## In of deviations from these theories and the

In the year 1908,

British mathematician Godfrey H. Hardy and German physician Wilhelm Weinberg were

said to have discovered the relationship between gene and genotype frequencies,

generally known as the Hardy-Weinberg principle, or the Hardy-Weinberg equilibrium

(Chen, 2010). Since when it has been discovered, the Hardy-Weinberg principle

has become a powerful research tool in both theoretical and applied research in

population and quantitative genetics (Chen, 2010).

The

Hardy-Weinberg principle states that; under the condition of a large

population size, diploid organisms with non-overlapping generations and random

mating, the genotype frequencies at a locus are determined by the allele

frequencies, and both the genotype and the allele frequencies will stay constant

in future generations when there is no condition of mutation, migration and selection.

(evolutionary forces). (Chen, 2010).

A tool in

population genetics that has been generally used to detect potential or

possible typing error is testing for Hardy-Weinberg equilibrium. It is also

much used to check both single nucleotide polymorphism (SNP) and microsatellite

genotype data (Chen, 2010). Hardy-Weinberg equilibrium is not very sensitive to

certain kinds of deviations from these theories and the effects of the

deviations from several theories can cancel the effects of each other out. So Therefore,

due to the ensuing consequences, violation from these theories may not

necessarily result in an observable deviation from Hardy-Weinberg proportions.

But deviation from the Hardy-Weinberg equilibrium itself strongly suggests that

at least one of the assumptions/theories is violated. There are many

possible reasons for a significant deviation from Hardy-Weinberg equilibrium.

For instance, population stratification could result in non-random mating.

Alternatively, the researcher might have not correctly specified the underlying

genetic basis for the trait of interest. The realization of significant

deviation from Hardy-Weinberg equilibrium can potentially lead to a better

genetic model and establishing interesting alternative hypotheses for further

investigation. Because of its elegance and theoretical importance, the

Hardy-Weinberg principle has become an important starting point for population

genetic investigations. (Chen, 2010)

HARDY-WEINBERG LAW AND ESTIMATING ALLELE FREQUENCE

Statistically,

the keystone of population genetics is the Hardy-Weinberg

law or principle.

The law consists of two parts. They are as follows:

1.

The

first part; states that in a large, randomly mating population with two alleles

at a locus (e.g B & b), there is a simple relationship between these

allele frequencies (frequency of B = p; frequency of b = q)

and the genotype frequencies (p2, 2pq, or q2) which they define.

2.

The

second part; holds that this relationship between allele and genotype

frequencies (as I earlier explained), based on the binomial expansion of (p + q)2, do not change from one generation to the next.

When

a population follow these two parts of the law, it is in Hardy-Weinberg

equilibrium. In populations like that, the law is of major importance

in showing why the frequency of dominant traits do not increase from one

generation to the next and why recessive traits do not decrease. Furthermore,

the law is consistently used in when doing genetic counselling where estimates

of genotype, allele, and carrier frequencies are calculated from limited

phenotypic

information

in small families, with such estimates then being employed to estimate specific

genetic risk (Chen, 2010)). The study of deviation from

Hardy-Weinberg equilibrium using an Expectation-Maximization (EM) statistical

algorithm, is being used in the investigation of allelic frequency estimation (Chen,

2010).

IMPORTANCE OF HARDY-WEINBERG

PRINCIPLE

The

hardy-Weinberg principle as we have explained before is very Important in

population genetics, among the importance is the fact that, due to the fact

that there are many assumptions needed to derive the Hardy–Weinberg Law, we learned

that it plays a central role in the theory of population genetics. That

is due to two reasons;

a.

First of all; it is very

important due to the fact that it provides a route for researchers to estimate the

frequencies of alleles for a particular characteristic in which what we call heterozygotes

cannot be distinguished from the homozygotes, given the fact that we are

willing to assume that all of the assumptions apply to the population in which

we are working on.

b.

Secondly; using the

knowledge of hardy-weinberg principle, we know what will happen in a population

when there is no presence of any evolutionary force (e.g., mutation, selection,

adaptation etc.). referring to this, the known philosopher Elliott Sober, made

an important quote, “it plays an important role in the study of population genetic theory similar to the role

that we know that is performed by the first and second laws of motion play in

what is known as Newtonian mechanics” (Holsinger, 2001)

In

order for us to explain the words of the philosopher Elliott Sober, we explain

the first and second laws of newton and how we can compare it to the hardy

Weinberg principle for better explanation;

The first laws of motion which is also the law

inertia states that an object at rest will remain at rest and an object in

motion will remain in motion (in a straight line at a constant speed and

direction) unless if it is acted on by external forces. They are what can be termed as ‘zero-force laws’ because

they answer the question of what we should expect when no evolutionary forces (e.g., mutation, selection, adaptation etc.) act on an object.

Moreover, the 2nd law of motion give us the ability to judge

the magnitude and direction of any force operating on an object by the

acceleration to which it is subjected to. (Holsinger, 2001)

So, since we compared

the Hardy-Weinberg law to the first two laws of newton and we called the two

laws of newton zero-force laws, The Hardy–Weinberg law is what is known

as population genetics’ zero-force law. It makes us know how a

population will look like if a phenomenon such neither genetic drift (random

species movements) nor any evolutionary force (e.g.,

mutation, selection, adaptation etc.) affect it.