In this article we will discuss about the Hardy-Weinberg Equilibrium in Relation to Natural Selection:- 1. Meaning of Hardy-Weinberg Equilibrium 2. Elaboration of Hardy-Weinberg Equilibrium 3. A Case study of Natural Selection 4. Factors Effecting 5. Measurement of Fitness and Selection.

Contents:

  1. Meaning of Hardy-Weinberg Equilibrium
  2. Elaboration of Hardy-Weinberg Equilibrium
  3. A Case study of Natural Selection
  4. Factors Effecting Hardy-Weinberg Equilibrium
  5. Measurement of Fitness and Selection in Hardy-Weinberg Equilibrium

1. Meaning of Hardy-Weinberg Equilibrium:

It is a theory of population genetics, separately deduced by G. H. Hardy (1908) and W. Weinberg (1908) based on Mendel’s law of heredity. In this theory they proposed that, “if all other factors remain constant, the frequencies of particular genes and geno­types will remain constant in a population, generation after generation”. This genetic stability of population is known as Hardy – Weinberg equilibrium or genetic inertia.

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Explanation:

To understand this theory one have to be acquainted with following terminologies.

(i) Population:

An ecological popula­tion is a group of organisms of the same species living together within a common area at the same time and interbreeding with each other. Among geneticists a population is usual­ly defined as a community of sexually inter­breeding or potentially interbreeding individuals.

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Since Mendelian laws apply to the transmission of genes among these individu­als, such a community has been termed by Wright as a ‘Mendelian population’.

The size of the population may vary, but it is usu­ally considered to be a local group (also called deme), each member of which has an equal chance of mating with any other mem­ber of the opposite sex, i.e., random mating. As most of the theoretical discussions are made on the diploid organisms, we will con­sider here only diploid population.

(ii) Gene Frequencies:

These are simply the proportions of the different alleles of a gene in a population.

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Calculation:

Let us consider a diploid organism has only two genes at any locus in a Mendelian population. For example, if we consider the human MN blood group of 100 member population, there are a total of 200 genes in the population that contain 50-MM individuals, 20-MN individuals and 30-NN individuals. What will be the frequencies of M and N genes?

Solution:

200 genes are present in 100 persons, as humans are diploid. Among hun­dred people, there are 50MM, 20MN and 30NN individuals.’

Therefore,

50 MM people contain 50 x 2 = 100 M genes.

20 MN people contain 20 M genes and 20 N genes.

30 NN people contain 30 x 2 = 60 N genes.

Therefore, number of M genes in this population is 100 + 20 = 120 and that of N genes is 60 + 20 = 80.

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Now, using unitary method —

Among 200 genes M is 120 in number

among 1 gene M is 120/200 = 0.6 and similarly, among 200 genes N is 80 in number

among 1 gene N is 80/200 = 0.4.

So, the gene frequency of M is 0.6 and N is 0.4 in this population.

(iii) Genotype Frequency:

This is the simple proportion of different genotypes of a gene and its alleles in a population.

Example:

If we consider the same popu­lation as described in gene frequency — what will be the genotype frequencies?

Calculation:

As per example, number of MM genotypic individuals are 50, MN indi­viduals are 20 and NN are 30. Total number of individuals are 100.

Again, using unitary system.

Among 100 individuals MM are 50

So, among 1 ” ” 50/100 = 0.5

Similarly, among 100 individuals MN are 20

among 1 ” ” 20/100 = 0.2

And among 100 individuals NN are 30

among 1 ” ” 30/100 = 0.3

From this solution it is found that the fre­quency of MM genotype is 0.5, frequency of MN genotype is 0.2 and frequency of NN genotype is 0.3.

Calculation of Gene Frequency from Genotype Frequency:

The gene frequencies can be calculated from the genotype frequencies directly, using the following formula.

Frequency of a gene =

(as each heterozygote contains one such gene).

Example:

In our foregoing example of genotype frequency calculation, we find MM = 0.5, MN = 0.2 and NN = 0.3. Putting these values in the formula we can get the frequen­cies of M and N genes.

Solution:

1. Frequency of M gene =

= 0.5 + 0.2/2 = 0.5 + 0.1 = 0.6

2. Frequency of N gene =

= 0.3 + 0.2/2 = 0.3 + 0.1 = 0.4

This result corresponds to the result of the previous calculation of gene frequencies.

(iv) Gene pool:

It is the sum total of genes in the reproductive gametes of a popu­lation.

2. Elaboration of Hardy-Weinberg Equilibrium:

The general relationship between gene frequencies and genotype frequencies can be described in algebraic terms by means of Hardy-Weinberg principle as follows.

If p is the frequency of a certain gene in a panmictic population (suppose gene M) and q is the frequency of its allele (in this case N gene), so that p + q = 1 (i.e., there are no other alleles), the frequencies of the genotypes in the population in equilibrium will be p2 for MM, 2 pq for MN and q2 for NN and the sum of all these genotype frequencies will be equal to 1.

The same results are also produced by the expansion of the binomial (p + q)2 = p2 + 2pq + q2.

From our example of MN blood group of man we can see that p = M = 0.6 and q = N = 0.4 and p + q = 1. The genotype frequencies at equilibrium condition will be

MM = p2 = (0.6)2 = 0.36

MN = 2pq = 2 x 0.6 x 0.4 = 0.48

NN = q2 = (0.4)2 = 0.16

Then p2 + 2pq + q2 = 0.36 + 0.48 + 0.16 = 1

Therefore, it can be said that the popula­tion is in equilibrium state. If this popula­tion interbreeds, the next generation of this population will also show equilibrium. The proportion of the two genes will be same in the next generation.

But if selection pressure works on any genotype, then number of the particular genotype may change. Still the p2 + 2pq + q2 will show the value 1, gene­ration after generation. Natural Selection and Hardy-Weinberg

Prin­ciple:

According to Neutrality concept of molecular evolution, selection forces act at gene level. In general, a gene locus is considered to be polymorphic if at least two alleles are present in the popula­tion, with a frequency of at least 1 percent for the second most frequent allele.

The mainte­nance of different genotypes in a population through heterozygote superiority is termed as ‘balanced polymorphism’, which is neces­sary to preserve genetic variability through selection. Different polymorphic forms may become established in different environment.

3. A Case study of Natural Selection:

Industrial melanism:

The British pep­pered moth Bistort betularia was observed for a long period. They were nocturnal in habit and during day they used to rest on surfaces mainly on trunks. There were two types of moths, one with pale wings with minute black markings and is almost invisible on lichen covered tree trunks, and the other with black wings.

The number of different varie­ties of moth collected over a long period from Manchester is tabulated below:

Year, Pale Moth and Blck Moth

Explanation:

(i) This change from predominant pale- coloured population of moths to black (melanic) population took only 50 years and corresponds with the most rapid increase in industrial development.

(ii) The difference between pale moth (variety typica) and melanic form (variety carbonaria) is the differential selection of polymorphic forms of genes.

(iii) The genes responsible for production of melanic forms were probably hidden in the population for many years. But they were not selected in the non-industrial areas, where they were easily predated by the birds during day time, as they were con­spicuous in the usual lichen-covered tree trunk.

(iv) With the advancement of indus­trialization and pollution, the situa­tion becomes opposite. Due to pollu­tion, lichens became absent on the tree trunks. The pale moths thus become conspicuous and were sub­jected to predation. Thus, nature gradually selected the melanic forms.

4. Factors Effecting Hardy-Weinberg Equilibrium:

The genetic properties of a population are influenced by the process of transmission of genes from one generation to the next by a number of agencies, irrespective of whether the population is in equilibrium or in non-equilibrium.

There are two types of processes by which we can describe the changes of gene and genotype frequencies. One is the ‘systematic process’, which tends to change the gene frequency in a manner predictable both in ‘amount’ and in ‘direc­tion’.

The other is the ‘dispersive process’, which arises in small populations from the effects of sampling, and is predictable in ‘amount’ but not in ‘direction’. There are three systematic processes — migration, mutation and selection.

The dispersive process includes four consequences, random drift, differentiation between sub-popula­tions, uniformity within sub-populations and increased homozygosity. Due to lack of scope we will discuss only systematic processes here.

A. Migration:

The gene frequencies in the population may be changed by immigration or emigration of individuals from one population to the other. Therefore, number of individu­als will change from the existing condition. It may increase or decrease. In that case how we shall determine the gene frequency or genotype frequency?

Calculation of Gene Frequency in Case of Migration:

Suppose that a large population consists of a proportion x of new immigrants in each generation. Therefore, the remainder, 1 – x, will be natives.

Again, let the frequency of a gene (sup­pose m gene) be qx among immigrants and q0 among the natives. Then the frequency of the m gene in the mixed population (suppose qz) Will be

qz = x.qx + (1 – x)q0

= x.qx + q0 – x.q0

= x.qx – x.q0 + q0

= x(qx-q0) + q0 (1)

The change of gene frequency, ∆q, brought about by one generation of immi­gration will be the difference between the frequency before immigration and the fre­quency after immigration. Therefore, ∆q will be like this —

∆q = qz-qo

= {x(qx – q0) + q0) – q0 … from Eq. No. (1)

= x(qx – q0) + q/0 q/0

= x(qx – q0) ………… (2)

So, it can be said that the rate of change of gene frequency (here m gene) in a popula­tion depends on the immigration rate and on the difference of gene frequency between immigrants and natives.

B. Mutation:

In a population we can observe two types of mutations. One is ‘non-recurrent’ and the other is ‘recurrent’ mutation. In case of non-recurrent mutation, just one represen­tative of the mutated gene or chromosome appears in the whole population. This type of mutation is of very little importance in changing the gene frequency in a population.

In most of the cases this mutation product gets lost from the population, after one or- two generations. The recurrent mutation results in the appearance of mutant gene which is never so low so as to get completely lost from the population. Therefore, it exerts a ‘pressure’ on the gene frequency of the population.

How this Pressure can be Estimated?

Suppose that gene m, mutates to m2 with a frequency u per generation, (u is the pro­portion of all m1 genes that mutate to m2 between one generation and the next). Let the frequency of m, in one generation is q0, then the frequency of newly mutated m2 genes in the next generation is u times of q0, i.e., u.q0. So the new gene frequency of m, in this generation is q0-u.q0. Therefore, the change of gene frequency is – u.q0 or

∆q = – u.q0

C. Selection:

All individuals of a population may not contribute equally their genetic materials to the next generation. This is because of the fact that individuals differ in viability and fertility. It is obvious that if individuals carrying gene a+ are more successful in producing viable and fertile offspring than individuals carrying its allele a+, then the frequency of a+ will tend to increase.

The wide variety of mechanisms that affect the reproductive success of a genotype is known collectively as ‘selection’, and the extent to which a genotype contributes to the offspring of the next generation is com­monly known as its ‘fitness, selective value or adaptive value’.

Therefore, if fitness is related with presence or absence of a particular gene (a–) in the individual’s genotype, then it can be said that ‘selection’ operates on that gene. Thus, the gene which is under selection pressure will not be in same frequency as the parents and offspring. In this way, along with selection comes a change of gene frequency and consequently change in geno­type frequency.

5. Measurement of Fitness and Selection in Hardy-Weinberg Equilibrium:

It can be measured by the number of fertile offspring’s produced by one genotype compared to those produced by another. Suppose, if individuals of genotype a+ produce an average 100 offspring’s that reach full reproductive maturity while genotype a+ individuals produce only 90 in the same environment.

The adaptive value of a– relative to a+ is reduced by ten offspring’s or the fraction 10/100 = 0.1. If we designate the adaptive value of a genotype as ‘w’ and the selective force acting to reduce its adaptive value as ‘s’ (the selection coefficient), then we can say that w = 1 and s = o for a+ genotype and w = 0.9 and s = 0.1 for a+. The relationship between w and s is therefore, simply w = 1 – s or s = 1 – w.

Types of selection:

Selection can act at a genotype in various stages of life-cycle. It may occur in either haploid (gametic) or diploid (zygotic) stage or both, depending on which of these stages, gene expression influences survival or fertility. The various stages are given in Fig. 4.4. In any of these stages if selec­tion works, then its effect may range from complete lethality or sterility (s = 1) to only slight reductions in adaptive value (e.g., s = 0.01).

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