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The Law of Independent Assortment: Dihybrid cross, Examples, Formulas used for calculation in Monohybrid, Dihybrid, and Trihybrid cross, Significance, Practice Problems and FAQs

The Law of Independent Assortment: Dihybrid cross, Examples, Formulas used for calculation in Monohybrid, Dihybrid, and Trihybrid cross, Significance, Practice Problems and FAQs

We all have some characters similar to our parents, right?. You studied this concept in lower classes. In the below given image, a family is given. They have two kids. You can see that the younger one got the beautiful blue eye colour from the mother and the eldest one got the brown eye colour from the father. Do you know why this is happening? Why aren't both getting the same eye colour?.

This happens due to the following reason. Eye colour is under the control of gene ‘B’. It has two alleles ‘B’ and ‘b’. Here the father is heterozygous for the gene ‘B’, which means he is ‘Bb’. Hence he has brown eye colour. The mother is homozygous recessive for the gene ‘B’ which means she is ‘bb’. So she has blue eye colour. The eldest son got ‘B’ allele from the father and ‘b’ allele from the mother. So he is ‘Bb’, that means heterozygous and has brown eye colour. The younger son got the ‘b’ allele from the father and the same ‘b’ allele from the mother. So he is ‘bb’ which means homozygous recessive and has blue eye colour.

Fig: Eye colour in a family

Have you ever thought why siblings can be so similar or even so dissimilar to one another?. We solved one problem now. I know there are several related questions in your mind and that can only be answered with the help of genetics.

The variations do occur during the time of gamete formation due to segregation of traits. During the time of gamete formation, alleles segregate randomly. The genes of mother and father equally segregate into gametes in such a way that each gamete contains one of the two alleles. The alleles of a gene segregate independently of each other. After fertilisation, the diploid zygote contains half the genetic material from the mother and half from the father. Therefore, siblings look similar to each other and to their parents in certain characteristics. Let’s take a deep dive into the details of the law of independent assortment in this article and try to find out the answers for some of the questions in your mind.

Table of contents

  • Mendelism
  • Dihybrid cross
  • Law of independent assortment
  • Examples to prove law of independent assortment
  • Formulas used for calculation in monohybrid, dihybrid, and trihybrid cross
  • Significance of law of independent assortment
  • Practice problems
  • FAQs

Mendelism

Mendelism refers to the theoretical principles of heredity put forward by Gregor Johann Mendel based on his studies on Pisum sativum or garden pea. These are also known as Mendel's laws of heredity. For great contribution to genetics, Gregor Johann Mendel is known as the father of genetics.

Fig: Gregor Johann Mendel

Laws of Mendel

Mendel proposed that heredity is controlled by factors now called genes. He said that factors are present in the cells of the body and are transmitted to the next generation through gametes. During his studies, he put forth three laws of inheritance. Mendel’s laws are known as laws of inheritance which are as follows:

  • Law of dominance (First law)
  • Law of segregation (Second law)
  • Law of independent assortment (Third law)

Brief account of Mendel’s experiments

Mendel selected 14 true breeding garden pea plant varieties for his research. As seen in the table below, each of the seven types of plants had at least one character with two dissimilar traits (dominant and recessive). By enabling the plant to self-pollinate, Mendel was able to verify that each character was the result of true breeding. A true breeding or pure line is one plant that, after going through numerous generations of continual self-pollination, exhibits consistent trait inheritance and expression. Any plant that displayed a deviation was eliminated from the studies. The characters studied by Mendel are as follows:

Character

Contrasting traits

Images

Dominant

Recessive

 

Stem height

Tall (T)

Dwarf (t)

Fig: Stem height

Flower colour

Violet or red (W)

White (w)

Fig: Flower colour

Flower position

Axial (A)

Terminal (a)

Fig: Flower position

Pod shape

Inflated (I)

Constricted (i)

Fig: Pod shape

Pod colour

Green (G)

Yellow (g)

Fig: Pod colour

Seed shape

Round (R)

Wrinkled (r)

Fig: Seed shape

Seed colour

Yellow (Y)

Green (y)

Fig: Seed colour

Dihybrid cross

Dihybrid cross is a cross between two organisms of a species with two different observable characters. In simple words it is a cross involving two pairs of contrasting characters. Mendel chose true breeds or pure lines of pea as parent plants. For example, a cross involving pea plants that produce yellow round (YYRR) and green wrinkled (yyrr) pea seeds.

Example of dihybrid cross

Mendel performed his experiments in three stages as follows:

  • Selection of pure or true breeding parents.
  • Hybridisation and obtaining the F1 generation of plants.
  • Self pollination of hybrid plants to raise subsequent generations like F2.

Selection of parents

Mendel selected a true breeding pea plant which produces yellow round (YYRR) seeds with a true breeding pea plant which produces wrinkled green seeds (yyrr) as parents.

Fig: Selection of true breeding parents

Hybridisation of F1 generation

Mendel cross pollinated plants with two pairs of alternative forms of traits. He cross-pollinated the flowers by dusting the stigma with pollen from the other 50% of the flowers, which he employed as male flowers by bagging their stigma. He emasculated (removed anthers) 50% of the flower of the same plant to function as female plants. The hand pollinated flowers were covered with paper bags to prevent contamination from foreign pollen grains.

He preserved the seeds from this cross and planted them to create the first hybrid plants, which he referred to as the F1 generation or the first filial generation. Mendel noticed that all of the progeny in the F1 generation produced only yellow round (YYRR) seeds.

Fig: Cross between true breeding pea plant with yellow round (YYRR) seeds and a true breeding pea plant with green wrinkled (yyrr) seeds

He discovered that the F1 generation consistently represented only one of the parental traits (dominant) while the other trait disappeared in the F1 generation after carrying out the same cross for different pairs of characters.

Self pollination of hybrid plants to raise subsequent generations like F2

The F1 hybrids were then self-pollinated, and the progeny generation was referred to as the second filial generation or the F2 generation. Mendel discovered that some of the second filial generation offspring displayed the appearance of the green seed (yy) colour and wrinkled (rr) condition. In the F2 generation 9/16 of the total number of progeny appeared to be yellow round seeds (YYRR), 3/16 of the total number of progeny appeared to be yellow wrinkled seeds (YYrr), 3/16 of the total number of progeny appeared to be green round seeds (yyRR), and 1/16 of the total number of progeny appeared to be green wrinkled seeds (yyrr).

Fig: F2 generation of dihybrid cross

In this dihybrid cross, the dominant traits are round (RR) and yellow (YY) seeds, whereas the recessive traits are green (yy) and wrinkled (rr) seeds.

Fig: Dominant and recessive traits

Explanation of the example taken

For a dihybrid cross, Mendel took pure line parents i.e. they are homozygous dominant and homozygous recessive. The homozygous dominant genotype is YYRR (Yellow round seed), whereas the homozygous recessive genotype is yyrr (green wrinkled seed). Let us segregate one pair of genes R and r.

The R gene is present in 50% of the gametes, whereas the r gene is present in the other 50%. Now, in addition to the gene R or r, each gamete will also have the allele Y or y. The crucial point to note here is that segregation of 50% R and 50% r is distinct from segregation of 50% Y and 50% y. Therefore, 50% of gametes that bear r have Y allele and the rest 50% have y allele. Similarly, 50% of gametes that bear R have Y allele and the rest 50% have y allele.

Thus, there are four types of genotypes obtained: YR (Yellow round), Yr (Yellow wrinkled), yR (Green round) and ry (Green wrinkled). Each gamete has a frequency of 25% or 1/4th of the total gametes produced.

Fig: Gamete formation in dihybrid cross

After gamete formation, the F2 generation is obtained as:

Fig: F2 generation in dihybrid cross

Phenotypic ratio of dihybrid cross

Phenotype is the physical property of an organism that can be observed. The phenotypic ratio obtained from the dihybrid cross is 9:3:3:1.

Fig: Phenotypic ratio of dihybrid cross

Genotypic ratio of dihybrid cross

Genotype is described as the genetic makeup of an organism. The genotypic ratio obtained from the dihybrid cross is 1:2:1:2:4:2:1:2:1.

Fig: Genotypic ratio of dihybrid cross

Law of independent assortment

“According to the law of independent assortment, the segregation of one pair of characters is independent of the other pair of characters when two pairs of traits are joined in a hybrid.”

or

“If we consider the inheritance of two or more allele pairs at a time, their distribution in the gametes and in the subsequent generations is independent of each other.”

The Punnett square is used to understand the independent segregation of two pairs of genes. The segregation occurs during the formation of gametes via meiosis.

In the dihybrid cross, the F1 generation obtained is YyRr. Consider the segregation of one pair of genes, R and r. During gamete formation, 50% of gametes receive R gene and other 50% of gametes receive r gene. Along with R or r, the gametes also receive Y or y. The important thing to note here is that the segregation of 50% of R and 50% of r is independent from the segregation of 50% of Y and 50% of y. Therefore, 50% of R bearing gametes has Y and the other 50% of R bearing gametes has y. As a result, four genotypes of gametes are produced, YR (Yellow round), Yr (Yellow wrinkled), yR (Green round) and yr (green wrinkled).

Fig: Independent assortment during gamete formation in dihybrid cross

Formulas used for calculation in monohybrid, dihybrid, and trihybrid cross

There are some formulas that are commonly used to calculate the number of gametes, number of genotypes and number of phenotypes without forming a Punnett square. These are applicable for monohybrid, dihybrid, and trihybrid cross. These formulas are listed below:

  • To find the number of types of gametes

Types of gametes=2n

  • To find the number of types of phenotypes in case of self fertilisation

Types of phenotypes=2n

  • To find the number of types of genotypes in case of self fertilisation

Types of genotypes=3n

Here, ‘n’ represents the number of heterozygous gene pairs.

Monohybrid cross

Let’s see some applications of the above formulas using monohybrid cross, where the number of heterozygous gene pairs are one.

The number of types of gametes in a monohybrid cross

  • To find the number of types of gametes in a monohybrid cross, where n = 1:

Types of gametes = 2n = 2

Fig: The number of types of gametes in a monohybrid cross

The number of types of phenotypes in a monohybrid cross

  • To find the number of types of phenotypes in a monohybrid cross, where n = 1:

Types of phenotypes = 2n = 2

Fig: The number of types of phenotypes in a monohybrid cross

The number of types of genotypes in monohybrid cross

  • To find the number of types of genotypes in monohybrid cross, where n = 1:

Types of genotypes = 3n = 3

Fig: The number of types of genotypes in a monohybrid cross

Dihybrid cross

Let’s see some applications of the above formulas using dihybrid cross, where the number of heterozygous gene pairs are two.

The number of types of gametes in a dihybrid cross

To find the number of types of gametes in a dihybrid cross where n = 2;

Types of gametes = 2n = 22

= 4

Fig: The number of types of gametes in a dihybrid cross

The number of types of phenotypes in a dihybrid cross

To find the number of types of phenotypes in a dihybrid cross, where n = 2:

Types of phenotypes = 2n = 22

= 4

Fig: The number of types of phenotypes in a dihybrid cross

The number of types of genotypes in dihybrid cross

To find the number of types of genotypes in dihybrid cross, where n = 2:

Types of genotypes = 3n =32

= 9

Fig: The number of types of genotypes in a dihybrid cross

Example to prove law of independent assortment

Let us take an example to prove the law of independent assortment. Let’s make a cross between the following two parents. The first parent produces violet axial flowers (WWAA) and the other parent produces white terminal flowers (wwaa). Both the parents are homozygous for their traits. The flower colour violet (WW) is dominant over the flower colour white (ww). In the same way, the flower position axial (AA) is dominant over the flower position terminal (aa).

The genotypes of parent plants are WWAA (violet axial) and wwaa (white terminal).

Fig: Flower colour

WWAA ✕ wwaa - Parent generation

WwAa

(Heterozygous plant with violet axial flowers - F1 generation)

The F1 generation obtained has heterozygous genotype i.e. WwAa. All the flowers produced in the F1 plant were violet and axial in position. It is then self pollinated to produce the F2 generation as follows:

WwAa ✕ WwAa

WA

Wa

wA

wa

WA

WWAA (Violet axial)

WWAa (Violet axial)

WwAA (Violet axial)

WwAa (Violet axial)

Wa

WWAa (Violet axial)

WWaa (Violet terminal)

WwAa (Violet axial)

Wwaa (Violet axial)

wA

WwAA (Violet axial)

WwAa (Violet axial)

wwAA (White axial)

wwAa (White axial)

wa

WwAa (Violet axial)

Wwaa (violet terminal)

wwAa (White axial)

wwaa (White terminal)

Here, the dihybrid phenotypic ratio obtained is 9:3:3:1 and the dihybrid genotypic ratio obtained is 1:2:1:2:4:2:1:2:1.

Significance of the law of independent assortment

The following are the significances of the law of independent assortment:

  • Independent assortments produce new combinations of alleles.
  • There are several points at which in sexual reproduction genetic variation can increase. For example, in prophase I of meiosis I, crossing over occurs. Independent assortment that occurs during anaphase results in sets of chromosomes with new combinations of alleles.
  • The law of independent assortment explains the method by which different genes independently separate from one another during gamete formation.
  • The law of independent assortment enables us to understand the pattern of inheritance of two pairs of contrasting characters.
  • It gives us insight into how characteristics are passed down from one generation (parent) to the succeeding generation (offspring).
  • It helps in understanding how pairs of gene variants are separated in reproductive cells.

Practice Problems

Q1. What is the phenotype of the F1 offspring of a pea plant hybrid in which one parent is a pure line for round seeds (RR) and the other parent is a pure line for wrinkled seeds (rr)?

  1. Only round seeds
  2. Only wrinkled seeds
  3. Both round and wrinkled seeds
  4. Partially round seeds

Solution: A pure line is described as the homozygous plant whose both the alleles are same. The trait of producing round seeds is dominant and the trait of producing wrinkled seeds is recessive. Therefore, the allele for round seeds is R and the wrinkled seeds is r. The genotype of a plant producing round seeds is RR and the genotype of a plant producing wrinkled seeds is rr. The cross between these two parents are as follows:

RR (Round seed) ✕ rr (Wrinkled seed) - Parental generation

(Round seed - Heterozygous) Rr - F1 generation

Hence, the correct option is a.

Q2. When does the law of independent assortment take place?

Answer: “According to the law of independent assortment, the segregation of one pair of characters is independent of the other pair of characters when two pairs of traits are joined in a hybrid.” It is the third law of heredity proposed by Gregor Johann Mendel. The Punnett square is used to understand the independent assortment of two pairs of genes with contrasting characters during a cross. The segregation occurs during the formation of gametes via meiosis. Hence the law of independent assortment is applicable to this stage.

Q3. What is phenotype?

Answer: Phenotype is the physical property of an organism that can be observed. The phenotypic ratio obtained from the dihybrid cross is 9:3:3:1 and the monohybrid cross is 3:1. Examples include the eye colour and the hair colour in humans.

Q4. Find the number of types of gametes in a trihybrid cross?

Answer: In a trihybrid cross, the number of heterozygous gene pairs are three and therefore, n = 3,

Types of gametes=2n

=23 = 8

Hence, the number of types of gametes produced in a trihybrid cross is eight.

FAQs

Q1. What would happen if there is no phenomenon of independent assortment?
Answer: If there is no independent assortment during gamete formation, there might be a chance that two characters inherit as a pair. For example, if we consider yellow round seeds (YYRR) and green wrinkled seeds (yyrr), then round (R) and yellow (Y) alleles might stay together and inherit together. In the same way green (y) and wrinkled (r) alleles stay together and inherit together. This will not result in any variations in the offspring.

Q2. Does the law of independent assortment apply to the linked genes?
Answer: Linked genes are genes that present close together on the same chromosome and cannot assort independently during the time of gamete formation. They are normally inherited together. Examples include genes of some eye colour and hair colour which are linked and inherited together. The law of independent assortment does not apply to the linked genes because these genes are present on the same chromosome and they inherit together. They can be segregated by recombination.

Q3. How does independent assortment create variations?
Answer: The segregation of one pair of characters is independent of the other pair of characters when two pairs of traits are joined in a hybrid is called independent assortment. The phenomenon of independent assortment produces new combinations of alleles which in turn create genetic variations. Each gamete contains a different set of chromosomes.

Q4. Does independent assortment occur in mitosis?
Answer: The independent assortment does not occur in mitosis. It only occurs during meiosis I when gamete formation takes place.

Related Topics

Law of Dominance, Practice Problems and FAQs

Law of Segregation: Dihybrid cross, Practice Problems and FAQs

Incomplete dominance ,Codominance,practice problems and FAQs

Multiple Allelism,Practice problems and FAQs

Chromosomal theory of inheritance: Sutton and Boveri Experiments, Practice Problems and FAQs

Sex determination: Genotypic and environmental sex determination, Genic balance theory of sex determination, Practice Problems and FAQs

Mendelian disorder: Haemophilia, Colour blindness, Sickle cell anemia, Thalassemia, Phenylketonuria, Practice problems and FAQs

Chromosomal disorders: Ploidy, Chromosomal aberrations, Common Chromosomal Disorders Practice Problems and FAQs

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