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.

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, p 2 + 2pq+ q 2 = 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 = p 2 + 2pq+ q 2 } F M A(p) a(q) A(p) AA (p 2 ) Aa ( pq ) a(q) Aa ( pq ) Aa (q 2 ) F M A (p) B (q) C (r) A (p) AA ( p 2 ) AB ( pq ) AC (pr) B (q) AB ( pq ) BB (q 2 ) BC ( rq ) C (r) AC (pr) BC ( rq ) CC (r 2 ) Three alleles ( p+q+r ) 2 = p 2 +q 2 +r 2 +2pq+2pr+2qr

8. EXAMPLE: 1. P opulation of penguins = 1000 F oot 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.,q 2 = = 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 (p 2 ) (0.89) 2 = 0.79 Yy (2pq) 2 (0.89) (0.11) = 0.2 yy (q 2 ) (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 (p 2 & 2pq) Yellow= 9 kernels= Recessive (q 2 ) 9 q 2 = = 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 p 2 2pq q 2

13. Random mating of the genotypes (AA, Aa , aa ) would have the following frequencies: AA (p 2 ) Aa (2pq) aa (q 2 ) AA (p 2 ) AA x AA p 4 AA x Aa 2p 3 q AA x aa p 2 q 2 Aa (2pq) AA x Aa 2p 3 q Aa x Aa 4p 2 q 2 Aa x aa 2pq 3 aa (q 2 ) AA x aa p 2 q 2 Aa x aa 2pq 3 aa x aa q 4

14. Mating Probability Frequency of progeny AA Aa aa AA x AA p 4 p 4 AA x Aa 4p 3 q 2p 3 q 2p 3 q AA x aa 2p 2 q 2 2p 2 q 2 Aa x Aa 4p 2 q 2 p 2 q 2 2p 2 q 2 p 2 q 2 Aa x aa 4pq 3 2pq 3 2pq 3 aa x aa q 4 q 4

15. Frequency of AA progeny: = p 4 + 2p 3 q + p 2 q 2 =p 2 (p 2 + 2pq+ q 2 ) = p 2 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/EvolGenet_L3_HWE.pdf