It is the fundamental law of population genetics and provides the basis for studying Mendelian populations ( Mendelian population: A group of sexually inbreeding organisms living within a circumscribed area). It describes populations that are not evolving.

1. COLLEGE OF AGRICULTURAL TECHNOLOGY
(Affiliated to Tamil Nadu Agricultural University,Coimbatore-3)
(Accredited by Indian Council of Agricultural Research, New Delhi)
Kullapuram, Via Vaigai dam, Theni-625562
Course Teacher Presented by
Dr. M. Kanimoli Mathivathana Priyadharshini. M
Assistant Professor ID NO.: 2017021049
Department of Plant Breeding & Genetics
HARDY WEINBERG’s LAW

2. Hardy-Weinberg law:
It is the fundamental law of population
genetics and provides the basis for studying
Mendelian populations ( Mendelian
population: A group of sexually inbreeding
organisms living within a circumscribed area)
It describes populations that are not
evolving.

3. Proposed independently by a British
Mathematician G. H. Hardy and a German
Physician Wilhelm Weinberg independently
in 1908.
The law states that “ the allele and
genotype frequencies in a population remain
constant generation after generation if there is
no selection, mutation, migration or random
drift ”.
G.H.Hardy Wilhelm Weinberg

4. Assumptions of Hardy- Weinberg law:
Organisms are diploid
Only sexual reproduction occurs
Population must be large
No immigration or emigration
No mutation (when mutation occurs it
leads to genetic drift)
Natural selection is not acting on the
population (all genotypes have an equal chance of
surviving and reproducing)
Mating is at random.

5. In general, a gene contains two alleles (a dominant one and a
recessive one).
Random union of gametes:
Consider the equations,
p+ q = 1 (in case of alleles)
where,
p= frequency of the allele A (dominant)
q= frequency of the allele a (recessive)

6. In case of genotypes, the Hardy-
Weinberg equilibrium is represented by the
equation,
p2+ 2pq+ q2 = 1
Frequency of genotype AA
Frequency of genotype Aa
Frequency of genotype aa
(Heterozygous genotype)
(Homozygous dominant) (Homozygous recessive)

7. Results of random mating in a population:
Two alleles {(p+q) 2= p2+ 2pq+ q2 }
F
M
A(p) a(q)
A(p) AA (p2) Aa (pq)
a(q) Aa (pq) Aa (q2)
F
M
A (p) B (q) C (r)
A (p) AA (p2 ) AB (pq) AC (pr)
B (q) AB (pq) BB (q2) BC (rq)
C (r) AC (pr) BC (rq) CC (r2)
Three alleles (p+q+r) 2 = p2+q2+r2+2pq+2pr+2qr

8. EXAMPLE:
1. Population of penguins = 1000
Foot color phenotypes: yellow (dominant)
blue (recessive)
If 12 of them have blue feet, find the
frequency of alleles and the genotypes.
Assume that the population is in Hardy-
Weinberg equilibrium.

9. Yellow foot allele = Y (frequency = p)
Blue foot allele = y (frequency = q)
Frequency of blue alleles in population = 12
12
i.e.,q2 = = 0.012  q = 0.11
1000
Since p + q = 1, p = 1 – 0.11 = 0.89
Allele
Allele
frequency
Y 0.89
y
0.11

10. Genotype Genotype
frequency
YY (p2) (0.89)2 =
0.79
Yy (2pq) 2 (0.89)
(0.11) =
0.2
yy (q2) (0.1)2 =
0.01
Phenotype

11. 2. In corn, purple kernels are dominant to yellow
kernels. A random sample of 100 kernels is taken
from a population in Hardy- Weinberrg
equilibrium. It is found that 9 kernels are yellow
and 91 are purple. What is the frequency of
yellow allele in the population?
Purple= 91 kernels= Dominant
(p2 & 2pq)
Yellow= 9 kernels= Recessive
(q2)
9
q2 = = 0.09  q= 0.3
100

12. Random mating among genotypes:
The frequency of mating between male
and female of any given genotype(s) will be
the product of the frequencies of the
frequencies of the concerned genotypes in the
population.
Genotype AA Aa aa
Frequency p2 2pq q2

13. Random mating of the genotypes (AA, Aa, aa)
would have the following frequencies:
AA (p2) Aa (2pq) aa (q2)
AA (p2) AA x AA
p4
AA x Aa
2p3q
AA x aa
p2q2
Aa (2pq) AA x Aa
2p3q
Aa x Aa
4p2q2
Aa x aa
2pq3
aa (q2) AA x aa
p2q2
Aa x aa
2pq3
aa x aa
q4

14. Mating Probability Frequency of progeny
AA Aa aa
AA x AA p4 p4
AA x Aa 4p3q 2p3q 2p3q
AA x aa 2p2q2 2p2q2
Aa x Aa 4p2q2 p2q2 2p2q2 p2q2
Aa x aa 4pq3 2pq3 2pq3
aa x aa q4 q4

15. Frequency of AA progeny:
= p4 + 2p3q + p2q2
=p2 (p2+ 2pq+ q2)
= p2
Frequency of aa progeny:
= p
2
q
2
+ 2pq
3
+ q
4
=q
2
(p
2
+ 2pq+ q
2
)
=q
2
Frequency of Aa progeny:
= 2p
3
q + 2p
2
q
2
+ 2p
2
q
2
+ 2pq
3
= 2pq (p
2
+ 2pq+ q
2
)
= 2pq

16. Significance of Hardy- Weinberg law:
• Not only gene frequencies but also genotype
frequencies of different alleles in a population
remain constant.
• A population in Hardy- Weinberg equilibrium
does not show evolution. In other words, for
evolution to occur the population should not
follow Hardy- Weinberg equilibrium
• All genotypes in a population reproduce
equally and successfully.

17. Reference:
Kavitha, B. Ahluwalia. 2009. Genetics,
New Age International Publishers, Pp:418-420.
Singh, B. D. 2007. Fundamentals of
Genetics, Kalyani Publishers, Pp:613-627.
Paul, A. 2011. Textbook of Genetics,
Books & Allied (P) Ltd., Pp:995-999.
Verma, P.S. and Agarwal, V.K. 2009.
Genetics, S.Chand Puublishing, New Delhi,
Pp:978-983.

18. https://www.nature.com/scitable/definition/hardy-
weinberg-equilibrium-122
https://www.britannica.com/science/Hardy-
Weinberg-law
http://evol.bio.lmu.de/_teaching/evogen/EvolGen
et_L3_HWE.pdf