This document discusses random mating and non-random mating in populations. It describes assortative mating where individuals mate with similar partners, and disassortative mating where individuals mate with dissimilar partners. The effects of these on genotype frequencies are explained. The concept of genetic equilibrium is introduced. Inbreeding is discussed for idealized, isolate, and real populations. Formulas are provided for the rate of inbreeding increment under different population structures. Effective population size is also covered as it relates to rates of inbreeding and genetic drift in small populations.

1. 1
WELCOME

2. Submitted to:-
 Dr. M.P.Patel
 Professor & H.O.D,
Dept. of GPB
 SDAU, S.K. Nagar
Submitted by:-
 Vaghela Gauravrajsinh K
 M.Sc. (Agri.)
 Reg.no:-04-AGRMA-01840-2018
 SDAU, S.K. Nagar
Non Random Mating to change
Genetic Equilibrium through Inbreeding
in small population

3. WHAT IS RANDOM MATING?
Each male of a population has equal
chance of mating with any female of
population or vice-versa called as Random
mating or Mendelian population or
Panmixia or Panmictic population.

4. WHAT IS NON-RANDOM MATING?
 When the probability that two individuals in a
population will mate is not the same for all
possible pairs of individuals.
OR
 In a population male does not mating with any
female of population is called as non-random
mating.

5. Types of Non-Random Mating
 Disassortative- Individuals only mate with
others who are phenotypically different from
themselves for selective traits (opposites).
 Assortative- Individuals mate with others who
are like themselves phenotypically for selected
traits (similar).

6. Assortative Mating
 There are only three possible mating patterns
with respect to genotypes for traits controlled by
two alleles (A and a).
AA × AA Aa × Aa aa × aa

7. Net affect of Assortative Mating
 Progressive increase in the number of homozygous
genotypes (AA & aa).
 Corresponding decrease in the number of heterozygous
genotype (Aa).
 This trend will continue from generation to generation.
POSITIVE ASSORTATIVE MATING
Possible parent
mating pattern
Expected off spring genotypes
AA Aa aa
AA × AA 4
Aa × Aa 1 2 1
aa × aa 4
Total 5
(42%)
2
(17%)
5
(42%)

8. Disassortative Mating
 There are six possible mating patterns with
respect to genotypes for traits controlled by two
alleles (A and a).
AA × Aa Aa × aa aa × AA
AA × aa Aa × AA aa × Aa

9. Net affect of Disassortative Mating
 Progressive increase in the frequency of
heterozygotes (Aa).
 Corresponding decrease in the number of
homozygous genotypes (AA and aa).
 This trend will continue from generation to
generation.
 It has the opposite effect as Assortative mating.

10. Net affect of Disassortative Mating
NEGATIVE ASSORTATIVE MATING
Possible parent
mating pattern
Expected off spring genotypes
AA Aa aa
AA × Aa 2 2
AA × aa 4
Aa × AA 2 2
Aa × aa 2 2
aa × AA 4
aa × Aa 2 2
Total 4
(17%)
16
(67%)
4
(17%)

11. WHAT IS GENETIC EQUILIBRIUM?
 1st reported by Yule (1902), Castle (1903) and Pearson
(1904).
 W.E.Castle actually founder of genetic equilibrium
principle.
 Genetic Equilibrium means no change in genetic
structure of population (Gene & Genotype Frequency)
from one generation to the next.
 The principle of genetic equilibrium in a large random
mating population can be applied for any value of gene
frequencies.
 Therefore, this law of genetic equilibrium under random
mating is known as the Hardy-Weinberg law or
Hardy-Weinberg principle.

12. INBREEDING
 Mating between two individuals related by descent
(i.e having a common ancestor)
 To study the Inbreeding , there are three types of
population :-
1) Idealized population
2) Isolates
3) Real population

13. TYPES OF POPULATION
 Idealized population :- In which all types of mating
occur including self- fertilization. The average rate of
change in heterozygosity can be illustrated very simply
and clearly in an idealized population.
 Isolates :- Only the most distinct relatives may be
mating with maximum avoidance of inbreeding.
OR
Continue mating of close relative breaks the entire
population into lines of descents as Isolates or groups.

14.  Real population :- In natural or Real population , the
total no of individuals may be large but they all may not
contribute to the genetic composition of the next
generation because some of the them may not reach the
sexual maturity, other may not be able to mate while
other which mate may not leave offspring that survive to
maturity in the next generation.
 Inbreeding changes genotype frequencies not allele
frequencies.

15. Idealized Population
 RATE OF INBREEDING INCREMENT:-
 Consider that in an idealized population there are N
individuals, each shedding equal number of gametes
which unite at random.
 The male & female gametes produced by N individuals
can be shown as under ;
Individuals 1 2 3 Nth
Male gametes A1A2 A3A4 A5A6 A2N-1A2N
Female gametes A1A2 A3A4 A5A6 A2N-1A2N
CONT.

16.  Any random pairs of opposite sex gametes will have
(1/2N) chance for carrying identical genes.
F1 = 1/(2N)
 In second generation, identical homozygotes will be
produced from inbreeding in the 1st generation & from
new replication of genes.
 Probability of random pairs to be identical:- 1/(2N)
{newly replicated genes}
 Probability of remaining pairs(1-1/2N) to be identical:-
(1-1/2N)F1 {due to previous inbreeding}
F2=1/2N + (1-1/2N)F1
Ft=1/2N + (1-1/2N)Ft-1
=New Inbreeding + Old Inbreeding
CONT.

17.  Rate of inbreeding increment is 1/2N & symbolized by
ΔF.
Ft= 1 + Ft-1 - Ft-1
2N 2N
= Ft-1 + 1 - 1 Ft-1
2N 2N
=Ft-1 + 1 - Ft-1
2N
= Ft-1 + 1 - Ht-1 ={Old inbreeding + New
2N inbreeding(ΔF)}
CONT.

18. Ft= 1/2N + (1-1/2N)Ft-1
= ΔF + (1-ΔF) Ft-1
= ΔF +Ft-1 –ΔF Ft-1
= Ft-1 +ΔF (1-Ft-1)
Thus, ΔF = Ft -Ft-1
1-Ft-1
Therefore, the rate of inbreeding increment (ΔF) each
generation in an idealized population is:-
ΔF = 1/2N
= 1- Ft-1
2N
ΔF = 1 Ht-1
2N

19. Isolates
 The continued mating of close relatives breaks the entire
population into lines of descents called as Isolates or
Group.
 The isolate size N = 2k which is the number of mating
individuals in a group or isolate.
 The N remain constant from generation to generation.
 The different isolates / groups are of different size , viz
 Selfed individual with N = 20 = 1.
 Full sibs with N = 21 = 2
 Double first Cousin = 22 = 4
 Quadruple second Cousin = 23 = 8
 Octuple third Cousin = 24 = 16
 Most distant Cousins have an isolate size of N = 2k

20.  For an example, in an isolate of size 4 (double first
cousin mating's) it was observed that,
H1 = 1/2 Ht-1 + 1/4 Ht-2 + 1/8 Ht-3
 The expressions of change (decrease) in heterozygosity
per generation under different systems of close
inbreeding.
 In deriving these expressions it was obvious that
coefficient of loss in H (ΔH) was (
1
2
)2-K for distantly
related cousin mating.
 This coefficient is 1/4 times the reciprocal of isolate size
N.
 Therefore, (
1
2
)2+K =
𝟏
𝟒𝐍
and hence,

21.  ΔH = -
1
2
2+K
= -
𝟏
𝟒𝐍
Since N= 2k, the multiple of 2.
 The heterozygosity in t generation ;
Ht = Ht-1 -
1
2
2+K Ht-(2+k)
= Ht-1 -
𝟏
𝟒𝐍
Ht-(2+k)
= (𝟏 −
𝟏
𝟒𝐍
) Ht-1 approximately.
 This indicates that H is decreasing at a rate of 1/4N per
generation.

22. Real Population
 Real population do not have self fertilization, have
unequal number of breeding males and females, have
varying number of breeding individuals in different
generation, differential contribution of parents,
overlapping generations, and minimum inbreeding.
 In natural or Real population, the total no of individuals
may be large but they all may not contribute to the
genetic composition of the next generation because
some of the them may not reach the sexual maturity,
other may not be able to mate while other which mate
may not leave offspring that survive to maturity in the
next generation.

23.  In this male has lesser in number of contribution to
equal to that of female which are more in number.
 So number of individuals affecting genetic constitution
of next generation may be lesser than the real
population.
 Effective population size was introduced by Wright
(1931).
 In small population, there is increase in homozygosity
(inbreeding effect) and a random drift in gene
frequencies due to sampling variance.

24.  The concept of effective population size can be made
more clear by considering the different situations of real
population that differ from ideal population.
 The different equations for different deviated situations
will be derived situations will be derived to convert the
actual number (N) to the effective number (Ne) so as the
rate of inbreeding increment become equal in real and
ideal populations.
 The is ΔF is related to population size in an ideal
population as :- ΔF = 1/2 N
 The effective size is related is ΔF as Ne = 1/2 ΔF.
 The rate of inbreeding (ΔF) can be estimated after
knowing the effective population size as :-
ΔF = 1/2Ne

25. REFERENCES
1. Text book of Population Genetics (Vol. I.
Qualitative Inheritance) By S.S.Tomar.
2. Genetics By B.D.Singh