Introduction:

Gene frequency evaluates the frequency in the population of a particular gene relative to other genes at its locus. It is deduced as a proportion (between 0 and 1) or percentage (between 0 and 100%).  A genetic equilibrium is at hand for an allele in the gene pool if the frequency of that allele is not changing. For this to be the case, evolutionary forces acting on the allele should be equivalent and opposite. The only fundamental requirement is that the population be large adequate that the effects of genetic drift are minimized.

Genetic frequency:

Genetic or Allele frequency is the proportion of all copies of a gene which is made up of a specific gene variant. In another words, it is the number of copies of a specific allele divided by the number of copies of all alleles at the genetic place in the population. It can be deduced for illustration as a percentage. In population genetics, allele frequencies are employed to depict the amount of genetic diversity at the individual, population and species level. It is as well the relative proportion of all alleles of a gene which are of a designated kind.

Given the following:

A) A particular locus on the chromosome and the gene occupying that the locus.

B) A population of N individuals carrying n loci in each of their somatic cells (example: two loci in the cells of diploid species that include two sets of chromosomes)

C) Different alleles of the gene exist

D) One allele exists in the copies

Then the allele frequency is the fraction or percentage of all the occurrences of that locus which is occupied through a given allele and the frequency of one of the alleles is a/(n*N). For illustration, if the frequency of an allele is 20% in a given population, then among population members, one in five chromosomes will carry that allele. Four out of five will be taken by other variant(s) of the gene. Note that for diploid genes the fraction of individuals that carry this allele might be almost two in five (36%). The reason for this is that when the allele distributes randomly, then the binomial theorem will apply: 32% of the population will be heterozygous for the allele (that is, carry one copy of that allele and one copy of the other in each and every somatic cell) and 4% will be homozygous. Altogether, this means that 36% of diploid individuals would be expected to carry an allele that consists of a frequency of 20%. Though, alleles distribute arbitrarily only under certain suppositions, comprising the absence of selection. When such conditions apply, a population is stated to be in Hardy-Weinberg equilibrium. The frequencies of all the alleles of a given gene often are graphed altogether as an allele frequency distribution histogram, or allele frequency spectrum. Population genetics studies the various 'forces' which might lead to changes in the distribution and frequencies of alleles-in another word, to evolution. Apart from selection, such forces comprise genetic drift, mutation and migration.

Computation of Genetic Frequency:

If f(AA), f(Aa) and f(aa) are the frequencies of the three genotypes at a locus having two alleles, then the frequency p of the A-allele and the frequency q of the a-allele are obtained by counting the alleles. Because each and every homozygote AA comprises only of A-alleles and because half of the alleles of each and every heterozygote Aa are A-alleles, the net frequency p of A-alleles in the population is computed as:

p = f(AA) + 1/2 f (Aa) = frequency of A

Likewise, the frequency q of the a allele is given through

q = f (aa) + 1/2 f (Aa) = frequency of a

It would be anticipated that p and q sum to 1, as they are the frequencies of the just two alleles present. Certainly they do:

p + q = f(AA) + f(aa) + f(Aa) = 1

And from this we get:

q = 1 - p and p = 1 - q

When there are more than two dissimilar allelic forms, the frequency for each and every allele is simply the frequency of its homozygote plus half the sum of the frequencies for all the heterozygote in which it comes out. Allele frequency can for all time be computed from genotype frequency while the reverse needs that the Hardy-Weinberg conditions of random mating apply.

This is partially due to the three genotype frequencies and the two allele frequencies. It is simpler to decrease from three to two.

In the simplest case, gene frequency is evaluated by counting the frequencies of each gene in the population. When a genotype includes two genes, then there are a total of 16 genes per locus in a population of eight individuals:

Aa AA aa aa AA Aa AA Aa

In the population above,

Frequency of A = 9/16 = 0.5625

Frequency of a = 7/16 = 0.4375.

Algebraically, we can state p as the frequency of A and q as the frequency of a. p and q are for all time termed as 'gene' frequencies, however in a strict sense they are termed as allele frequencies: they are the frequencies of the various alleles at one genetic locus.

The gene frequencies can be computed from the genotype frequencies (P, Q, R):

p = P + 1/2Q

q = R + 1/2Q

(p + q = 1). The computations of gene from genotype frequencies are highly significant. However the gene frequencies can be computed from the genotype frequencies, the opposite is not true: the genotype frequencies can't be computed from the gene frequencies (p, q).

The effect of mutation:

Let ú be the mutation rate from allele A to some other allele a (that is, the probability that a copy of gene A will become a throughout the DNA replication preceding meiosis). When p_t is the frequency of the A allele in generation t, then q_t = 1 - p_t is the frequency of a allele in generation t, and if there are no other causes of gene frequency change (that is, no natural selection, for illustration), then the change in allele frequency in one generation is:

Δp = p_t - p_t-1 = (p_t-1 u'p_t-1) - p_t-1 = - u'p_t-1

Here p_{t -1} is the frequency of the preceding generation. This state's us that the frequency of A reduces (and the frequency of a rises) by an amount which is proportional to the mutation rate u' and to the proportion p of all the genes which are still accessible to mutate. Thus Δp gets lesser as the frequency of p itself reduces, as there are less and less A alleles to mutate to a alleles. We can make estimation that, after n generations of mutation,

p_n = p_oe^-na

Population Genetics and the Hardy-Weinberg Law:

A genetic equilibrium is at hand for an allele in the gene pool if the frequency of that allele is not changing (that is, when it is not evolving). For this to be the case, evolutionary forces acting on the allele should be equivalent and opposite. The only fundamental requirement is that, acting on the allele should be equivalent and opposite. The only fundamental requirement is that the acting on the allele should be equivalent and opposite. The only fundamental requirement is that the population be large adequate that the effects of genetic drift are minimized.

The Hardy-Weinberg formulas let scientists to find out whether evolution has occurred. Any changes in the gene frequencies in the population over time can be noticed. The law basically states that when no evolution is occurring, then equilibrium of allele frequencies will remain in effect in each succeeding generation of sexually reproducing individuals. In order for equilibrium to remain in effect (that is, that no evolution is occurring) then the following five conditions should be met:

1) No mutations must take place so that new alleles don't enter the population.

2) No gene flow can take place (that is, no migration of individuals into, or out of, the population). 

3) Random mating must take place (that is, individuals should pair by chance).

4) The population must be large so that no genetic drift (that is, random chance) can cause the allele frequencies to change.

5) No selection can take place so that some alleles are not selected for, or against.

Evidently, the Hardy-Weinberg equilibrium can't exist in real life. A few or all of these kinds of forces all act on living populations at different times and evolution at some level takes place in all living organisms. The Hardy-Weinberg formulas let us to detect some allele frequencies which change from generation to generation, therefore letting a simplified process of finding out that evolution is occurring. There are two formulas which should be memorized: 

p² + 2pq + q² = 1 and p + q = 1 

p = frequency of the dominant allele in the population

q = frequency of the recessive allele in the population

p² = percentage of homozygous dominant individuals

q2 = percentage of homozygous recessive individuals

2pq = percentage of heterozygous individuals

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