Population Genetics

Population: Genetically, a population is defined as a group of interbreeding individuals. As a

result of interbreeding there is exchange among the individuals of a population and hence they
contribute to the gene pool of the progeny generation. The gene exchange is thus the main and
important factor to define a population.
Genetics: part of biological sciences .William Bateson (1906) coined the term genetics for the
study of heredity and variation from the Greek word gen.
The term genetics is defined as the study of heredity (Transmission of traits from parents to
offspring) and variation. Or "Genetics is the science of the material bases and the rules
governing the existence of heritable traits and their transfer from parents to offspring".

Population Genetics: The “Mendelian Genetics” extended at the level of population is the
Population Genetics and is defined as the study of genetic structure of population and changes
that occurs from generation to generation and the amount of genetic variation with in a
population along with the effect of forces that change and shape the genetic variation in the
population over time
Animal genetics: The study of the principles of inheritance in animals is called the animal
genetics.
Gamete: Reproductive cell (ova, sperm) which unite to form the zygote.
Genetic description of a population for qualitative traits:
The genetic structure of a population is described by it’s gene and genotype frequencies for a
particular characteristic.
Gene: is the basic unit of inheritance. Or gene is a functional unit of DNA
Allele – is an alternate form of a gene. Usually there are two alleles for every gene; sometimes
there may be as many as three or four alleles at a locus.
Gene frequency or allelic frequency: is defined as “the proportion of a given allele (gene) in a
pair of alleles or in a series of multiple allele at a locus to the total number of alleles (genes) at
that locus in the population. The relative frequencies range from zero to one or zero to hundred
percent. The frequencies of all genes at any locus must add up to unity or 100 %.
So a gene frequency or allelic frequency is the relative frequency of a particular allele in a
population. It is a measure of how common that allele is relative to other alleles that occurs at that
locus. For example- If an allele does not exist in a population, its gene frequency is zero. If it is the
only allele at this locus in the population, its gene frequency is one.
Genotype: is the genetic makeup of an animal. Or Genotype is the particular assemblage of the
genes carried by an individual.
Genotype Frequency: is defined as the proportion or percentage of a particular genotype among
the individuals in a population and the frequencies of all the genotypes together must add up to
unity, or 100%.
So a genotype frequency is the relative frequency of a particular one locus genotype in a
population.
For example- considering two alleles at a locus
When there are only two alleles at a given locus they may be denoted either by A1 and A2 or A
and a. The frequencies of these two alleles in the population are represented by p and q,
respectively.
In a diploid population (two alleles at a locus) of N indidividuals with A1 and A2 alleles, the
possible genotypes in the population at this locus are A1 A1, A1 A2 and A2 A2.Thus there are only
three possible combinations (genotypes) of the two alleles with the frequencies of the three
genotypes be represented as D, H and R respectively.

Genes Genotypes
A1 A2 A1 A1 A1 A2 A2 A2
Frequencies p q D H R

So that, p + q = 1, and D + H + R = 1,
Since each individual contains two genes, the frequency of A1 gene is ½ (2 D + H), and of A2
gene is ½ (2 R + H), and
The relationship between gene frequency and genotype frequency among the individuals
counted is as follows:
No. of A1 alleles
Freq. of (A1) allele (p) =---------------------- = ½ (2 D + H) = D + ½ H
No. of total alleles

No. of A2 alleles
Freq. of (A2) allele (q) =-------------------- = ½ (2 R + H) = R + ½ H
No. of A2 alleles

The genotypic frequencies can not be estimated from the gene frequencies, unless there is
random mating in the population and both gene and genotypic frequencies remain constant from
one generation to the next and show the following relation:
(p +q) ² = p² + 2pq + q², i.e. (sum of gene freq.)² =genotype frequencies = D + H + R
This relationship between gene frequencies and genotype frequencies has a great significance in
many calculations.
Differences between gene frequency and genotype frequency
1. The genotype frequency represents the proportion of individuals having a particular
genotype at a particular locus or loci affecting a character among the total individuals of
population. While the gene frequency represents the proportion of a particular allele
in a pair of alleles or in a series of multiple alleles at a locus among the total number of
alleles of that locus in a population.
2. The gene frequency in a population depends on the genotypic frequencies in the present
generation whereas in the subsequent generation the genotypic frequencies depend on the
gene frequencies of the parent generation.
3. The gene frequencies may be same in different populations but with different genotype
frequencies.
4. The gene frequencies are estimated from genotype frequencies but the genotype frequencies
can not be estimated from gene frequencies if the population is not in genetic equilibrium.
 Genetic Equilibrium Law (Hardy Weinberg Equilibrium Law)
Genetic Equilibrium: Genetic equilibrium means no change in genetic structure of population
gene and genotype frequencies) from one generation to the next.

Hardy, G. H. (1908) of England (Mathematician of Cambridge University) and Weinberg, W.

(1908) of Germany (Physician) reported independently the principles of genetic equilibrium,
which is known as Hardy –Weinberg law or principle of genetic equilibrium. This law states that
in a large random mating population the gene and genotype frequencies remains constant from
generation to generation in the absence of mutation, migration, and selection and there is a
relationship between the gene frequencies among parents and the genotype frequencies among
progeny. When this law holds true in a population, the genotypic frequencies among progeny are
obtained by the square of the sum of gene frequencies among parents.

Example: At a locus with two alleles (A and a), with their frequencies as p and q, in parents, three
genotypes will be produced (AA, Aa. and aa) with their respective frequencies as p², 2pq and q²
among offspring as:-

Square of sum of gene frequencies among parents = Genotypic frequency among progeny

(p +q)² = p² + 2pq +q², Such that p + q = 1.0 and p²+2pq +q² = 1.0

Therefore, this law is also known as square law.

A large random population with constant genetic structure from one generation to the next is said
to be in genetic equilibrium and the genotypic frequencies are known as H. W. genotype
frequencies. The necessary conditions to hold true the H. W. law are:

(1) Large population- Means the population should be large enough to avoid the chance effect in
changing the gene frequency in the population.

(2) Random mating among parents: Random mating means each individual should get equal
opportunity to mate with each individual of opposite sex in the parent’s population.

(3) Absence of evolutionary forces (migration, mutation and selection) – there should not be any
migration, mutation and selection in the population, as these forces always affect the gene and
genotype frequencies in the population.

Factors affecting gene frequency

There are two sort of process which changes the gene frequencies in a population.
(I) Systematic processes: which tend to change the gene frequency in a manner predictable in
both amount and in direction? This includes migration, mutation and selection.
(II) Dispersive process: This arises in small population from the effect of sampling, and is
predictable in amount but not in direction.
(I) Systematic processes:
(i)Migration:
 Let a large population consists of a proportion, m, of new immigrants in each generation and
the remainder, 1-m, being natives.
 Let the frequency of a certain gene be qm among the immigrants and qo among the natives
 Then the frequency of the gene in the mixed population, q1, will be
q1 = mqm + (1 – m) qo
= m (qm – qo) +qo
 The change of gene frequency, q , brought about by one generation of immigration is the
difference between the frequency before immigration and the frequency after immigration will be
q = q1 – qo
= m (qm – qo)
 The rate of change of gene frequency in a population subject to immigration depends on:
(i)The immigration rate and
(ii)The difference of gene frequency between immigrants and natives.
(ii)Mutation
• Non-recurrent mutation- is of little importance as a cause of change of gene frequency,
because the product of a unique mutation has an infinitely small chance of surviving in a large
population, unless it has a selective advantage.
• Recurrent mutation- each mutational event recurs regularly with characteristic frequency,
and in a large population the frequency of a mutant gene is never so low that complete loss can
occur from sampling
 Measurements of mutation rates indicate values ranging between about 10-4 and 10-8 per
generation
 Studies of reverse mutation (from mutant to wild type) indicate that it is usually less frequent
than forward mutation (from wild type to mutant), on the whole about one tenth as frequent
 There could be an increased mutation rates such as might be caused by an increase of the level
of radiation to which the population is subjected
(iii) Selection
• We know individuals differ in viability and fertility, and they therefore, contribute different
numbers of offspring to the next generation.
• The proportionate contribution of offspring to the next generation is called the fitness of the
individual or adaptive value, or selective value. If the difference of fitness is in any way
associated with the presence or absence of a particular gene in the individual’s genotype, then
selection operates on that gene.
• When a gene is subject to selection its frequency in the offspring is not the same as in the
parents, since parents of different genotypes pass on their genes unequally to the next generation.
• The change of gene frequency due to is more complicated to describe because the differences
of fitness that give rise to the selection are an aspect of phenotype. We therefore have to take
account of the degree of dominance shown by the gene in question, which is as follows;

(ii) Dispersive process: It differs from the systematic processes in being random in direction, and
predictable only in amount but not in direction and results due to chance factor/ sampling, in
small population. The gametes that transmit genes to the next generation carry a sample of the
genes in the parent generation, and if the sample is not large the gene frequencies are liable to
change between one generation and the next. This random change in gene frequency is the
dispersive process. The change in gene frequency due to chance factor in a small population is
known as “Genetic drift.”
The dispersive process has three important consequences.
(i) It results in the differentiation between sub populations / local groups because mating
takes place more often between inhabitants. Domesticated or laboratory populations, in the same
way are often subdivided in to herds or strains.
(ii) It causes the reduction of genetic variation within a small population and individuals of
the population become more and more alike in genotype and this genetic uniformity is the reason
for the widespread use of inbred strains of laboratory animals in physiological and allied field of
research
(iii) It leads to the dispersive process which results in an increase in the frequency of
homozygote at the expense of heterozygote. This coupled with the general tendency for
deleterious alleles to recessive, is the genetic basis of the loss of fertility and viability that

Sex Linked Genes

The relationship between gene frequency and genotype frequency in the homogametic sex is the
same as with an autosomal gene, but the heterogametic sex has only two genotypes and each
individual carries only one only one gene instead of two. For this reason two– third of the sex
linked genes in the population are carried by the homogametic sex and one – third by
heterogametic. In mammals the heterogametic sex is male and homogametic sex is female but
reverse is true in avian.
Considering two alleles A1 and A2 with frequencies p and q and let the genotypic frequencies be as
follows
Females Males
Genotype A1 A1 A1 A2 A2 A2 A1 A2
Frequencies D H R Q S

The frequency of A1 allele among the females is then pf = D + ½ H, and the frequency among the
males is pm = Q. The frequency of A1 in the whole population is

p =2/3 pf + 1/3 pm
= 1/3 (2 pf + pm)
= 1/3 (2D + H+ Q)

Similarly the frequency of A2 allele in the females is qf = R +1/2H and the frequency among the
males qm = S. The frequency among the whole population is

q = 2/3 qf + 1/3 qm
= 1/3 (2pf + qm)
= 1/3 (2R + H + S)

Now if the gene frequencies among males and females are different, the population is not in
equilibrium. The gene frequencies in the population as a whole does not change, but its distribution
between two sexes oscillates as the population approaches equilibrium.
 Sex influenced traits
Due to the genotype environment interaction, different genotypes respond differently in different
environment and changed their phenotypic expression. The environment may be external or
internal to the body. Sex hormones are different in two sexes and this changes the expression of
some genes (dominant recessive relationship) according to the sex of the individual. As a result
one allele of a gene pair shows dominance over its allele in one sex but behave as recessive allele
in another sex. Thus the dominance recessive relationship of the alleles of a gene pair is reversed
in the two sexes. This makes the heterozygous genotype to produce different phenotypes in the two
sexes. Such genes whose phenotypic expression is sex dependent are called as sex influenced
genes and the characters controlled by these genes are called as sex influenced traits. Thus sex
influenced traits are expressed differently in two sexes. For e.g. Presence or absence of horns in
some breeds of sheep, Mahogany and white colour in Ayrshire breed of cattle. Pattern baldness,
short length of index (Second) finger, white forelock and beardness in goats shows dominance in
males but recessive in females. The inheritance pattern of index finger in human can be shown as
under.
Genotypes Phenotypes
_______________________ __________
Men Women
________________________________________________________________
F1`F1 Short finger Short finger
F1F Short Long
FF Long Long
__________________________________________________________________

The frequency of recessive allele (q) is estimated as the square root of the frequency of recessive
phenotype in one sex q = q2 and the frequency of p is estimated from recessive phenotype of
opposite sex as p = p 2 . The (p+q) will approach to unity if the gene frequencies are in
equilibrium.
Problems:-
1. Calculate gene frequency of A and a alleles in a random mating population having
500AA, 600Aa and 950aa individuals. What is the expected number of each genotype if
the above population is in H.W E.?
2. What is frequency of heterozygote Aa in a random mating population
(i) If the frequency of recessive phenotype is as 0.09
(ii) If the frequency of all the dominants is 0.19
3. Consider three genotypes (PP, Pp and pp) in a random mating population of cattle (PP
and Pp being polled and pp being non- polled). 36 out of 100 animals are non polled.
Calculate the relative frequencies of (i) two alleles (ii) 3 genotypes and (iii) two
phenotypes
4. In a random mating population, it was found that one- fourth of the normal individuals
were carriers for a defect controlled by single locus two alleles. Find out the frequency of
recessive allele.

5. Assume a cattle population that is all horned and thus all animals are pp genotype, in to
which polled bulls (PP) are introduced to undertake 15% of the mating. The original
frequency of the P allele in the original population (qo ) was 0 and that of the immigrants
(qm) was 1.0, the value for m is 0.15 and since polled bulls replace horned ones the
formula for change becomes:
q1 = 15/2 (1.0 – 0) = + 0. 075
The division of 15 by 2 occurs because only males are introduced.