutates towards A 'with the same frequency with which A' mutates towards A.

Any demonstration of the Hardy-Weinberg law implies the basic principle of probability theory, that is, that the probability of simultaneous occurrence of two or more independent events is equal to the product of the probabilities of each event. Normally, the frequency of each allele represents its probability of occurrence. So, to obtain the probability of a given genotype in the progeny, the frequencies of the alleles involved are multiplied together.

Given the gene frequencies (allelic) in the gene pool of a population, it is possible to calculate (based on the probability of gamete binding) the expected frequencies of progeny genotypes and phenotypes. If p = percentage of allele A (dominant) and q = percentage of allele a (recessive), the checkerboard method can be used to produce all possible random combinations of these gametes.

Hardy-Weinberg's law has been extended to cases of multiple alleles, multiple loci, linked genes, sex-linked genes and haploid organisms. With regard to multiple loci, the balance according to the expectations of the Hardy - Weinberg law are reached after a generation of random mating. However, when two loci are considered simultaneously, the genotypes reach equilibrium over several generations. This phenomenon occurs both in independent segregation loci and in linked loci (ie, loci that are physically close together in the same chromosome).

This phenomenon is called gametic imbalance, definable as the non-random association of alleles at different loci in the gametes.

The basic conditions for the application of the Hardy-Weinberg law rarely occur in a natural population:

• Random fluctuations in gene frequencies occur given the finite size of a population. This intergenerational sampling error is called gene drift.

• The requirement of panmixia is rarely met, either by preferential crossing (may be inbreeding, that is, preferential crossing within a defined group, or exogamy, that is, crossing outside of that group) or sexual selection.

• In many cases, there is a differential success rate in the perpetuation of certain alleles. This difference constitutes natural selection.

• Mutations often occur more frequently in a certain direction.

• Migration leads to the introduction of new gene varieties in a population.

Thus, despite these violations of the Hardy-Weinberg restrictions, most genes behave within statistically acceptable limits with the equilibrium conditions between two successive generations.

The law is a theoretical statement, representing a static situation in which the gene structure of a population does not change. When presenting the characteristics of a population not influenced by evolutionary forces, its non-compliance in one implies the action of evolutionary forces in said population.

In this way, the Hardy-Weinberg law constitutes a null hypothesis, useful for exploration purposes: If the observed genotypic frequencies deviate significantly from those calculated according to an assumption of equilibrium, something is happening in the population at the of evolutionary forces, which forces to deepen its study.

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