Sex-linked genes in population

1. AN ASSIGNMENT ON
GENETIC EQUILIBRIUM FOR SEX LINKED GENES
AND PROPERTIES OF GENETIC EQUILIBRIUM WITH
RESPECT TO SEX LINKED GENES
Submitted to:
Dr. P. C. Patel
Assistant Proffesor,
Dept. of Genetics & Plant Breeding
C.P.C.A. , S.D.A.U.,
Sardarkrushinagar.
Submitted by:
Akhil R. Donga
Reg.no.:04-AGRMA-2215-2020
Dept. of Genetics & Plant Breeding,
C.P.C.A., S.D.A.U.,
Sardarkrushinagar.
GP 506 : Population Genetics

2. INHERITANCE PATTERN
• Sex linked gene : the present on sex chromosome called as the sex
linked gene .
• Homogametic sex :one of the two sexes has two x chromosome
(XX) which are equally in size and shape hence homologus. Ex.
Female in mammals and drosophila, some birds and reptiles, the
homogametic sex is the male
• Heterogametic sex :Other sex has one X chromosome and Y
chromosome (XY) which are not equal in size and shape hence not
homologus to each other(XY)
• Y chromosome is short and don’t have a gene

3. MODE OF INHERITANCE
Female parent Male parent
Genotypes XX XY
Genes
X and X X and Y
offspring
XX XX XY XY
 Thus male parent does not contribute any sex linked gene to its male offspring(sons) hence the genetic
contribution of male parent is not equal to their offspring of two sexs.

4. • The female have two sex linked genes and hence there are three
genotypes among female population.
• The relation between gene and genotypic frequencies among female
for sex linked genes is the same as for autosomal genes.
• Other hand male have only one sex linked gene at a locus and hence
only two genotype are presence in male population.

5. Considering a single locus with two alleles (A1 and A2) the genotypes and their
frequencies in two sexes of plants will be as under in an equilibrium population
Males(XY) Females(XY)
Genotype A1Y A2Y A1A1 A1A2 A2A2
Frequencies p q p2 2pq q2
The gene frequencies for sex linked gene among males and females are equal in
equilibrium state.

6. GENETIC EQUILIBRIUM
• When matting frequencies are determined randomly and the allelic frequencies
are same in the two sexes it can be shown that the population remain at
equilibrium.
• The frequencies of six type of matting and the expected progeny at equilibrium
for X linked alleles are sown in the table

7. MATING FREQUENCIES
Females
Males p2 (A1A1) 2pq(A1A2) q2(B2B2)
p(A1Y) p3 2p22q Pq2
q(A2Y) p2q 2pq2 q3

8. EXPECTED
PROGENY
PRODUCED
AT EQUILIBRIUM
Mating
type
Frequenc
y of
mating
progeny
female males
A1A1 A1A2 A2A2 A1Y A2Y
A1A1 X
A1Y
P3 P3 P3
A1A2 X
A1Y
2p2q p2q p2q p2q p2q
A2A2 X
A1Y
pq2 pq2 Pq2
A1A1X
A2Y
P2q p2q p2q
A2A= X
A2Y
2pq2 pq2 Pq2 pq2 pq2
A2A2 X
A2Y
q3 q3 q3
Total 1.0 p2 2pq q2 p Q

9. PROPERTIES OF EQUILIBRIUM POPULATION
1)Gene frequency in male (pm):
This depends on the gene frequency of their mothers because the males get
their X-linked alleles only from their mothers. Therefore, the gene frequency in any generation is the
same as was in the females of the preceding generation.
pm = p’f
pf = p’m

10. 2)Gene frequency in females (pf):
This is the mean of the gene frequencies of
their both the parents and hence equal to the average gene frequency
of two sexes in preceding generation.This is because the females get
X-linked alleles equally from both the parents.
pf = ½ (p’m + p’f)

11. 3)Difference in gene frequency between two sexes (d) :
The difference is halved in each generation of
random mating but with opposite sign.
d = pf – pm
= ½ ( p’m + p’f ) – p’f
= ½ p’m + ½ p’f – p’f
= ½ p’m – ½ p’f
= -½ (p’f – p’m )
d = -½ d’
where, d indicates the difference
prime (‘) indicates the proceding generation

12. 4)Average gene frequency in the whole population of two
sexes( p ):
p = 1/3 pf + 2/3 pf
= 1/3 ( pm + 2pf )
= 1/3 ( p’m + 2p’f)
=Equilibrium gene frequency
=constant
The equilibrium value of gene frequency (p) is approached in both sexes
and this can be calculated from any generation.
The genes remain shuttling from one sex to the other and this shuttling of
genes does not affect the relative frequencies of two alleles among the
total number of X chromosomes. After a number of generations of
random mating, the gene frequency in both the sexes approaches
equality with no difference in gene frequency between two sexes (d= 0)
and p is equilibrium value common to the two sexes.

13. 5) Deviation of gene frequency from equilibrium value :
This can be obtained for any generation by putting the equation of p as
follows-
pm – p = -2 ( pm + 2pf) [putting p value from 4th property]
pm = -2 ( pf- p )
This shows that in any generation, the deviation of pm from equilibrium values
is twice as great as that of the deviation of p but on the other side of the
equilibrium value. The above equation of pm-p = -2 (pf - p) together with Pm=P’f
and Pf = ½ (p’m + P’f) gives the following.
pm- p = -2 (pf – p ) = - ½ (p’m – p) = (-½)n [ p’m – p ]

14. 6) Alternate properties about gene frequencies:
(i) Gene frequencies in two sexes:
(A) From the above equations the gene frequencies in either sex (pm and
pf) can also be estimated as under
pm= 3p – 2pf
= 1.5 p – ½ p’m = ½ (3p – p’m)
= 1.5 p – ½ p’f = ½ (3p – p’f)
(B) The gene frequency in either sex of any generation is the average of
the gene frequencies of two proceding of the same sex.Therefore:
pm = ½ ( p’m + p’’m )
pf = ½ ( p’f + p’’f )

15. (ii) Average gene frequency:
The equilibrium value ( p ) can also expressed in terms of the difference in
gene frequencies (d) between two sexes as:
p = 1/3 pm + 2/3 pf
= pf – 1/3d
= pm + 2/3d
[Where , d = pf – pm]
Thus, p is one-third the distance from pf and two-third the distance from pm.The
equation p =1/3pm + 2/3pf = pf – 1/3d =pm + 2/3d can be verified by taking
2/3pf =pf – 1/3pf and 1/3pm = pm – 2/3pm as:
p = 1/3 pm + 2/3 pf
= (pm – 2/3 pm) + 2/3 pf
= pm + 2/3 ( pf –pm )
= pm + 2/3d {since pf – pm = d}

16. similarly, p = 1/3 pm + 2/3 pf [ putting value of 2/3pf ]
= 1/3 pm + pf – 1/3 pf
= pf – 1/3 (pf – pm )
= pf – 1/3 d

17. Thank you !
Have a nice day !