Introduction:

Population genetics is basically the study the interconnected patterns of phenotypic, genotypic and allelic frequencies in populations. Such frequencies are usually stated in relatively formal statistical notation.

1) For each and every genetically controlled characteristic or trait, a population will exhibit a characteristic distribution of the probable phenotypes. For instance, when the gene in question is the brown or black fur color gene in gerbils, some part of the population will be brown and the remaining will be black. The frequency of brown gerbils would be exhibit as f (Brown), and would be computed as the number of brown gerbils in the population divided by the net number of gerbils in the population. The frequency of black gerbils f (black) would be the number of black gerbils divided by the net number of gerbils. It must be noted that when these are the mere two colors of gerbils in the population, their frequencies must add up to 1.0.

2) Obviously, the phenotypes of the gerbils are the outcome of their genotypes. Genotypic frequencies in this instance would be f (BB), f (Bb) and f (bb). Again, when this gene consists of only such two alleles, these three frequencies must add up to 1.0. Not as well that the f (black) will be equivalent to the f (bb), and that the f (brown) will be equivalent to the sum of the f (BB) and f (Bb).

3) At the core of the whole genotypic and phenotypic variation are, obviously, alleles. And the frequencies of such alleles are at the core of the computations of population genetics. In our instance, the frequencies of our two alleles would be f (B) and f (b). When there are merely two alleles for this gene in the population, then f (B) and f (b) will add up to 1.0 This is much common in population genetics to employ the symbols p and q to symbolize these allelic frequencies. When there is a dominant allele, its frequency will be symbolized as p. Therefore f (B) = p and f (b) = q. When there is no dominance (as in incomplete or co-dominance) either letter might be employed for either allele. When the gene consists of more than one allele, the frequency of the third allele would be symbolized as r.

Deriving Gene or Allelic Frequencies:

From the given knowledge of genotypic frequencies, it is probable to compute the allelic frequencies for any population.

1) f(A) = p; f(a) = q.

2) p = f(A) = #A/total # alleles = f(AA) + 1/2 f(Aa)

3) q = f(a) = #a/total # alleles = f(aa) + 1/2 f(Aa) OR q = 1 - p. (keep in mind that p + q = 1.)

4) This computation makes no suppositions regarding the condition of the population. (In other words, it does not need that the population be in any type of equilibrium.)

Hardy-Weinberg principle:

Fundamental population genetics starts with the perception of a 'perfect' population in which the entire allelic frequencies are constant and in which the entire mating is random. This ideal population is termed as a Hardy-Weinberg population, after the statisticians accountable for building up the concept. A population that simulates the ideal population is frequently explained as being 'in equilibrium'. The relationship among the allelic and genotypic frequencies in this ideal population is explained by the Hardy-Weinberg equation (that is, H-W equation).

To regulate for allelic frequencies to be stable, there are five conditions which should be met.

a) There should be totally non-random mating.

b) There should be no selection, artificial or natural.

c) There should be no mutation. Note that this is an unfeasible condition, as mutation rates can't be decreased to zero.

d) There should be no migration of species members from exterior populations (since they might come from a population with dissimilar allelic frequencies).

e) There should be no genetic drift. Genetic drift outcomes from chance alterations in the allelic frequencies, and again can't realistically be decreased to zero. Genetic drift can be minimized when the population is very big. The smaller the population, the more powerful genetic drift will be.

Four factors influencing the Hardy Weinberg principle:

The Hardy-Weinberg conditions are as follows:

1) Random mating.  The selection of mating pairs is not affected by the phenotype of the individuals, however is governed by the rules of chance.  Keep in mind that mating choice require only be arbitrary with respect to the trait or characteristic being studied.  

2) No mutation or migration.  The allele frequencies should not be modified as of mutations or since individuals with strange allele frequencies are entering or leaving the group. 

3) Large population: In small populations, arbitrary events can considerably vary allele frequencies.  This random procedure is termed as genetic drift. To avoid drift, the Hardy-Weinberg conditions comprise supposition of an infinitely big population number.

4) No selection.  The different phenotypes generated by each and every genotype must cope uniformly well with the environment and be likewise fertile at the time of reproduction.

When any one of such conditions is not met, the Hardy-Weinberg equilibrium will be upset, and a population will be developing, not static. 

Modern evolutionary synthesis:

The math of population genetics was initially developed as the starting of the modern evolutionary synthesis. According to Beatty in the year 1986, population genetics states the core of the modern synthesis. In the initial few decades of the 20th century, most of the field naturalists continued to consider that Lamarckian and orthogenic methods of evolution provided the best description for the complexity they seen in the living world. Though, as the field of genetics continued to build up, such views became less acceptable. Throughout the modern evolutionary synthesis, such ideas were purged and only evolutionary causes which could be stated in the mathematical framework of population genetics were kept. Harmony was reached as to which evolutionary factors may influence evolution, however not as to the relative significance of the different factors. 

Theodosius Dobzhansky, a postdoctoral worker in the T.H. Morgan's lab, had been affected by the work on genetic diversity by means of Russian geneticists like Sergei Chetverikov. He assisted to bridge the divide among the foundations of microevolution build up by the population geneticists and the prototypes of macroevolution seen by field biologists, with his book in the year 1937 'Genetics and the Origin of Species'. Dobzhansky observed the genetic diversity of wild populations and exhibited that, contrary to the suppositions of the population geneticists, such populations had huge amounts of genetic diversity, with marked differences among sub-populations. The book as well took the highly mathematical work of the population geneticists and places it into a more accessible form. A lot of biologists were affected by population genetics through Dobzhansky than were capable to read the highly mathematical works in the original. 

The Hardy-Weinberg Law:

The HW law is the combining concept of population genetics. It was named after the two scientists who concurrently discovered the law. The law forecasts how gene frequencies will be transmitted from generation to generation given a particular set of suppositions. Particularly, if an infinitely big, random mating population is free from exterior evolutionary forces (that is, mutation, migration and natural selection), then the gene frequencies will not modify over time and the frequencies in the subsequent generation will be:

p² for the AA genotype (that is, homozygous dominant)

2pq for the Aa genotype (that is, heterozygous), and

q² for the aa genotype (that is, homozygous recessive).

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