This document discusses population genetics and the Hardy-Weinberg principle of genetic equilibrium. It defines key terms like allele frequencies, genotype frequencies, and gene pools. It also describes how to calculate allele frequencies and genotype frequencies in a population. The document concludes by explaining that under certain conditions like a large panmictic population with random mating, the genetic structure will remain in equilibrium with allele and genotype frequencies remaining constant from generation to generation based on the Hardy-Weinberg principle.

1. Population Genetics
(Calculation of allele frequencies, Calculating frequency of
sex-linked alleles)
Presented to
Dr. Sunita Patel
Assistant Professor
School of Life Sciences
Central University of Gujarat
Presented by
Mr. Suraj Singh
Student (M.Sc. in Life Sciences)
School of Life Sciences
Central University of Gujarat 1

2. Population Genetics
deals with genes as alleles and gene
frequencies as allele frequencies.
- The frequencies of individual alleles
- All the alleles of all individuals in the population
These are two major attributes of a population.
2

3. Population
• A group of organisms of the same species that live in the
same area and interbreed producing fertile offspring.
• Different population of a single species are usually
isolated geographically so that exchange of genetic
material between them occurs less frequently.
• Because of less frequent interbreeding, the gene pools of
different populations show more differences.
3

4. Mendelian Population
• Mendelian population is defined as a
• Each member has an equal oppurtunity of mating with
any other member of the opposite sex.
4

5. Figure 1 - The interbreeding relationship between the individuals of a population and between the gene pools of different populations,
races and species. Free interbreeding is found among the members of population but interbreeding becomes less frequent among
sister populatios, races or species.
5

6. Attributes of a Mendelian Population
• Individuals of a Mendelian Population have somewhat
similar genetic constitution and gene alignment except for
some uniqueness.
• Individual variation often reflect genetic variation
(differences in the composition of their genes).
• A population possesses a given gene pool and all the
members of a population share in the same gene pool and
contribute to it.
• There is a free gene flow among all the members of a
population because of free interbreeding. 6

7. Attributes of a Mendelian Population - continued
• Each member of a population has equal chances of
mating with any other member of opposite sex.
• The sister populations of a species are in occasional
reproductive contact, but the chances of interbreeding are
less than among the individuals of the same population i.e.
interpopulation interbreeding is occasional and
intrapopulation interbreeding is frequent.
• Because of occasional breeding between individuals of
sister populations, their gene pools are interconneted
and gene pool of the entire species get reshuffled
continuously. 7

8. Gene Pool
• Sum total of all the copies of every type of allele at every locus in all the
members of a Mendelian Population
Gametic pool - sum total of alleles present in the gametes of a Mendelain
populaion
• A gene pool provide information about -
• If only one allele exists for a particular locus in a population, that allele is said
to be fixed in the gene pool.
8

9. Figure 2 - The gene pool of a population for gene locus X is represented by three alleles
X1, X2 and X3. Each of the colored circles represents an individual.
9

10. Integrity of Gene Pool
• Gene pool maintains its integrity as long as there is no
interbreeding between populations.
• Because of interbreeding between sister populations, the genes
from one sister population enter the other populations and vice
versa.
• This transfer of gene is called gene flow.
• Gene flow leads to mixing and reshuffling of gene pools.
10

11. Figure 3 - Gene flow from one population to another population by interbreeding.
11

12. Equilibrium
• The gene pool maintains or tries to maintain a dynamic
equilibrium in the gene and genotype frequencies but
these change due to mutations, preferetial interbreeding
and natural selection.
12

13. Fluctuation in Size of Gene Pool
• The size of the gene pool depends on the number of genes and
the individuals carrying these genes.
• The gene pool becomes large by the addition of the genes to
the gene pool. This is brought about by immigration and
mutation.
• The gene pool decreases in size by the removal of genes which
is brought about by emigartion, natural selection and genetic
drift
• Genetic drift aka allelic drift or the Wright effect
13

14. • To measure genetic variation in a Mendelian populations, we
need to count every allele at every locus in every individual in it.
• This will provide information about the frequencies of all alleles
in the population c/a allele frequency / gene frequency.
• The
is also called gametic frequency or allelic
frequency and the
represents genotype
frequency.
14

15. • It refers to the proportion of an allele in the
gene pool as compared with other alleles at
the same locus, with no regards to their
distribution in organisms.
15

16. Figure 4 - Diagram showing frequency of three genotypes among females and males for a locus with two
alleles (A,a), in one generation, the allele frequencies among their eggs and sperm, and the genotype
frequencies among the resulting offspring. 16

17. • Imagine a hypothetical population of hamsters with black and gray hair. These
are controlled by two alleles located on the same locus.
• These are A and a, of which A is dominant and a is recessive .
• Three types of genotypes may exist in the population when there are two alleles
as follows :
AA - Homozygous dominant = 25%
aa - Homozygous recessive = 25%
Aa - Heterozygous = 50%
• The ratio of A allele to a is the frequency of A allele and
the ratio of a and A is the frequency of allele a.
• Incase allele frequencies in parental generation are A = p = 0.7 and of a = q = 0.3; in
offsprings of second, third or further generations, the genotypic ratio and gene frequencies
will remain the same as in the parental generation in case population follows Hardy -
Weinberg principle. 17

18. • Suppose a diploid population has 1000 individuals and that for a particular
gene locus in that population, there are only two alleles A and a or A1 and
A2.
• There will be three possible genotypes for this locus AA and aa (or A1A1
and A2A2), both homozygous and Aa or A1A2 heterozygous.
• Let us say that out of 1000 individuals 400 have genotype AA (or A1A1),
other 400 are heterozygous with Aa (or A1A2) genotype and 200 are aa or
A2A2.
• Then allele frequency of A and a in a population can be calculated by the
following formula:
18

19. Calculation of allele frequency or gene frequency
i. Allele frequency of A or A1
p = =
ii. Allele frequency of a or A2
q = =
19
Aa

20. The above numericals can be represented as follows:
i. Total no. of individuals = N
ii. Total no. of alleles A and a (since the organisms is diploid) = 2N
iii. No. of homozygous dominanat = D
iv. No. of homozygous recessive = R
v. No. of heterozygotes = H
vi. Total no. of dominant allele (A) = 2D + H
a. The no. of dominanat allele (A) contributed to the gene pool by homozygous dominants =
2D
b. The no. of dominant allele (A) contributed to the gene pool by heterozygous = H
vii. The frequency of allele (A) : (2D + H) / 2N
viii.The no. of recessive allele (a) contributed to the gene pool = 2R + H
a. Contributed by homozygous recessive (aa) = 2R
b. Contributed by heterozygotes (Aa) = H
ix. Frequency of allele a = (2R + H) / 2N 20

21. If frequency of allele A is represented by p and that of a by q and
at gene equilibrium their total frequency is represented by 1,
then equilibrium :
p + q = 1
or, p = 1 - q = 2D + H/2N
or, q = 1 - p = 2R + H/2N
21

22. Genotype Frequency
• The genotype frequency is the
all of which exhibit similar
character with respect to the locus under consideration.
• In a population, there are two alleles at one gene locus (A1 and
A2) and they are related as dominant and recessive.
• Naturally, individuals with three genotypes, i.e., homozygous
dominant, heterozygous and homozygous recessive will occur
in the population.
22

23. If N = Totoal no. of individuals in the population
D = No. of homozygous dominant
H = No. of heterozygous individuals
R = No. of homozygous recessive
Then, genotype frequency of A1A1 individuals = D/N
genotype frequency of A1A2 individuals = H/N
genotype frequency of A2A2 individuals = R/N
It means that genotype frequency for a particular type of gene
combination on the same locus can be determined by dividing the
number of individuals with that genotype by the total number of
individuals in the population. 23

24. Calculation of Genotype Frequency
A. The frequency of homozygotes is calculated by squaring
the frequency of the allele A and allele a.
B. The frequency of heterozygotes is calculated as follows:
a) Gene frequency of A allele = p
b) Gene frequency of a allele = q = 1 - p
c) Genotype frequency of AA = p2
d) Genotype frequency of aa = q2 = 1 - p2
e) Genotype frequency of Aa = 2pq
24

25. Example
a. Genotype frequency of recessive allele (aa) in human
population, i.e., q2 = 0.00005
b. Gene frequency of recessive allele aa,
i.e., q = (0.00005)1/2 = 0.007
a. Gene frequency of dominant allele A1 or A,
i.e., p = 1 - q = 1 - 0.007 = 0.993
a. Genotype frequency of heterozygotes Aa,
i.e., 2pq = 2 ×(0.993 × 0.007) = 0.014
a. Genotype frequency of homozygous (AA)
p2 = 0.993 × 0.993 = 0.986
25

26. Calculating frequency of sex-linked alleles
• Let’s consider a diploid population with X-Y sex determination
(Female - XX; Male - XY)
• We want to study evolution of a locus with two alleles on the X-
chromosome (with no counterpart on the Y-Chromosome).
• Assumption -
pf(t) = frequency of the A allele among X gametes in females
in generation t
pm(t) = frequency of the A allele among X gametes in males in
generation t
26

27. • Under the H-W assumptions, the following offspring
genotype frequencies are found to be -
ØIn daughters
AA : PAA (t+1) = pf (t) pm (t)
Aa : PAa (t+1) = pf (t) [ 1 - pm (t) ] + pm (t) [ 1- pf (t) ]
aa : Paa (t+1) = [ 1 - pf (t) ] [ 1 - pm (t) ]
ØIn sons
AY : PAY (t+1) = pf (t)
aY : PaY (t+1) = 1 - pf (t) 27

28. • Allele frequencies among the offspring are:
Average of allele frequencies in both parent
sexes
pf (t+1) = 1/2 [ pf (t) + pm (t) ]
the allele frequency among just the female
parents
pm (t+1) = pf (t)
28

29. Conclusion
• The frequencies of different alleles at each locus and the
frequenceis of different genotypes in a Mendelian population
describe its
• Allelel frequencies measure the amount of genetic variation
in a population
• Genotype frequencies show how a population’s genetic
variation is distributed among its members.
29

30. HARDY - WEINBERG EQUILIBRIUM
• In 1908, British mathematician, Godfrey Hardy and German
physician, Wilhelm Weinberg independently derived a
mathematical equation to represent the distribution of alleles and
genotypes pertaining to a specific gene locus in a panmictic
Mendelian population.
• Later, in 1920-30, R.A. Fisher and J.B. Haldane in England and
Sewall Wright in United States worked out that under certain
conditions, the genetic structure of a population may not
change over time.
• They established the concept of “Hardy - Weinberg Principle
of Equilibrium.” 30

31. HARDY - WEINBERG EQUILIBRIUM conti....
• The principle of genetic equilibrium states that
31

32. Explanation
• Hardy - Weinberg law desribes a theoretical situation in which a
population is undergoing no evolutionary change.
• It explains that
– if the evolutionary forces are absent,
– the population is large,
– its individuals have radom mating,
• Each parent produces roughly equal number of gametes, the allele
frequencies are identical in males and females and the gametes
produces by the mates combineat random and the gene frequency
remains constant, then the genetic equilibrium of the genes in question
is maintained and the variability present in the population is preserved.
32

33. AA Aa aa
Genotype frequencies 36% 48% 16%
0.36 0.48 0.16
Allele Frequency A 60% or 0.6
a 40% or 0.4
• Since AA individuals make up 36% of the total population, they will contribute
approximately 36% of all the gametes formed in the population. These
gametes will possess gene A.
• Similarly, aa individuals will produce 16% of all the gametes.
• But gametes from individuals Aa will be of two types, i.e., with gene A and with
gene a roughly in equal proportion.
• Since these contitute 48% of the total
population, they will contribute 48%
gametes, but out of them 24% will
have gene a.
• Hence, the overall output of the gametes
will be:
Parents Gametes Parents Gametes
36% AA 36% A 16% aa 16% a
48% Aa 24 % A 48% Aa 24% a
Total 60% A 40% a
33

34. Figure 5 - Calculating alllele and genotype frequencies with the help of Hardy-Weinberg equation 34

35. • The above concept can be translated into a simple mathematical expression:
Frequency of gene A is represented by = p
Frequency of gene a is represented by = q
and there is random union of the gametes with gene A and a.
At the equilibrium state, the population will contain following frequencies of the
genotypes and genes A and a generation after generation:
AA + 2Aa + aa = genotype frequencies
or, p2 + 2pq + q2
• The above results are explained by relying on the theory of probability.
Sl.No. Parents Sperm Ova Gene Frequency in
Offspring
Offspring
genotype
1 AA 60 60 60×60 = 36% AA
2 Aa 60 40 60×40 = 24% Aa
3 aA 40 60 40×60 = 24% Aa
4 aa 40 40 40×40 = 16% aa
35

36. In a population of large size:
– Probability of formation of AA individuals = p × p = p2
– Probability of formation of aa individuals = q × q = q2
– Probability of formation of Aa individuals = 2 × p × q = 2pq
• In the next generation, the probability of frequency AA, aa and Aa individuals will
again be p2, q2 and 2pq.
• The relationship between gene frequency and genotype frequency can be expressed
as :
a) if gene frequencies of two alleles A and a are p and q : p+q = 1
b) the genotype frequencies in the population will be:
(p + q)2 = (1)2
p2 + 2pq + q2 = 1
It is known as
.
From this binomial expression, it is clear that in a large and randomly mating population
both gene and genotype frequencies remain constant or tend to remain constant.
36

37. According to Hardy - Weinberg principle, the gene and genotype
frequencies of each allele in a population remain at an equilibrium
(static) generation after generation, if that population exhibits
following attributes :
- The equilibrium in gene and genotype frequencies
occurs only in large sized populations.
In small populations, there will be significant sampling errors and radom
fluctuations in the gene frequency by chance the so called genetic
drift or random drift. 37

38. • The population should be panmictic where every gamete has an
equal opportunity of fusing with any other gamete of the opposite
sex.
• This nonpreferential fusion of gametes is called random mating.
• The natural populations may not fulfill this equality, because
individuals show preferential mating within a subset of the
population and random mixing of gametes fails to occur.
38

39. 39
3.
Hardy - Weinberg principle is applicable only for biparent
sexually reproducing species.
Unisexual or asexually reproducing populations do not
follow Hardy - Weinberg Law.

40. A population normally consists of individuals at different stages
of reproductive maturity.
According to Hardy and Weinberg, the population must be
homogenous in this regard.
40

41. • The gene frequency will remain static only in the absence of evolutionary forces
like mutations, selection, genetic drift and migration.
• There will be no gene mutations, because mutations affect allele frequencies.
• There shall be no gene flow either by immigration or emigration
• All genotypes in a population shall reproduce equally. There shall be no
selection and no preference for specific genotype or phenotype for mating.
• The absence of selection means every gamete is viable, all gametes have
equal chances of becoming a zygote, every gametic union (zygote) also
survives and gametes or zygotes are not segregated into claases of varying
survival value.
– Under these conditions the genetic composition of population will remain
unchanged. 41

42. • From the above discussion it becomes clear that
populations exhibiting genetic equilibrium or following
Hardy - Weinberg’s principle are static with zero
evolutionary rate.
• This means such populations do not evolve and any
population evolving is not static and does not exhibit
genetic equilibrium.
42

43. Examples -
• Among the many variations in proteins on the surface of human red blood
cells are those resulting from variation at the MN locus.
• Two alleles (M, N) and three genotypes (MM, MN, NN) are distinguished
by blood grouping.
• A sample of 320 people in the Sicilian village of Desulo yieled the
following numbers of people carrying each genotype:
MM =187, MN =114, NN = 19
• We can now estimate the frequency of each genotype as the proportion of
the total sample that carries that genotype. Thus,
Frequency of MM = D = 187/320 = 0.584
Frequency of MN = H = 114/320 = 0.356
Frequency of NN = R = 19/320 = 0.059
• Note that these frequencies, or proportions, must sum to 1. 43

44. • Now we can calculate the allele frequencies.
• Each person carries two gene copies, so the total sample represents
320 × 2 = 640 gene copies.
• Because MM homozygotes each have two M alleles and MN
heterozygotes have one, the number of M alleles in the sample
= (187 × 2) + (114 × 1) = 488.
• The number of N alleles = (19 × 2) + (114 × 1) = 152.
Hence,
frequency of M = p = 488/640 = 0.763
frequency of N = q = 152/640 = 0.237
44

45. Significance of Hardy-Weinberg Principle
• The Hardy - Weineberg principle is the foundation on which
almost all of the theory of population genetics of sexually
reproducing organisms - which is to say, most of the genetic
theory of evolution - rests.
• It has two important implications
1. Genotype frequencies attain their H-W values after a single
generation of random mating. If some factor in the past had caused
genotype frequenceis to deviate from H-W values, a single generation
if random would erase the imprint of that history.
2. According to the H-W principle, not only genotype frequencies, but
also allele frequencies, remain unchanged from generation to
generation. 45

46. Hardy-Weinberg Principle and Evolution (Factor that
Change Gene Frequency)
• Unlike the theoretical static Hardy-Weinberg model of a genetic
population, a natural biological population is dynamic.
• Its gene equilibrium changes from one to next generation by the
disruptive action of ecolutionary forces.
• The evolutionary forces change the gene pool of the population.
• These include genetic polymorphism or genetic variability
(caused by gene mutations, chromosomal aberrations,
hybridisation, change in chromosome number and immigration
or gene flow), genetic drift and selection. 46

47. Figure 6 - Factors that upset Hardy - Weinberg eqilibrium in a population. 47
Equilibrium in
gene frequencies
and genotype
frequencies in
the gene pool
changes

48. Polymorphic population
– means in the gene pool of populations, each gene is present in
the form of two or more variants or alleles.
– exhibit varied degree of genetic variability.
– all natural population are polymorphic population.
Monomorphic population
– a population of only one variant of character.
48

49. Essentiality of Genetic Variability
• Genetic variability in populations is essential for evolution.
• Evolution will be very slow if populations are genetically
uniform and mutations arise only occasionally to replace the
pre-existing genotypes.
• There will be no evolution & no genetic variability without
mutations.
• The rate at which mutations arise at a single locus is usually low
that their occurence results in very small deviations from Hardy -
Weinberg expectations.
• It means for large deviations other forces also introduce genetic
variability.
49

50. Factors Responsible for Genetic Variability in Populations
• Gene mutation that introduce multiple loci
• Gene recombination produced during sexual reproduction, i.e.,
1. at the time of gamete formation i.e., meiosis
2. due to non-random fusion of genetically different gametes at
fertilisation.
• Changes in the arrangement of genes in individual chromosomes
• Changes in the number of genes in individual chromosomes
• Changes in the number of chromosomes
• Gene flow due to introgression or interogressive hybridisation (
50

51. • A population may receive alleles from a nearby
population in a process known as gene flow or
sometimes as migration because individuals move from
population to population, taking their genotypes with them.
• Gene flow may be between populations with similar allele
frequencies or between populations with different allele
frequencies.
51

52. • The rate of gene flow among natural populations can be
estimated by following the dispersal of marked individuals
or their gametes.
• Following three factors have an impact on the recipient
population.
52

53. • Genetic drift is one of the most important of such random
or non-directional forces, is a consequence of random
fluctuations in gene frequencies that arise in small
populations.
• They show non-directional fluctuations generation after
generation purely by chance.
• These deviations are nondirectional and nonadoptive.The
harmful alleles may increase and rare advantageous alleles
may be lost because of genetic drift.
• In larger populations, genetic drift is countered by selection.
53

54. • The reason for such non-directional deviations in allele
frequencies in small populations are :
1. Bottleneck Effect
2. Founder’s Effect
54

55. • Large populations occassionally pass through
seasonal or yearly phenomenon of cycle fluctuation
in their population density leaving only a few individual to survive.
• These few surviving individuals form the origenitors for the future generation.
• The period of low population density in the seasonal cycles represents a
bottleneck period and changes in allels frequencies occuring during this
bottleneck period constitute bottleneck effect.
• The bottleneck effect may result in the loss of some advantageous alleles or in
the increased frequencies of even harmful alleles.
• The lost of alleles in different subpopulations or demes of the same large
population may be different depending on chance. 55

56. • When a few individuals become
isolated from a large population and
invade a new isolated geographical
region and establish a new population, they become
founder members.
• They will carry only a limited portion of parental gene pool.
• The population arising from these founder members is unlikely to
have all the alleles from the gene pool of source population.
• The resulting diversion in the gene pool of new population is
called founder effect.
56

57. • Natural selection is based on differnetial success in survival and
reproduction.
• Individuals in a population that are better suited to their environment
tend to produce more offspring than those with traits that are not suited
so well.
• The relative success of different phenotypes within a population leads
to change in allele frequencies and thus disturbs Hardy-Weinberg
equilibrium.
• It is determined by the average number of offspring they produce over
their lifetimes.
• Therefore, natural selection is described as the differential reproduction
of genotypes and is linked to increased adaptibility to the environment.
57

58. • Parents represent a random sample of genes and gene
frequencies from the gene pool of a population.
• Heterozygotes for any gene pair produce two kinds of gametes
in equal frequency showing complete segregation of alleles of a
gene pair.
• Both the parent are equally fertile.
• All the gametes are equally fertile and have equal chances of
survival and forming a zygote.
58

59. • All the zygotes formed have equal chances of survival and
developing into an adult.
• Gene frequencies are the same in both male and female parents.
• Mating between the two sexes is non-preferential and random.
• All genotypes have equal reproductive ability and equal chances
of contributing the genes/alleles to the gene pool of the
population.
59

60. 1. Parents represent a random sample
of the gene frequencies in the
population.
A. Provide gene frequency in
parents
60
2. Gene segregate normally into
gametes (homo or heterozygotes)
3. Parents are equally fertile
4. The gametes are equally fertile.
5. The population is very large.
B. Provide gene frequency in
gametes
C. Provide gene frequency in the
gametes that form the zygote

61. 61
8. All genotypes have equal
reproductive ability.
7. Gene frequencies are the same in
both male and female parents.
E. Provide genotype frequencies in
the zygotes
F. Repeat of steps A,B,C,D,E, etc.
D. Provide gene frequency in the
zygotes
6. Mating between parents is random.

62. • Organic evolution by Veer Bala Rastogi
• Evolution by Douglas J. Futuyma Mark Kirkpatrick
• Evolution Principles and Processes by Brian K. Hall
• https://www.expii.com/t/what-is-the-bottleneck-effect-definition-
examples-10503
62

63. 63

64. 64