Population Genetics and

Hardy-Weinberg Equilibrium.

Godfrey Harold Hardy. Wilhelm Weinberg

•Study of the frequency of genes and genotypes in a mendelian population is known as Population Genetics.•It has been recognized that although the inheritance of individual genes may be governed by mendelian principles, but the frequencies of the individuals carrying this genes may depend on several factors, which include frequency of a particular gene, size of population and other factors.

•A population consists of a community of sexually or potential inbreeding organisms inhabiting in a geographical area.

•Sewall Wright called these populations as ‘Mendelian populations’ .

•Before dealing with population genetics, it is essentialto define mendelian population, gene frequencyand genotype frequency.

Mendelian Population

Two features:-1. Random Mating.( Panmictic population)2. Equal survival of all genotypes.

Random Mating individuals belong to the same species and same gene pool.

Gene pool - sum total of genes in mendelian population.

Gene Frequency.

Proportion of different alleles of a gene in a random mating population is referred as gene frequency.Estimation of gene frequency in a population consists of three important steps:

1. Sampling2. Classification3. Calculation of gene frequency.

Suppose a random sample of 100 individuals was drawn from a random mating population of Mirabilis jalapa.Out of 100 plants, 30 were red, 40 were pink, 30 were white flowers.So, the allele frequency is worked out as follows:

•Red colour are homozygous for dominant allele (RR).•White colour are homozygous for recessive allele (rr).•Each heterozygous individual pink colour will have dominant (R) and recessive (r) alleles in equal number.

1. Number of R alleles in a sample (30 individual)= 2 (No.of red individuals) + No.of pink individuals=(2x 30)+ 40 = 100

2. Proportion of R alleles in the sample= No.of RR alleles 2( total plants in a sample)= 100/(2x 100)=0.50

Similarly, no.of r alleles = (2x30)+ 40= 100Proportion of r alleles =100/(2x100)

=0.50

Therefore, the frequency of RR and rr alleles is 0.50 each.

Genotype frequency

Genotypic frequencies at a specific locus can be calculated by counting number of individuals with particular genotype and divide this number by the total number of individuals in the populations.

So, from the above sample the genotypic frequency of each individual is calculated as follows:

1. Frequency of Red (RR) individuals = 30/100 = 0.302. Frequency of Pink (Rr) individuals = 40/100 = 0.403. Frequency of White (rr) individuals = 30/100 = 0.30

Hardy- Weinberg Law

•In 1908, Hardy an English Mathematician and W. Weinberg, a German Physician independently discovered a principle concerned with the frequency of genes(alleles) in a population.

•W.E. Castle (a geneticist) was first to recognize the relationship between gene and genotypic frequencies.

•The law is also referred to as the Castle-Hardy-Weinberg law.

Godfrey Harold Hardy. Wilhelm Weinberg W.E. Castle

The law states that:

“In a infinitely, random mating population, the frequency of genes and genotypes remains constant generation after generation, if there is no selection, mutation, migration and random genetic drift.’’

A mathematical relationship was developed to describe the equilibrium between alleles. The frequencies of three genotypes for a single locus with two alleles (A and a) are in the ratio of,• p²AA: 2pqAa: q²aa, where p and q are the frequencies of allele A and a respectively.

• p+q are always equal to 1.

•p+q = 1 or p = 1-q or q = 1-p.

A

sperms

a

EggsA a

A/A(p²)

A/a(pq)

A/a(pq)

a/a(q²)

Selection:-•The word itself defines ...i.e to select desirable individual which favours survival and reproduction in a population.•Here, the fittest individual survive and rest are wiped out which is known as natural selection. Fitness:-•The relative reproductive success of different genotypes of a population in the same environment under natural selection.•It is denoted by W. If W = 1 than 100% survival and vice-versa.•Survival depends on two factors:-The no.of seeds produced by each genotype.-The proportions of seeds of each genotype which reaches maturity and produces offspring.• The value of W ranges between 0 and 1.

Mutation:-•A sudden heritable change in the features of an organism.•The frequency of mutation is extremely low (1x10-6).•Mutation leads to alterations of gene frequencies in a population.•It may occur in both forward and reverse direction, but the frequency of forward mutation is higher than reverse mutation.•When mutation is in both the direction the equilibrium condition can be expressed as follows:T mutates to t at a rate u and frequency of T in a population is p.t mutates to T at a rate v and frequency of t in a population is q or (p-1).Thus, decrease in T = upand increase in T = v(1-p)

Therefore, condition of equilibrium will be;up = v(1-p)up = v – vpup + vp = vp(u + v) = vp = v/(u + v)

Similarly, q = u/v + u

Migration:- It refers to the movement of individuals into a population from a different populations. Migration may introduce new alleles into the population. This new alleles after mating with the individuals of original population may alter gene and genotypic frequencies in a population. The rate of change in gene frequency, through migration depends on the number of migrants.

Genetic Drift:-Random drift or genetic drift refers to random change in gene frequency due to sampling error. Large sample size provides true representative value of a population or value which is nearer to the population mean. However, random genetic drift is a non-directional factor because it does not change the gene frequency in a particular direction.Causes of genetic drift:-1. Small populations2. Founder effect (When population is initially small) and 3. Bottleneck effect (population drastically reduced to small)

Founder Effect.

Bottleneck Effect.

Thank you…