Population genetics

HARDY WEINBERG LAW AND ITS
APPLICATION IN PLANT BREEDING
Presented by
GOKULAN D

Introduction:
• In a random mating population, each individual of the population has equal
opportunity of mating with any other individual of that population is called
Mendelian population or panmictic population.
• Gene pool may be defined as the sum total of all the genes present in a
population.
• A population, in this case, consists of all such individuals that share the same
gene pool, i.e., have an opportunity to intermate with each other and
contribute to next generation of the population.
28-11-2019 Gokulan D (Msc.Ag) 2

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.
• This is also referred to as the
Castle-Hardy-Weinberg law.
W.E. Castle Godfrey Harold Hardy. Wilhelm Weinberg

• This law states that “the gene and genotypic frequency in a
Mendelian population remains constant generation after generation if
there is no selection, mutation, migration or random drift”.
• Random mating involving the locus (A/a) will yield the following
genotypes: AA, Aa, and aa, with the corresponding frequencies of p2,
2pq and q2, respectively. The gene frequencies must add up to unity.
Consequently, p2 + 2pq + q2 = 1. This mathematical relationship is called
the Hardy–Weinberg equilibrium.

GENE FREQUENCY:
• Let us consider a single gene with two alleles(B,b) in a random mating
population.
P = (2D + H)/2N or
B- Brown = (D + ½ H)/N
b- blue q = (2R + H)/2N or
= (R + ½ H)/N
BB Bb bb The value of p(frequency of B allele)
(D) (H) (R) and q(frequency of b allele) are gene
frequency.

• Imagine if a segregating F2 population (80 plants) having this type of
genotypes with 4 BB, 24 Bb and 52 bb.
Allelic frequency can be obtained as
p(BB) + q(bb) = 1
[4 + ½(24) ]/80 [52+ ½(24) ]/80
0.2 0.8 = 1

BB
p2
Bb
pq
Bb
pq
bb
q2
B
(p)
b (q)
b
(q)
B (p)
p2 + 2pq + q2 = 1
BB Bb bb
The value of p2, q2 and 2pq is the genotypic frequency i.e., the
proportion of a genotype, BB, Bb and bb in a population.
GENOTYPIC FREQUENCY:
M/F

• Genotypic frequency can be obtained as from the above example,
p(BB) + q(bb) = 1
0.2 0.8
p2 + 2pq + q2 = 1
(BB) (Bb) (bb)
(0.2)2 2×0.2×0.8 (0.8)2

Random mating in next generation:
M/F
BB
(0.04)
Bb
(0.32)
bb
(0.64)
BB
(0.04) 0.0016 0.0128 0.0256
Bb
(0.32) 0.0128 0.1024 0.2048
bb
(0.64) 0.0256 0.2048 0.4096
Parental
mating
Offspring genotype
frequencies Total
frequencyBB Bb bb
BB × BB 0.0016 0.0016
BB × Bb 0.0128 0.0128 0.0256
BB × bb 0.0256 0.0256 0.0512
Bb × Bb 0.1024 0.1024
Bb × bb 0.2048 0.2048 0.4096
bb ×bb 0.4096 0.4096
Total 0.04
(p2)
0.32
(2pq)
0.64
(q2)
= 1.00

FACTORS AFFECTING THE EQUILIBRIUM IN
POPULATIONS:
Gene frequency in a population may be changed by one of two
primary types of processes – systematic or dispersive. A systematic
process causes a change in gene frequency that is predictable in both
direction and amount. A dispersive process, associated with small
populations, is predictable only in amount, not direction. Such systematic
processes are listed as
• Migration
• Mutation
• Selection
• Random Drift

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.

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 = up
and increase in T = v(1-p)
Therefore, condition of equilibrium will be;
up = v(1-p)
up = v – vp
up + vp = v
p(u + v) = v
p = v/(u + v)
Similarly, q = u/v + u

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.

Key application to plant breeding:
• Selection is most effective at intermediate gene frequency (q=0.5)
and least effective at very large or very small frequencies (q=0.99 or
q=0.01). Furthermore, selection for or against a rare allele is
ineffective. This is so because a rare allele in a population will
invariably occur in the heterozygote and be protected (heterozygote
advantage).
• Migration increases variation of a population. Variation of a population
can be expanded in a breeding program through introductions (impact
of germplasm). Migration also minimizes the effects of inbreeding.

• Plant breeders employ this process to change frequencies when they
undertake introgression of genes into their breeding populations.
• The breeding implication is that for open-pollinated (outbreeding)
species, the frequency of the immigrant gene may be low, but its
effect on the host gene and genotypes could be significant.

• In both natural and breeding populations, there appears to be a
selective advantage for the heterozygote (hybrid). Alleles with low
selection pressure may persist in the population in the heterozygote
state for many generations.
• As population size decreases, the effect of random drift increases.
This effect is of importance in germplasm collection and maintenance.
The original collection can be genetically changed if a small sample is
taken for growing to maintain the accession.

• In the absence of the other factors or processes, any one of the
frequency altering forces will eventually lead to fixation of one allele
or the other. The forces that alter gene frequencies are usually
balanced against each other (e.g., mutation to a deleterious allele is
balanced by selection).
• Natural mutations are of little importance to practical plant breeding.
However, breeders may artificially induce mutation to generate new
variability for plant breeding.

Thank u…

Population genetics

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