Genetics, Class 12, Biology | IBPS PO Prelims & Mains Preparation - Bank Exams PDF Download

Introduction - Principles of Inheritance and Evolution, Biology, Class 1

INTRODUCTION

Genetics term was given by W. Bateson. W. Bateson is Father of Modern Genetics.

Genetics = Collective study of heredity & Variations.

Heredity = Transmission of genetic characters from parent to offsprings.

Variation = individuals of same species have  some differences, these are called variation.

• History of reserches in genetics.

Muller – Proposed the term "Cytogenetics" (Cytology + Genetics) Father of Actinobiology Actinobiology - study the effect of radiation on living organisms.

Morgan – Father of Experimental genetics He experiment on Drosophila & proposed various concepts.

Gene theory - According to gene theory ; genes are linearly located on chromosome.

Linkage term, Theory of sex linkage, Crossing over term, Criss - cross inheritance, Linkage map on Drosophila given by Morgan.

• A. Garrod = Father of human genetics & Biochemical genetics. Garrod discovered first human Metabolic genetic disorder which is calledalkaptonuria(black urine disease). In this disease enzyme homogentisic acid oxidase is deficient. Gave the concept 'One mutant gene one metabolic block'  

VARIATION

PRE-MENDELISM

To explain the like begets like (offsprings are similar to their parents) several theories were given. They are collectively known as Theories of Blending Inheritance. Some of them are as follows –

1. Vapour fluid theory – Greek philosopher Pythagoras [500B.C.] proposed this theory.

According to this theory, at the time of coitus of male and female, moist vapour secretes from the brain and due to this offsprings are similar as their parents.

2. Semen theory :- This theory has given by Empedocles.

According to his view, the semen of male and female is mixed during coitus. Characters of parents appear into the offsprings due to the mixture.

According toAristotle - a semen of male is considered as "highly purified blood". Which has power of life and it is nourished by semen of female.

3. Preformation theory :- According to this theory germinal [reproductive] cell contains "a miniature figure of a man"

According to Swammerdam  preformation of a miniature of man is found inside the egg is called Mankin.

Those scientists  who believed in the hypothesis of Swammerdam are known as Ovists. On contrary, according to Hartsoeker preformed miniature of man is present in sperm.

A miniature of man is present in sperm, he called - Homunculus Scientists, who believed in  Hart soeker view, are called "spermist."

4. Encasement theory :- This theory was proposed by Charles Bonnet.

According to his view, body of female is just like a chinese box. The all future progenies are packed in the body of female like chinese box.

5. Epigenesis theory :- This theory was proposed by K.Wolf.

According to his view, germinal cells possess an undifferentiate material. This material develops step by step [gradually] after the fertilization. Such type development is known as Epigenesis.

6. Pangenesis theory :- The theory of pangenesis was described by C.Darwin.

This theory postulated that all part of a living body [tissues] synthesize "micro molecules." these micro molecules are known as Pangene or Gemmules.

The male and female pangenes fuse together during the fertilization  these are, further again distributed in the various organs of the body at the time of development.

7. Germplasm theory :- The view was proposed by A.Weisman (1886).

According to him living body of an individual possess two different types of fluid material - Somatoplasm and Germplasm.

Somatoplasm does not participate in the formation of germinal cells.  Therefore, variations are not transferred into the progeny. somatoplasm is mortal because eventually it dies.  

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Mendel's Pea Plant Exeriment - Principles of Inheritance and Evolution, Biology, Class 12

MENDELISM

Experiments performed by Mendel on genetics and description of mechanisms of hereditory processes and formulation of principles are known as Mendelism.

Mendel postulated various experimental laws in relation of genetics.

Gregor Johann Mendel (1822 - 1884) :- Mendel was born on July 22,1822 at Heinzendorf  in Austria at Silesia village. Mendel worked in Augustinian Monastery as monk at Brunn city, Austria.

In 1856-57, he started his historical experiments of heredity on pea(Pisum sativum) plant. His experimental work continued  on pea plant till 1865 (19^th century).

The results of his experiments were published in the science journal, "Nature For schender varein" in 1866.

This  journal was in Germen language. Title was "verschue uber Pflangen Hybridan".

This journal was published by 'Natural History society of Bruno'.

A paper of Mendel by the name of "Experiment in plant Hybridization" published in this journal.

Mendel was unable to get any popularity. No one understood of him. He died in 1884 without getting any credit of his work (due to kidney disease (Bright disease) After 16 years of Mendel's death in 1900, Mendel's postulates were rediscovered.

Rediscovery by three scientists independently.

1. Carl Correns - Germany - (Experiment on Maize)

2. Hugo deVries (Holland) (Experiment on Evening Primerose) He republished  the Mendel's results in 1901 in Flora magazine

3. Erich von Tschermak Seysenegg - (Austria) (Experiment on different flowering plants)

The credit of rediscovery of Mendelism goes to three scientists.

Correns gave two laws of Mendelism.

Law of Heredity/Inheritance/Mendelism

I^st Law - Law of segregation.

II^nd Law - Law of independent assortment.

Mendel experiments remain hidden for 34 years.

Mendel results remain hidden due to : 

1. At that time Darwin's book "Origin of Species" published. Scientists  were busy in discussion with this book.

2. Mendel's ideas were ahead of that time.

3. Mendel used higher statistical calculation in his experiments so the results were complicated to understand.

4. Mendel also performed his experiments on Hieraceum plant on suggestion of Karl Nageli but Mendel did not get succeed because in Heiracium, Parthenogenesis is present.

Reasons for Mendel's success : 

1. Mendel studied the inheretance of one or two characters at a time unlike his predecessors who had considered many characters at a time. (Kolreuter-Tobacco plant, John Goss & Knight -Pea plant). 

2. Selection of Material –

Selection of garden Pea plant is suitable for studies ;which have the following advantages :
(i) Pea plant is annual plant with short life cycle of 2-3 months so large no. of offsprings can be analysed within a
short period of time.
(ii) It has many contrasting traits.
(iii) Natural self pollination is present in pea plant.
(iv) Cross pollination can be performed in it artificially so hybridization can be made possible.
(v) Pea plant easy to cultivate.
(vi) Pea seeds are large. In addition to pea, Mendel worked on rajama and honey bee.
3. Mendel quantitatively analyse the inheritance of qualitative characters.
4. He maintained the statistical records of all the experiments.

Average of all traits studied 2.98: (= 3:1)

•  In Pea plant sead coat colour and Flower colour are regulated by same gene.

Gene which controls more than one character is called as pleiotropic gene.

•  Mendel obtained wrinkled seeds due to absence of Starch Branching enzyme (SBE)

In Wrinkled seed free sugar is more in place of starch.

Special Point :
S. Blixt concluded that the genes studied by Mendel are located on four different pairs of chromosomes.

Pod colour --------------  Ch. no. 5^th
Seed form ----------------- Ch. no. 7^th
Two of the genes are on chromosome 1^st and three are on chromosome 4, genes are located far apart on the chromosome except genes controlling plant height and pod shape.
Mendel did not study the gene controlling plant height and pod shape so Mendel did not detect linkage.

Technique of Mendel

He developed a technique Emasculation and Bagging for hybridization in plants.

Flowers of pea plant are bisexual. In this method one considered as male and another as female.

Stamens of the plant which is used as female, are removed at juvenile stage, this is called Emasculation.

Emasculation is done to prevent self pollination.

Emasculated flowers covered by bags, this is called bagging.

Bagging is only used to prevent undesirable cross pollination.

Mature pollen grains are collected from male plants and spread over emasculated flower.

Seeds are formed in the female flower after pollination.

The plants that are obtained from these seeds are called First Filial generation or F₁ generation according to Mendel.

Mendel was great plant breader(true breader).

SOME GENETICAL TERMS
1. Factors :- Unit of heredity which is responsible for inheritance and appearance of characters.

These factors were referred as genes by Johannsen(1909). Mendel used term "element" for factor.

Morgan first used symbol to represent the factor. Dominant factors are represented by capital letter while recessive factor by small letter.

2 Allele :- Alternative forms of a gene which are located on same position [loci] on the homologous chromosome is called Allele. Term allele was coined by Bateson.

3. Homozygous :- A zygote is formed by fusion of two gametes having identicle factors is called homozygote and organism developed from this zygote is called homozygous.

Ex. TT, RR, tt

4. Heterozygous :- A zygote is formed by fusion of two different types of gamete carrying different factors is called heterozygote (Tt, Rr) and individual developed from such zygote is called heterozygous.

The term homozygous and heterozygous are coined by Bateson.

5. Hemizygous :- If individual contains only one gene of a pair then individual said to be Hemizygous. Male individual is always Hemizygous for sex linked gene.

6. Phenotype :- It is the external and morphological appearance of an organism for a particular character.

7. Genotype :- The genetic constitution or genetic make-up of an organism for a particular character.

Genotype & phenotype terms were coined by Johannsen.

8. Phenocopy :- If different genotypes are placed in different environmental conditions then they produce same
phenotype. Then these genotypes are said to be Phenocopy of each other.

MONOHYBRID CROSS
When we consider the inheritance of one character at a time in a cross this is called monohybrid cross. First of all, Mendel selected tall and dwarf plants.

Checker Board Method :

First time, it was used by Reginald. C. Punnett (1875 - 1967)
The representation of generations to analyse in the form of symbols of squares. Male gamets lie horizontally and female gametes lie vertically.

T T = Tall (dominant homozygous),

T t = Tall (dominant heterozygous),

t t = Dwarf (recessive homozygous).

The ratio of characters (traits) appear/ visible morphologically is phenotypicratio. It is 3: 1. Genetic constitution is called Genotype [using symbols for genes] it is 1 : 2 :1

Conclusions (results) of Monohybrid Cross

I^st Conclusion (Postulate of paired factors) :

According to Mendel each genetic character is controlled by a pair of unit factor. It is known as conclusion of
paired factoror unit factor.

II^nd Conclusion (Postulate of Dominance):
This conclusion is based on F₁ - generation. When two different unit factors are present in single individual, only one unit factor is able to express itself and known as dominant unit factor. Another unit factor fails to express is the recessive factor. In the presence of dominant unit factor recessive unit factor can not express and it is known as conclusion of dominance.

•  There are two exceptions of law of dominance. [A] Incomplete dominance, [B] Co-dominance,

III^rd Conclusion (Law of segregation):

During gamete formation ; the unit factors of a pair segregate randomly and transfer inside different gamete.

Each gamete receives only one factor of a pair; so gametes are pure for a particular trait. It is known  as conclusion of purity of gametes or segregation.

• There is no exception of Law of segregation. The segregation is essential during the meiotic division in all sexually reproducing organisms. (Nondisjunction may be exception of this law).

DIHYBRID CROSS

A cross in which study of inheritance of two pairs of contrasting traits.

Mendel wanted to observe the effect of one pair of heterozygous on other pair.

Mendel selected traits for dihybrid cross for his experiment as follows :-

[1] Colour of cotyledons→ Yellow (Y)  & Green (y)

[2] Seed form → Round (R) and Wrinkled (r) yellow and round characters are dominant and green and wrinkled are recessive characters.

Mendel crossed, yellow and round seeded plants with green and wrinkled seeded plants.

All the plants in F₁–generation had yellow and round seeds.

When F₁ plants were self pollinated to produce four kinds of plants in F₂ generation such as yellow round, yellow–wrinkled, green round and green wrinkled,  there were in the ratio of 9 : 3 : 3 : 1. This ratio is known as dihybrid ratio.

Expression of yellow round (9) and green wrinkled (1)  traits shows as their parental combination.

Green Round and yellow wrinkled type of plants are produced by the results of new combination.

Demonstration by checker board method :-

F₂ - Generation 

Phenotype :-

Yellow Round = 9/16

Yellow Wrinkled = 3/16

Green Round = 3/16

Green Wrinkled = 1/16

Thus, Phenotypic Ratio = 9 : 3 : 3 : 1

Genotype:-

Homozygous yellow & Homozygous Round – YY RR = 1

Homozygous yellow & Heterozygous Round – YY Rr = 2

Heterozygous yellow & Homozygous Round – Yy RR = 2

Heterozygous yellow & Heterozygous Round – Yy Rr = 4

Homozygous yellow & Homozygous wrinkled – YY rr = 1

Heterozygous yellow & Homozygous wrinkled – Yy rr = 2

Homozygous green & Homozygous Round – yy RR = 1

Homozygous green & Heterozygous Round – yy Rr = 2

Homozygous green & Homozygous wrinkled – yy rr = 1

Thus, Genotypic Ratio = 1:2:2:4:1:2:1:2:1

Fork line method -To find out the composition of factors inside the gamete, we use fork line method.

AaBb = 4 types of gamete

Type of gamete / phenotypic category = 2ⁿ

 n = No of hybrid character or heterozygous pair.

Type of genotype = 3ⁿ

eg in dihybrid cross = 32 = 9 genotype

No. of zygote produced by selfing of a gen otype = 4ⁿ

Conclusion (Law of Independent Assortment): The F₂ generation plant produce two new phenotypes, so inheritance of seed colour is independent from the inheritance of shape of seed. Otherwise it can not possible to obtain yellow wrinkled and green round type of seeds.

This observation leads to the Mendel's conclusion that different type of characters present in plants assorted independently during inheritance.

This is known as Conclusion of Independent Assortment. It is based on F₂ - generation of dihybrid cross.

The nonhomologous chromosome show random distribution during anaphase-I of meiosis.

Explaination :-

A pure yellow and round seeded plant crossed with green and wrinkled seeded plant which are having genotype YYRR and yyrr to produced F₁ generation having YyRr genotype.

Both the characters recombine independently from  each other during gamete formation in F₁ generation .

Factor (R) of pair factor (Rr) is having equal chance to (Y) factor or (y) factor of gametes during recombination to form two type of gametes (YR) and (yr).

Similarly (r) factor also having equal chance with (Y) factor or (y) factor of gametes to form a two type gametes - (Yr) and (yr).

Thus, total four types of gametes - (YR), (yR), (Yr), and (yr) are formed.

Therefore, during the gametes formation in F₁ generation , independent recombination is possible.

– The law of independent assortment is most criticised. Linkage is the exception of this.

BACK CROSS

A back cross is a cross in which F₁ individuals are crossed with any of their parents.

(1) Out Cross : When F₁ individual is crossed with dominant parent then it is termed out cross. The generations obtained from this cross, all possess dominant character. so the any analysis can not possible in F1 generation.

[2] Test Cross : When F₁ progeny is crossed with recessive parent then it is called test cross. The total generations obtained from this cross, 50% having dominant character and 50% having recessive character. [Monohybrid test cross]. Test cross helps to find out the  genotype of dominant individual.

[a] Monohybrid Test Cross :- The progeny obtained from the monohybrid test cross are in equal proportion , means 50%  is dominant phenotypes and 50% is recessive phenotypes.

It can be represented in symbolic forms as follows.

[b] Dihybrid Test Cross:- The progeny is obtained from dihybrid test cross are four types and each of them is 25%.

   The ratio of Dihybrid test cross = 1:1:1:1

Conclusion:-  In test cross phenotypes and genotypes ratio are same.  

RECIPROCAL CROSS
When two parents are used in two experiments in such a way that in one experiment "A" is used as the female parent and "B" is used as the male parent, in the other experiment "A" will be used as the male parent and "B" as the female parent. such type of a set of two experiments is called Reciprocal cross.
Characters which are controlled by karyogene are not affected by Reciprocal cross. In case of cytoplasmic inheritance result change by Reciprocal cross.

GENE INTERACTION

Gene interaction is two types :

(i) Allelic interaction/Intragenic interaction 

(ii) Non allelic interaction/Intergenic interaction 

(i) Allelic interaction/Intragenic interaction: Allelic interaction takes place between allele of same gene which are present at same locus.

Example of Allelic interaction are as follows :–

[1] Incomplete dominance :- According to Mendel's law of dominance, dominant character must be present in F₁ generation. But in some organisms, F₁ generation is different from the both parents.

Both factors such as dominant and recessive are present in incomplete dominance but dominant factors is unable to express its character completely, resulting Intermediate type of generation is formed  which is different from the both parents. Some examples are –

• (a) Flower colour in Mirabilis jalapa : Incomplete dominance was first discovered by Correns in Mirabilis jalapa. This plant is called as '4 O' clock plant 'or'Gul-e-Bans'. Three different types of plant are found in Mirabilis on the basis of flower colour, such as red , white and pink.

& When plants with red flowers is crossed with white flower, plants with pink flower obtained in F₁ generation. The reason of this is that the genes of red colour is incompletely  dominant over the genes of white colour.

& When, F₁ generation of pink flower is self pollinated then the phenotypic  ratio of F₂ generation  is red, pink, white is 1:2:1 ratio in place of  normal monohybrid cross ratio 3:1.

& The ratio of phenotype and genotype of F₂ generation in incomplete dominance is always same.

(b) Flower colour in Antirrhinum majus :- Incomplete dominance is also seen in flower colour of this plant.This plant is also known as 'Snapdragon ' or 'Dog flower'. Incomplete dominance is found in this plant which is the same as Mirabilis.

(c) Feather colour in Andalusian Fowls :- Incomplete dominance is present for their feather colour.

When a black colour fowl is crossed with a white colour fowl, the colour of F₁ generation  is blue.

[2] Co-dominance :- In this phenomenon, both the gene expressed for a particular character in F₁ hybrid progeny. There is no blending of characters, wherease both the characters expressed equally.

Examples :- Co-dominance is seen in animals for coat colour. when a black parent is crossed with white parent, a roan colour F₁ progeny is produced.

When we obtain F₂ generation from the F₁ generation, the ratio of black ; black-white (Roan) ; white animals is  1 : 2 : 1

Note :-  F₂ generation is obtained in animals by sib-mating cross.

It is obvious by above analysis that the ratio of phenotype as well as genotype is 1:2:1 in co-dominance.

Sp. Note :- In incomplete dominance, characters are blended phenotypically, while in co-dominace, both the genes of a pair exhibit both the characters side by side and effect of both the character is independent from each other.

Other Examples of Co-dominance :
(ii) AB blood group inheritance (I^AI^B)
(iii) Carrier of Sickle cell anaemia (Hb^A Hb^S)

[3] Multiple allele :– More than 2 alternative forms of same gene called as multiple allele. Multiple allele is formed due to mutation. Multile allele located on same locus of homologous chromosome.

A diploid individual contains two alleles and gamete contains one allele for a character.

Ex. Blood group - 3 alleles Coat colour in rabbit - 4 alleles

If n is the number of allele of a gene then number of different possible genotype = 

Example  of multiple allele : 

1. ABO blood group → ABO blood groups are determined by allele I^A, allele I^B, allele I^O

I^A = dominant

I^B = dominant

I^O = recessive Possible phenotypes - A, B, AB, O

2. Coat colour in rabbit → Four alleles for coat colour in rabbit

Wild type = Full coloured = agouti = C⁺

Himalayan [white with black tip on extremities (like nose, tail and feet)] = c^h

 Chinchilla [mixed coloured and white hairs] = c^ch

albino = Colourless = c^a

These alleles show a gradient in dominance  C⁺ > c^ch > c^h > c^a

Possible genotypes –

Coloured = C+C+, C+c^ch, C+c^h C+c^a

Chinchilla = c^chc^ch , c^chc^h , c^chc^a

Himalayan = c^hc^h , c^hc^a

Albino = c^ac^a

Possible genotype  =    = 10 genotypes

Eye colour in Drosophila  and self incompatibility genes in plants are also the example of multiple allelism.

[4] Lethal gene :– Gene which causes death of individual in early stage when it comes in homozygous condition called lethal gene. Lethal gene may be dominant or recessive both, but mostly recessive for lethality. Many of these genes which do not cause definite lethality are called semilethals. In semilethal gene death occurs in late stage.

1. Lethal gene was discovered by L. Cuenot in coat colour of mice.
Yellow body colour(Y) was dominant over normal brown colour(y).
Gene of yellow body colour is lethal.
So homozygous yellow mice are never obtained in population. It dies in embryonal stage.
When yellow mice were crossed among themselves segregation for yellow and brown body colour was obtained in 2 : 1 ratio.

YY - death in embryonal stage modified ratio = 2 : 1

2. In plant lethal gene was first discovered by E. Baur in Snapdragon (Antirrhinum majus)

Homozygous golden leaves are never obtained.

3. Sickle cell anaemia in human. In human, gene of sickle cell anaemia HbS is the example of lethal gene.
When two carrier indivudials of sickle cell anaemia are crosed then offsprings are obtained in 2 : 1 ratio.

Sublethal gene but ratio 2 : 1

[5] Pleiotropic gene :– Gene which controls more than one character is called pleiotropic gene. This gene shows multiple phenotypic effect.
For example :

(1) In Pea plant : Single gene influences 
                                                                 

2) In Drosophila recessive gene of vestigial wings also influence the some another characters–

• Structure of reproductive organs
• Longevity (Length of Body)
•  Bristles on wings.
• Reduction in egg production.

(3) Examples of  pleiotropic gene in human. 

(a) Sickle cell anaemia - Gene Hb^S_β provide a classical example of pleiotrophy. It not only causes haemolytic anaemia but also results increased resistance to one type of malaria that caused by the parasite Plasmodium falciparum. The sickle cell Hb^S_β allele also has pleiotropic effect on the development of many tissues and organs such as bone, lungs, kidney, spleen, heart.

(b) Cystic fibrosis – Hereditary metabolic disorder that is controlled by a single aoutosomal recessive gene.
The gene specifies an enzyme that produces a unique glycoprotein.
This glycoprotein results in the production of mucous.
More mucous interfere with the normal functioning of several exocrine glands including those in the skin, lungs, liver and pancreas.

(ii) Non allelic interaction/Intergenic interaction When interaction takes place between non allele is called non allelic gene interaction. It changes or modifies other non allelic gene.
Examples of nonallelic interaction.

1. Epistasis :- When, a gene prevents the expression of another non-allelic gene, then it is known as epistatic gene and this phenomenon is known as Epistasis.
Gene which inhibit the expression of another non alleleic gene is called epistatic gene and expression of gene which is suppressed  by epistatic gene called hypostatic gene.
 

Example :- 

Hair Colour in Dog :-

B = Dominant allele for black colour of hairs.
b = Recessive allele for brown colour of hairs.
I = Epistatic gene.
If the genotype bbii for brown colour and BBII for white colour.
Following types of generation will be obtained by following crosses.

It is obviously clear by above analysis, the phenotypic ratio of F_{2 -} generation in epistasis is  - 12:3:1

2. Inhibitory gene - Inhibitory gene itself have no phenotype but inhibits the effect of other non allelic gene. Non allelic gene behaves as  recessive. * Inhibitory gene must be in dominant stage & inhibit the effect of only dominant gene.
Ex., Leaf colour in Rice
R – Purple
r – Green
I – Inhibitory gene
R – I – Green – 9
R – ii – Purple – 3
rr – I – Green – 3
rr – ii – Green – 1
13 (Green) : 3(Purple)

3. Complementary Gene :- Two pair of non allelic genes are essential in doninant form to produce a particular character.
Such genes that act together to produce an effect that neither can produce, it's  effect separately are called complementary genes.
Both types of gene must be present in dominant form.
 

Example :- Colour of flowers in Lathyrus odoratus :-

C – P Purple coloured

C – pp colour less

cc – P colour less

cc – pp colour less

Thus phenotypic ratio of complementary genes = Coloured : Colourless   9  :  7

4. Duplicate Genes :-

Two pairs of non-allelic genes require  are for a character . If any one of them gene is dominant, then this character is expressed such type of gene is called duplicate gene.

Example :- Fruit shape in Capsella. Two pair of non-allelic genes are present in Capsella for triangular shape of fruits.

If any one gene out of them is dominant, the shape of fruit is triangular and no one gene is dominant than fruits will be elongated.

If  TTDD = For triangular shape      

ttdd = For top shape of fruits

Phenotypic ratio of F₂ -> Triangular : Top shaped 15    :   1

5. Additive Gene effect : In additive gene effect if non allelic gene seperately in dominant stage phenotype is same but both gene come dominant stage together phenotype is change due to additive effect. eg. Fruit shape in cucumber

A – bb→ spherical

aa B→ spherical

A – B – discoid (new phenotype)

aa bb – cylinderical

6. Collaboratory Gene :- Two pairs of non-allelic gene interacting together to produce a new phenotypic character.

Example :- Comb - shape in Chickens -

If, RR = For Rose comb

PP = For Pea comb

Both R & P = For walnut comb

rr pp = for single comb

A new type of phenotype walnut - (Rr Pp) comb is produced by the cross in between Rose comb (RR pp) and Pea comb (rr PP)

Thus, phenotypic ratio of collaboratory gene = Walnut : Rose : Pea : Single   = 9 : 3 : 3 :  1

7. Supplementary gene or Recessive Epistasis :- A pair of gene change the effect of another non allelicgene, is called supplementary gene.
Example :- Coat colour in Mice.
If alleles,   C = Black coat colour                  

c = Albino (Colourless coat) or (It has no effect)                  
A = Supplementary geneWhen black coat mice crossed with albino mice, the F₁ generation is Agouti.
It means, here the effect of non allelic gene is changed.

Thus, Recessive epistasis or supplementary gene ratio in F₂ -  Agouti : Black : Albino

                                                                                                         9    :     3    :    4

POLYGENIC INHERITANCE
Inheritance of characters in which one character is controlled by many genes and intensity of character depends upon the number of dominant allele.
Polygenic inheritance first described byNilsson - Ehlein kernal colour of wheat.
Nilsson - Ehle said that kernal colour of wheat is regulated by two pairs of gene.

                    RR BB              ×                rrbb Red White

Example-2. :- Colour of the skin in Human.
The inheritance of colour of skin in human studied by Devenport.
Five types of phenotype of colour of skin are found in human.
When a Negro (AA BB) phenotype crossed with white (aa bb) phenotype, intermediate phenotype produced in F₁ generation . Phenotypes of F₂ generation as follows.

Phenotypic ratioof F₂ generation of quantitative inheritance as

• In new discovery human skin colour and kernal colour in wheat is regulated by 3 pairs of alleles so phenotypic ration of F₂ generation.

CYTOPLASMIC INHERITANCE
Inheritance of characters which are controlled by cytogene or cytoplasm is called cytoplosmic inheritance. Genes which are present in cytoplasm called 'cytogene' or 'plasmagene' or extra nuclear gene.
Total cytogene present in cytoplasm is called 'Plasmon'.
A gene which is located in the nucleus is called 'karyogene'.

• Inheritance of cytogene in organisms occurs only through the female. Because female gamete has karyoplasm, simultaneously it has cytogene because of more cytoplasm.
• The male gamete of higher plant is called male nucleus. It has very minute [equivelent to nil] cytoplasm. so male gamete only inherited karyogene.
• Thus, inheritance of cytogene occurs only through female. (also called maternal inheritance)
• If there is a reciprocal cross in this condition, then results may be effected.

Cytoplasmic inheretance are of three types :

1. Cytoplasmic inheritance involving essential organelles like, Chloroplast and mitochondria called as organellar genetics.

2. Maternal effect depending indirectly on nuclear genes and involving no known cytoplasmic hereditary unit called aspredetermination. In this maternal effect is determined before fertilization.

3. Cytoplasmic inheritance involving dispensable and infective hereditary particle in cytoplasm which may or may not depend on nuclear genes called as Dauermodification.

Example of Organellar Genetics : (True examles of cytoplasmic inheritance)
(a) Plastid inheritance in Mirabilis jalapa – cytoplasmic inheritance first discovered by Correns in Mirabilis jalapa. InMirabilis jalapa branch (leaf) colour is decided by type of plastid present in leaf cells. So it is an example of cytoplasmic inheritance.
Branch colour

(b) Male sterility in maize plant : Gene of male sterelity present in mitochondria. If a normal male plant crossed with a female plant which has genes of male sterility then all the generation of male become sterile because a particular gene was present with female which inherited by female.

(c) Albinism in plant : Gene of albinism found in chloroplast. Gene of albinism in Maize is lethal.

(d) Inheritance of Bacterial plasmid : In bacteria plasmid inheritance is due to conjugation.

(e) Petite form in yeast (mitochondrial gene) : Petite is mutant form of yeast. This mutant form  is slow growing on culture medium.

(f) Iojap inheritance in Maize : Iojap is characterized by constrasting strip of green and white colour of leaves.

(g) Poky Neurospora (mitochondrial gene) : Poky is mutant form of Neurospora. It is slow growing on culture medium.
Example of predetermination

Shell coiling in snail (Limnaea peregra) In snail shell coiling can be of dextral (Coiling to the right) or sinistral (coiling to the Left). This direction of coiling is genetically controlled. The dextral coiling  depends upon dominant allele 'D' and sinistral coiling depends upon recessive allele 'd'. So the dextral is DD, Dd and sinistral is dd.

Above reciprocal cross indicates that phenotype of offspring is decided by genotype of female parent not the phenotype of female parent. Even if female parent contains only one dominant gene 'D' then phenotype of all offsprings is dextral.
Example : 

Example of Dauermodification -

(a) Sigma particle in Drosophila:- These particles are virus like particles which are present in Drosophila and related to CO₂ sensitivity. Inheritance of sigma particle takes place through the egg cytoplasm.

(b) Kappa particle in Paramecium:- Kappa particles are found in certain "Killer strains" of Paramecium and are responsible for production of substance paramecin which is toxic to strain not prossessing Kappa. (Sensitive Strain) The minimum number of kappa particles is  required 400 to secrete paramecin. Kappa particles are symbiotic bacteria named "Caedobacter taeniospiralis".

CHROMOSOMAL THEORY OF INHERITANCE

This theory was proposed by Walter Sutton and Theodor Boveri (1902). Following are the main points of this theory

1. Gametes serve as the bridge between two successive generations.

2. Male and Female gametes play an equal role in contributing hereditary components of future generation.

3. Only the nucleus of sperm combines with ovum. Thus, the hereditary information is contained in the nucleus.

4. Chromatin in the nucleus is associated with the cell division in the form of chromosomes.

5. Any type of deletion or addition in the chromosomes can cause structural and functional changes in living beings.

6. A sort of parallelism is observed between Mendelian factors and chromosomes.

7. A number of genes or Mendelian factors are found in each chromosome.

8. Determination of sex in most of the animals and plants is affected by specific chromosomes. These chromosomes are called sex chromosomes.

Parallelism Between Gene and Chromosomes 

1. Chromosomes are also transferred from one generation to the next as in the case of genes (Mendelian factors).

2. The number of chromosomes is fixed in each living species.These are found as homologous pairs in diploid cells.

One chromosome from father and the other contributed by the mother constitute a homologous pair.

3. Before cell division, each chromosome as a whole and the alleles of genes get replicated and are separated during mitotic division.

4. Meiosis takes place during gamete formation. Homologous chromosomes form synapses during prophase-I stage which in later course get separated and transferred to daughter cells. Each gamete or a haploid cell has only one allele of each gene present in the chromosome.

5. A characteristic diploid number is again established by the union of the two haploid gametes.

6. Both chromosomes and the alleles (Mendelian factors) behave in accordance to Mendel's law of segregation.

In the homologus chromosomes of a pure tall plant, allele (T) is found for tallness in each chromosome. Likewise, in a pure dwarf plant (tt), allele (t) is present in each chromosome.

These homologous chromosomes get separated during meiotic divisoin. Hence, each gamete possesses only one chromosome of an each pair. Accordingly, all the gametes of tall plants possess a chromosome with an allele of tallness (T), while the gametes of dwarf plants possess a chromosome with an allele for dwarfness (t). Their cross to produce F₁ generation will yield tall hybrid plants with homologous chromosomal pair containing Tt allelic pair. In this generation two kinds of gamete will be formed during gametogenesis, 50% with the allele (T) for tallness and 50% with the allele for dwarfness (t).Random combination of these gametes will produce offsprings in F2 generation in the ratio of 25% pure tall (TT), 50% hybrid tall (Tt) and 25% dwarf (tt)

LINKAGE

Collective inheritance of character is called linkage. Linkage first time seen byBatesonandPunnett inLathyrus odoratus and gave coupling and repulsion phenomenon. But they did not explain the phenomenon of linkage. Sex linkage was  first discoverd by Morgan in Drosophila & coined the term linkage. He proposed the theory of linkage.

Linkage and independent assortment can be represented in dihybrid plant, as –

In case of linkage in dihybrid AaBb

In case of independent assortment in dihybrid AaBb

Theory of linkage 

1. Linked genes are linearly located on same chromosome. They get separated if exchange (crossing over), takes place between them.

2. Strength of linkage α1/ distance between the genes . It means, if the distance between two genes is increased then strength of linkage is reduced and it proves that greater is the distance between genes, the greater is the probability of their crossing over.

Crossing over obviously disturbs or degenerates linkage. Linked genes can be separated by crossing over.

Factors affecting crossing over (C.O) :-

(1) Distance ­  = C.O.­ 

(2) Temperature ­ = C.O.­ 

(3) X-Ray  ­ =  C.O.­ 

(4) Age ­ =  C.O.

(5) Sex - Male C.O.  (Crossing over totally absent in male Drosophila.)

Arrangement of linked Genes on Chromosomes :-The arrangement of linked genes in any dihybrid plant is two types.

[a] Cis - Arrangement :- When, two dominant genes located on one chromosome and both recessive genes located on another chromosome, such type of arrangement is termed as cis-arrangement. Cis-arrangement is  an original arrangement.

•  Two types of gamete can be produced in cis-arrangement → (AB) and (ab).

[b] Trans-arrangement :- When a chromosome bears one dominant and  one recessive gene, and another chromosome also possess one dominant and one recessive gene, such type of arrangement is called trans-arrangement.Trans-arrangement is not an original form. It is due to crossing over. Two types of gamete also formed in trans-arrangement but it is different from cis-arrangement (Ab) and (aB).

Types  of Linkage :- There are two types of linkage –

1 COMPLETE LINKAGE :- Linkage in which genes always show parental combination. It never forms new combination.

Crossing over is absent in it. Such genes are located very close on the chromosomes. Such type of  linkage very rare in nature. e.g. male Drosophila, female silk moth.

2. INCOMPLETE LINKAGE :- When new combinations also appear along with parental combination in offsprings, this type of linkage is called incomplete linkage, the new combinations form due to crossing over. The percentage of new combination is equal to the percentage of crossing over.(<50%)

Linkage group :- All the genes which are located on one pair of homologous chromosome form one linkage group. Genes which are located on homologous chromosomes inherit together so we consider one linkage group.

•  No. of Linkage group = haploid no. of homologous chromosomes.

Application of Linkage :-
 

Distance can be identified by the incomplete linkage. It's unit is centi Morgan.  

Genetic map/Linkage map/chromosome map - In genetic map different genes are linearly arranged according to % of crossing over (μ Distance) between them. With the help of genetic map we can find out the position of a particular gene on chromosome. Genetic map is helpful in the study of genome.

SEX LINKAGE

When the genes are present on sex-chromosome is termed as sex linked gene and such phenomenon is known as sex-linkage. Two - types of sex linkage :
 

1. X-linkage.
Genes of somatic characters are found on x-chromosome. The inheritance of x-linked character may be through the males and females. e.g. Haemophilia, Colour blindness

2. Y- linkage - The genes of somatic characters are located on Y- chromosome. The inheritance of such type of character is only through the males. Such type of character is called Holandric character. These characters
found only in male.

e.g. (1) Gene which forms TDF /sry-gene                   (3) Webbed toes
(2) Hypertrichosis (excessive hair on ear pinna.)       (4) Porcupine skin
Gene which is located on differential region of Y - chromosome is known as Holandric gene.

Example of X-Sex linkage :-
 [i] Eye colour in Drosophila :- Eye colour in Drosophila is controlled by a X–linked gene.

If a red eyed colour gene is represented as '+' and white eyed colour represented as 'w', then on basis of this
different type of genotypes are found in Drosophila.

Gene for red eye is dominant (+) and white colour of eye is recessive (w)

Homozygous red eyed female = X⁺X⁺
Heterozygous red eyed female = X⁺X^w
Homozygous white eyed female = X^wX^w
Hemizygous red eyed male = X⁺Y
Hemizygous white eyed male = X^wY

It is clear by above different types of genotype that female either homozygous or heterozygous for eye colour.
But, for the male eye colour, it is always hemizygous.

[ii] Haemophilia :-

Haemophilia is also called "bleeder's disease" and first discovered by John Otto (1803). The gene of
haemophilia is recessive and x-linked lethal gene.

On the basis of x-linked, following types of genotype are found.

X^h X = Carrier female
X^hX^h = Affected female
X^hY = Affected male.

But, X^hX^h type of female dies during embryo stage because in homozygous condition, this gene becomes lethal and causes death.

Haemophilia -A → due to lack of factor -VIII (Antihaemophilic globulin AHG)

Haemophilia B or Christmas disease - due to lack of factor - IX (Plasma thromboplastin component)

Haemophilia - C (Antosomal disorder) → due to lack of factor - XI (Plasma Thromboplastin antecedent)

[iii] Colour Blindness :- The inheritance of colour-blindness is alike as haemophilia, but it is not a lethal
disease so it is found in male and female.(discovered by Horner)

Three types of colour blindness are-
 [a] Protanopia :- It is for red colour.
[b] Deuteranopia :- It is for green colour
[c] Tritanopia :- For blue colour blindness. Colour blindness is cheked by ishihara - chart.

Other examples of X - sex linkage
[iv] Diabetesinsipidus (recessive).
[v] Duchenne muscular dystrophy (recessive).
[vi] Fragile xsyndrome(recessive).
[vii] Pesudoricketes (Dominant)
[viii] Defective enamel of teeth (Dominant)

Examples of X-Y linkage
(i) Xeroderma pigmentosum
(ii) Epidermolysis bullosa

Types of Inheritance of sex linked characters :-
 1. Criss cross inheritance (Morgan) :- In criss-cross inheritance male or female parent transfer a X- linked character to grandson or grand daughter through the offspring of opposite sex.

(a) Diagenic (Diagynic) :- Inheritance in which characters are inherited from father to the daughter and from daughter to grandson.

Father → daughter → grand son.

(b) Diandric :- Inheritance in which characters are inherited from mother to the son and from son to grand
daughter.

Mother → Son → Grand-daughter.

(2) Non criss-cross inheritance : In this inheritance male or female parent transfer sex linked character to grand son or grand daughter through the offspring of same sex.
(a) Hologenic (Hologynic) :- Mother → Daughter → Grand-daughter (female to female)
(b) Holandric :- Father → Son → Grand-son (male to male)

Sex-Limited Character :- These characters are present in one sex and absent in another sex. But their genes are present in both the sexes and their expression is depend on sex hormone.

Example :- Secondary sexual characters → these genes located on the autosomes and these genes are present in both male and female, but effect of these are depend upon presence or absence of sex-hormones.

For example - genes of beard-moustache express their effects only in the presence of male hormone - testosterone.

Sex Influenced Characters : - Genes of these characters are also present on autosomes but they are influenced differently in male and female. In heterozygous condition their effect is different in both the sexes.

Example :- Baldness :- Gene of baldness is dominant (B).

Gene Bb shows partiality in male and female, Baldness is found in male due to effect of this gene, but baldness is absent in female with this genotype.

SEX DETERMINATION

Establishment of sex through differential development in an individual at an early stage of life, is called sex
determination. There are different methods for sex determination in organisms like environmental, non-allosomic genetic determination, allosomic sex determination and haplodiploidy.

Sex Determination on the basis of fertilization.
 Three types –
 1. Progamic – Sex is determined before fertilization.
eg. - drone in honey bee

2. Syngamic - Sex is determined during fertilization.
eg. - most of plants & animals

3. Epigamic - Sex is determined after fertilization.
eg. - Female in honey bee.

Environmental Determination of Sex. It is non-genetic determination of sex which is based purely on environmental conditions. The organisms are potentially hermaphrodite and capable of expressing any of the
two sexes.

1. In marine worm Bonellia, larva develops into female if it settles down alone in an isolated place. Any larva
coming in contact with the already grown female, it changes into male, and lives as a parasite in the uterus of
female.

2. Crepidula (marine mollusca) where larva develops into male in the company of female and develops into
femaleifleftalone.

3. In crocodiles low temperature induces femaleness and high temperature maleness.

4. ln turtles temperature below 28°C induces maleness, above 33°C femaleness while between 28 - 33°C
equal number of male and female animals are formed.

5. In marine fish Medusa sex changes according to environmental condition, becoming male in cold water and
female in warm water.

Allosomic determination of sex –
Chromosomes are of two types -

(a) Autosomes or somatic chromosomes -
These regulate somatic characters.

(b) Allosomes or Heterosomes or Sex chromosomes -

These chromosomes are associated with sex determination. Term "Allosome" & "Heterosome" were given
by Montgomery.

Sex chromosomes first discovered by "Mc Clung" in grass hopper
X- Chromosome discovered by "Henking" and called 'x-body'.

Wilson & Stevens proposed chromosomal theory for sex determination.

(1) XX - XY type or Lygaeus type :- This type of sex determination first observed by Wilson & Stevens in
Lygaeus insect. Two types–

(a) XX female and XY male :- In this type of sex determination female is Homogametic i.e produces only
one type of gamete

•  Male is heterogametic (male produces two types of gamete)

In male X-chromosome containing gametes is called "Gynosperm" and Y- chromosome containing gamete is called "Androsperm".
eg. Man and dioecious plants like Coccinea, Melandrium

(b) XY female and XX male or ZW female and ZZ male :- In this type of sex determination female is
Heterogametic i.e produces two types of gamete and male individual is homogametic i.e produces one
type of gamete.
It is found in some insects like butter flies, moths and vertebrates like birds, fishes and reptiles.
In plant kingdom this type of sex determination is found in Fragaria elatior.

(2) XX female and XO male :- or "Protenor type" :- In this type of sex deternination deficiency of one chromosome in male. In this type, female is homogametic and male is heterogametic.

Example :–
– Grass hopper
– Squash bug Anasa
– Cockroach
– Ascaris and in plants like - Dioscorea sinuta & Vallisneria spiralis

Genic balance theory :- C.B. Bridges proposed genic balance theory for sex determination in Drosophila.
– According to Bridges in Drosophila Y-chromosome is heterochromatic so it is not active in sex determination
In Drosophila sex determination takes place by sex index ratio.

In Drosophila gene of femaleness (Sxl- gene) (Sxl=Sex lethal gene) is located on x-chromosome and gene of
maleness is located on autosome
Gene of male fertility is located on y-chromosome and in Drosophila, y-chromosome plays additional role in
spermatogenesis and development of male reproductive organ, so y-chromosome is essential for the production offertilemale.

Sex index ratio

(c) X/A = 1.5 → Super female or meta female (sterile) (2A + XXX)

(d) X/A = less than 0.5 → Super male or meta male (Sterile) (3A + XY)

(e) X/A = = In between 0.5 and 1 → Intersex (Sterile) (3A+XX)

Gynandromorph –
Body of some Drosophila has some cells with male genotype (X0) and some cells with female genotype (XX).
Body of such type of Drosophila has half lateral part of male and half lateral part of female and it is called bilateral gynandromorph. It is formed due to loss of one x-chromosome at metaphase plate during first zygotic division. Formation of gynandromorph is the best evidence that y-chromosome does not play any role in sex differentiation. 

 Haploid - diploid mechanism –
In insects of order Hymenoptera which includes ants,honey bees, wasps etc.
Sex determination takes place by sets of chromosomes.
Diploid (two sets) → Female
Haploid (One set) → Male
In honey bee, male individual (Drone) develops from unfertilized eggs (Haploid). Male is always parthenote.
Queen and worker bees develop from diploid eggs i.e. fertilized egg.

Sex determination by Hormone –
Dizygotic twins are common in cattle like cow, sheep, goat etc. Some times the placentae of the two dizygotic
twins fuse forming blood vascular connections between two developing foetus. If twins are dizygotic, one
foetus may be male and the other female.

•  Male hormone produced before female hormone by male twins which suppresses the differentiation of female internal sex organ. Such a sterile female with Under developed ovaries, oviducts, Uterous etc. is called free martin.  In free martin conditions, female is sterile & male is normal.

Cytological basis of sex determination –
Barr body technique or Lyon's hypothesis -

Interphasic nucleus of human female contains two X- chromosomes. Out of two, one X- chromosome becomes
heterochromatin and other X- chromosome is euchromatin. By staining X- heterochromatin, it appears as a
dense body which is called Barr body. (Facultative hetrochromatin)
No. of Barr body ⇒ (No. of X chromosomes – 1)
So in a Normal female (2A + XX) → One Barr body
Normal male (2A + XY) → Barr body absent
Turner syndrome (Sterile female) (2A + XO) → No. Barr body
Klinefelter syndrom (Sterile male)(2A + XXY) → One Barr body

Drum stick which occurs in blood of female of mammals, is also a type of barr body. Drum stick is absent in
neutrophils of Male.

Sex determination in human –
There occur a special gene on differential region of Y-chromosome of human, called Sry - gene (Sex determine
region on y chromosome ). This gene forms a proteinaceous factor called TDF (testes determining factor). TDF
responsible for the development of male reproductive organs. So presence and absence of Y- chromosome
determines sex.

Sex determination in plant –
 H.E. Warmke discovered sex determination in Melandrium plant.
In Melandrium Y- chromosome is long as compare to X- chromosome.
In plant sex chromosomes are found only in unisexual plant.
Pro. R.P. Roy gave the importance of Y-chromosome in plant.
He discovered sex determination in Coccinea indica (Family- cucurbitaceae)
Y- chromosome contains four regions and X- chromosome contains two regions. Different functions of these
regions-

1. I^st region - (Female suppressor region) :- This region suppresses the development of female reproductive structures.
2. II^nd region (Male promotor region) :- This region initiates or start the development of Anther
3. III^rd region (Male fertility region) :- This region induces the further development of Anther.
4. IV^th region (Homologous region) :- This region helps in the disjunction & Pairing of X and Y chromosome during meiosis.
5. V^th region (Differential region of X-chromosome) :- This region induces the development of female gonads

So when one or more than one Y- chromosome present then plant is male and in female plant Ychromosome
is absent.

Special Case :
If I^st region of Y chromosome is removed then plant becomes bisexual (XY).

If II^nd region of Y chromosome is removed then plant becomes female due to absence of II^nd region, I^st region of Y chromosome does not suppress the V^th region of X-chromosome.

If III^rd region of Y chromosome is removed then plant become sterile male due to absence of III^rd region so further development of anther does not take place.

PHENOTYPIC EXPRESSION IN HAPLOID ORGANISMS (Neurospora Genetics)

Diploid organisms such as pea and Drosophila, have two alleles for each gene on each chromosome (the exceptions are for the X linked genes in XY or XO males). With the result, the recessive allele is not expressed
in the phenotype in presence of the dominant one. However, this is not so in the case of haploid organisms. Contrary to diploid organisms, the genetics of haploid organisms exhibit the following features:\

1. Haploid organisms contain only one allele of a gene, so there is no complication of dominance. All the
genes, whether dominant or recessive, expresses itself in the offsprings.

2. In absence of dominance, any new mutation is immediately expressed in the phenotype, in haploid
organisms.

3. Study of inheritance of the mutated gene, its linkage, crossing over and biochemical consequence of a
mutation can easily be studied in haploid.

Linkage And Recombination in Neurospora (Drosophila of plant kindgom)
Detection of linkage and recombination of genes in haploid organisms as in fungi, bacteria etc. is comparatively
simple. Fungus Neurospora is one of the favourite material with geneticists, because :-
1. The life cycle of Neurospora is the product of a single meiosis.
2. The life cycle is of a short duration.
3. The meiotic products are linearly arranged in ascus as 8 ascospores as ordered tetrads (i.e, the eight
ascospores are arranged in the same order in which chromatids were on the meiotic metaphase plate).

Tetrad Analysis in Ordered Tetrads –
In Neurospora, the nuclei from hyphae of opposite mating type (+) and (–) fuse to form a diploid zygote. The
zygote is the only diploid stage in the life cycle of Neurospora. The zygote nucleus divides meiotically producing four haploid nuclei, each of which then undergoes mitosis. The eight cells produced this way, form 8 haploid ascospores enclosed in the ascus. The three divisions proceed along the longitudinal axis, so the ascospores are arranged in a line in a specific order that indicates the order of arrangement of chromatids on the meiotic metaphase plate. This is called linear or ordered tetrad. Each of the four products of meiosis can be cultured separately to study their phenotypes and genotypes. This is called tetrad analysis.

1. First Division Segregation Between Centromere and gene-a.
A cross between two strain of Neurospora, one normal (a⁺) and other mutant (a) strain produces 8-ascospores, out of which four are normal (a⁺) and other four mutants (a). The linear arrangement of ascospores in ascus is 4a⁺ : 4a. It indicates the absence of crossing over between locus-a and centromere. This is described as first divisionsegregation.

2. Second Division Segregation Between Centromere and Gene-a.
In a similar cross if crossing over takes place leading to paired arrangement of ascospores with a particular
gene, it is described as second division crossing over. The arrangement of ascospores in the sequence ( 2 :
2: 2 : 2) is as follows:

(i) a⁺ : a⁺ : a : a : a : a : a⁺ : a⁺
(ii) a : a : a⁺ : a⁺ : a⁺ : a⁺ : a : a
(iii) a⁺ : a⁺ : a : a : a⁺ : a⁺ : a : a

Single Gene Mapping in Neurospora
In Neurospora centromere behaves as a gene for mapping gene pair. In such a case distance of gene from the
centromere is calculated by calculating the percentage of cross overs between centromere and gene.
Que. If 10% asci show crossing over in ascocarp what will be distance between gene and centromere.
If total 100 asci are present in a Neurospora

asci is derivative of 4 chromatids
100 asci are derivative of 400 chromatids = total chromatids
10 asci are derivative of 40 chromatids
(Out of 40 only 20 will be the recombinant type)