Hardy-Weinberg Law K. Vanangamudi Factors of Hardy-Weinberg Law

1. Hardy-Weinberg Law
Prepared by
Dr. K. Vanangamudi
Formerly Dean (Agriculture), AC & RI, Coimbatore,
Dean, AdhiparashakthiAgricultural College,Kalavai,
Professor and Head - Seed Science and Technology,
Tamil Nadu Agricultural University, Coimbatore.
Hardy-Weinberg Law
 Cross pollinated crops are highly heterozygous due to the free inter
mating among them and these are random mating population/ genetic
population. Because, each individual of the population has equal
opportunity of mating with any other individual.
 It is also known as mendelian/panmictic population. A mendelian
population may be thought of having a gene pool consisting of all
gametes produced by the population. So, gene pool may be defined as
the sum total of all genes present in the population.
 A population, consists of all such individuals that share the same gene
pool, has an opportunity to inter mate with each other and contribute to
the next generation of the population.
 Each generation of a mendelian population may be considered to arise
from a random sample of gametes from the gene pool of previous
generation.
 Hence, it is not easy to follow the inheritance of a gene in a mendelian
population.
 Genetic makeup of such population cannot be estimated by using the
techniques of classical genetics. So, population genetics has been
developed.
 This law is independently developed by Hardy (1908) in England and
Weinberg (1909) in Germany. The law states that the gene and genotype
frequencies in a mendelian population remain constant from generation
after generation, if there is no selection, mutation, migration or
random drift.
 Frequencies of the these genotypes for a locus with two alleles A and a
would be P2 (AA), 2pq (Aa) and q2 (aa)

2.  Where, p= Frequency of A allele in the population.
 q= Corresponding frequency a allele in the population
 Sum of p+q is equal=1
 Such a population will be at equilibrium since the genotypic
frequencies will be stable, i.e., no change from one generation to the
next. This equilibrium is known as Hardy Weinberg equilibrium.
Factors
1. Migration
 Migration is the movement of individual into a population from a
different population.
 Migration may introduce new alleles into the population or may change
the frequency of existing allele.
 Amount of change in gene frequency q will primarily depend upon two
factors.
 Ratio of migrant individuals to those of the original population.
 Magnitude of difference between the values of q in the
population and in the migrants.
 So, in plant breeding migration is by inter varietal crosses or poly
crosses.
1. Mutation
 Mutation is a sudden heritable change in an organism and is generally
due to a structural change in a gene.
 It may produce a new allele not present in the population or may
change the frequency of existence allele.
3. Random drift or Genetic drift
 It is a random change in gene frequency due to sampling error.
 Random drift is more in small population than larger.
 Ultimately, the frequency of one of the allele becomes zero and that of
the other allele becomes one.
 Allele with the frequency one is fixed in the population, because there
would be no change in the frequency.
 So, all genes become homozygous.
 Genetic drift can be reduced by handling large population.

3. 4. Inbreeding
 Mating between individuals sharing a common parent in their
ancestry inbreeding reduces the proportion of the heterozygosity and
increase the frequency of homozygosity by the rate of decrease in
heterozygosity is equal to ½ N
 N- Number of plants in the population per generation in monocious
or hermaphrodite species.
 In diocious species and monoecious species where self-pollination
is prevented, the decrease in heterozygosity is lower.
 In small population, even with strict random mating/ strict cross
pollination, the frequency of homozygotes increases, while that of
heterozygotes decreases due to inbreeding.
4. Selection
 Refers to differential reproduction rates of various genotypes.
 In crop improvement selection is important, because it allows the selected
genotypes to reproduce.
 While, undesirable genotypes are eliminated.
 So, in random mating population selected genotypes would be fixed
and the fitness is zero for remaining genotype.
 Fitness of a genotype is defined as its reproduction rate in relation to
that of other genotypes.
 It is difficult to identify genotypes for dominance due to less than 100%
heritability especially for quantitative character and as a result, selection
is expected to change gene frequencies rather than to eliminate one or
other allele.
 Selection in a random mating population is highly effective in increasing
or decreasing the frequency of allele, but it is unable to either fix or
eliminate them.
 However, in combination with a system of inbreeding, selection is highly
efficient in the fixation and elimination of an allele.
 Most of the quantitative characters are of economic importance which are
governed by many genes. As these characters show a continuous
distribution, selection intensity is measured as the difference between
mean of the population and that of the selected individuals.
 It is expressed in terms of K standard deviation units from which the
selection differential K is calculated. Value of K is related to the per
cent of extreme individuals saved.

4.  Eg: When the extreme 5% of the population is saved, K=2.06.
Selection of the extreme phonotype increases the frequency of
desirable alleles in the population.
 It increases the frequency of desirable alleles and the frequency of
desirable genotypes will also increase new genotypes resulting in
producing more extreme genotypes.
 Therefore, mean of the population will change under selection. Variance
may decrease to some extent, but selection will show continuous gain for
several generations
 In case the quantitative character, it is governed by one or few genes with
large effect. The desirable genes may be fixed after some generation of
selection. So, gain under selection will continue for several generations,
but in the later generations, it will be small and discouraging.
 Progress under selection is retarded by non-additive gene action, low
heritability and limit on permissible selection intensity.
 Permissible selection intensity depends on fecundity i.e. reproductive
capacity of the species and the consideration of inbreeding.
 Inbreeding should be kept to a low level to maintain heterozygosity and
to avoid inbreeding depression. So, selected plants shall be relatively
large and cannot be too small.
 Breeder is interested in improvement more than one character.