Study Notes on Gene Frequency | Statistics

The below mentioned article provides a study note on gene frequency.

Population Genetics:

A population consisting of sexually interbreeding organisms carrying one or more particular genes, which follow the Mendelian Principles of Inheritance, is called ‘Mendelian Population’. Gene pool and gene frequencies are considered to be two important attributes of a population.

A gene pool is the sum total of genes in reproductive gametes of a population. The nature of gene pool depends on random mating of gametes to form zygotes in the next generation.

Gene frequency can be defined as proportions of different alleles of a gene in a population, and in a particular generation these frequencies depend on their frequencies in the previous generation and also on the proportion of various genotypes in total popu­lation.

In any population, if a character is controlled by two alleles, then the frequency of these alleles or genes can be calculated very easily by phenotypic observation of that character under homozygous and heterozygous conditions. The frequency of an allele in a population is the number of occurrence of that allele divided by the total number of alleles of that gene locus.

Measurement of Gene Frequency:

In a diploid species, a population having N individuals has 2N alleles for each gene locus. If there are two alleles ‘A’ and ‘a’ of a particular gene in this population, the number of A alleles is twice the number of AA homozygotes plus the number of Aa heterozygotes, as each homozygote has two ‘A’ alleles, and each heterozygote has one ‘A’ allele. So the frequency of ‘A’ is the number of ‘A’ alleles divided by total number of alleles, i.e., 2N.

If the number is denoted by ‘n’ then the equation can be written as:

It must be remembered that for all alleles the total frequency will be always 1, i.e., p + q = 1 and n_A + n_a = 2N.

Example 1:

In human population, a sample of 100 individuals for MN blood group character shows 50MM, 20MN and 30 NN individuals, then the frequency of M and N allele can be calculated using the above formula.

Genotype Frequency and Hardy-Weinberg Equilibrium:

In a randomly mating Mendelian population the gene and genotype frequencies reach to equilibrium in a single generation. The Hardy-Weinberg law states that the gene and genotype frequencies in a Mendelian population remain constant generation after genera­tion if there is no selection, mutation, migration or genetic drift.

Homozygotes (AA & aa) are produced by the union of gametes carrying similar alleles. The frequency with which a male gamete carrying allele A (frequency p) fuses with a female gamete carrying ‘A’ (also frequency p) will be p x p = p². Similarly the frequency with which a male gamete carrying allele ‘a’ (frequency q)”fuses with a female gamete also carrying ‘a’ will be q x q = q².

Heterozygotes (Aa) are produced by the fusion of gametes carrying different alleles, the frequency with which a male gamete carrying allele ‘A’ fuses with a female gamete ‘a’ will be p x q = pq. Similarly in opposite way the frequency with which a female gamete carrying allele ‘A’ fuses with a male gamete carrying ‘a’ will be p x q = pq. So, the total frequency of heterozygotes will be 2 pq.

According to the theory of probability, due to random mating, the genotype fre­quency can easily be calculated from the following formula:

(p + q) x (p + q) = p² + 2pq + q²

(p + q) = Total frequency of two alleles ‘A’ and ‘a’.

This equation is called Hardy-Weinberg equation which is named after British Mathematician G.H. Hardy and German Physician W. Weinberg.

As according to theory of probability the total frequency of p + q is always 1. So,

(p + q)² = p² + 2pq + q² = 1

In case of genes showing co-dominance, this equation can be used very easily to calculate the gene frequency by observing the phenotypic characters of homozygotes and heterozygotes.

Example 2:

In the following example it is shown how the observed value help to calculate the frequency:

If we put these two values in a frequency table we can get the expected number of phenotypes due to random mating of each allele as follows:

So, the expected values in total population can be calculated

p² = 0.2911 x 6129 = 1784.2

2pq = 2 x 0.2484 x 6129 = 3044.8

q² = 0.2121 x 6129 = 1300

The above calculation shows that the observed number of individuals and expected number of phenotypes are very close to each other which follows the Hardy-Weinberg Equilibrium Frequencies. In case of completely dominant genes of a population, the heterozygotes cannot be phenotypically distinguished from homozygotes for the dominant character.

In this case, by observing the recessive phenotype, the recessive allele frequency can be measured very easily using Hardy-Weinberg equation. The frequency of homozygotes of recessive allele is q². So the frequency of recessive allele in a population is √q² = q.

The frequency of dominant allele in that population is (1 – q) = p. This concept can also be applied to determine the number of individuals affected or carrying a particular disease, vis-a-vis, the frequency of the gene causing the disease.

PKU (Phenylketonuria) is a serious disease of human being which is a genetically controlled metabolic disorder. If in any population 0.04% is PKU affected then the frequency of PKU allele in that popu­lation is 7.0004 = 0.02 and the frequency of dominant allele is (1 – 0.02) = 0.98.

If in a population the frequency of deleterious allele is 0.01, assuming random mat­ing the frequency of homozygous population will be (0.01)² = .0001. Now the heterozy­gous frequency will be 2 x .01 x (1 – 0.01) = 2 x .01 x 0.99 = 0.0198.

So, about 1.98% population are carrier of this allele in heterozygous condition which is not expressed. If the frequency of recessive allele is too small then it is very difficult to measure it correctly, thus it is desirable to draw a large sample which will give more error free estimation.

Factors Affecting Gene Frequency:

Populations change over time. The number of individuals in a population may in­crease or decrease depending on food resources, climate, weather and the availability of breeding areas, etc. At the genetic level, a population may change because of mutation, migration, selec­tion and random genetic drift. These natural processes alter allele frequencies, thereby changing the fundamental makeup of the population.

1. Mutations produce new alleles, though the rate of mutation is too low to be noticeable. In case of deleterious mutation, selection counteracts the effect.

2. Migration changes the frequencies because the immigrants from a population have different genetic makeup. So, in a particular population the gene fre­quency changes due to genotype changes because of differential emigration from other locality.

3. Selection reduces the fertility or survival of certain genotypes. In many popu­lations survival and reproductive ability are variable traits. Some individuals may die before they reproduce, whereas others may have many progeny. The differential contribution of progeny implies that the alleles that are associated with superior fitness will increase in frequency in a population.

4. Random genetic drift (chance difference) causes small deviations from the predicted frequencies, especially in small samples. These deviations however are expected and allowed for on the basis of statistical tests.

5. Assortative mating of either similar or dissimilar genotypes results in an excess of homozygotes and heterozygotes respectively which changes the gene frequency.

6. Existence of subpopulations which are locally mating groups in a large popu­lation may be due to some ethnic causes or class grouping as in human, or due to low mobility of some organisms in a large area. These phenomena increase the frequency of homozygotes which is the result of inbreeding.