For example, each male and female monohybrid produces two gametes, therefore, there will be 2 X 2 = 4 gametic combinations and 4 squares in the checkerboard for a monohybrid cross. Likewise, a gametic checkerboard for dihybrid and trihybrid crosses would have 4 x 4= 16 and 8 x 8=64 squares, respectively. Example: The F2 results of the dihybrid cross between black short guinea pigs (BB SS) and brown long guinea pigs (bb ss) can be represented by Punnett’s gemetic checkerboard method as follows:
Punnett's gametic checkerboard displays the phenotypic and genotypic results of F2 side by side, therefore, has remain quite popular method among most text-books of genetics We have also made a frequent use of this method in explaining various examples of this text book. But, this system too is quite laborious, time consuming and offers more chances for error, therefore, recently few more methods have been evolved. Anyhow, this methods also provides an opportunity for the deduction of phenotypic and genotypic ratios of F2 of various types of hybrids, which can be tabulated as follows.
Dihybrid Crosses and Mendel's Law of Independent Assortment -
To formulate the law of segregation, Mendel considered the monohybrid crosses and noted the behaviour of a single pair of traits and single pair of alleles of a gene at a time. Later on, he tried to find out how different phenotypic traits would behave in relation to each other in their inheritance from generation to generation. For this purpose, he crossed two varieties of pea plants which were differing in two pairs of contrasting characters. Because the resulted offspring of such a cross were hybrids for two factors or genes, so are called as dihybrids. A dihybrid genotype is heterozygous at two gene loci (in monohybrid. the genotype is heterozygous at one gene loci only). A hybridization cross which considers the inheritance of two traits, each of which is specified by a different pair of genes on different chromosomes, is called a dihybrid cross.
Mendel's Dihybrid Cross -
Mendel in one of his experimental cross studied the inheritance of seed colour and seed shape. In the first case the two contrasting phenotypes were yellow and green; in the second round and wrinkled.
The F1 hybrids of such cross were found to have yellow round seeds. When the F1 hybrids were allowed to cross among themselves they produced four types of seeds in the ratio of 9: 3: 3: 1 (9 yellow round: 3 yellow wrinkled: 3 green round: 1 green wrinkled.
The results of such a dihybrid cross has been illustrated in figure.Thus, beside getting the phenotypic ratio of 3 : 1 of a monohybrid cross, he got the unusual ratio of 9 : 3 : 3 : 1. This kinds of irregularity in the ratio of F2 offsprings of a dihybrid cross was explained by his second law, the law of independent assortment.
Mendel's Law of Independent Assortment-
Mender’s law of independent assortment or recombination of genes states that when the gametes are formed the members of the different pairs of factors (genes) segregate quite independently of each other and that all possible combinations of the factors (genes) concerned will be found among the progeny.
A. Yellow Round
B. Green Wrinkle
C. Yellow Round
D. Yellow Round
E. Self Pollination
B. Green Wrinkle
C. Yellow Round
D. Yellow Round
E. Self Pollination
Mechanism of Independent Assortment -
The mechanism of independent assortment could be understood well after the discovery of meiosis. The Mendel's dihybrid cross of pea plants between yellow round seeds x green wrinkled seeds, may have following cytological mechanism: The homozygous pea plants with yellow round seeds have the alleles YY for yellow seed colour on the homologus pair of autosomal chromosomes and alleles RR for round shape of the seeds on another homolagous pairs of chromosomes.
Likewise, the homozygous pea plants with green wrinkled seeds have the yy and rr alleles for green colour and wrinkled shape of the seeds respectively, on different homologous pairs of chromosomes. During gametogenesis, the homologous chromosomes of each parent plant segregate from each other to produce the gametes with the genotype of YR or yr, as has been shown in figure. The YR and yr gametes unite to produce the F1 heterozygotes with the phenotype of yellow and round and genotype of Yy Rr displaying the completed dominance of Y and R alleles over the y and r alleles. In the cells of F1 heterozygote, on one homologous pair of chromosomes occur the alleles for yellow (Y) and green (y) seed colours and on the other pair of homologous chromosome are the alleles for round (R) and wrinkled (r) seed shapes.
During gametogenesis of F1 yellow round heterozygotes, the segregation of the seed colour alleles occurs independently of the segregation of the seeds shape alleles because each pair of homologous chromosomes behaves as independent unit during meiosis. Furthermore, because the orientation of bivalents on the first meiotic metaphase plate is completely at random, four combinations of factors (alleles) could be found in the metiotic products, i.e., the gametes. The resultant gametes, thus will be genetically different and of following four types:
1. Yellow Round (YR).
2. Yellow Wrink1ed (Yr).
3. Green Round (yR).
4. Green Wrinkled (yr).
These four types of gametes of F1 dihybrids unite at randomly in the process of fertilization and produce sixteen types of individuals in F2 in the ratio 9: 3: 3: 1 as has been shown in Figure.The genotype and phenotype of this dihybrid cross can be summarized in following table. The phenotype and genotype of F2 of a dihybrid cross between pea plants with yellow round and green wrinkled seeds.
These results prove the law of independent assortment and show that each pair of allele behaves independently and bears no permanent association or relation with particular character. The allele Y was associated with allele R in parent but it does not always remain associated with it and also becomes associated with the allele r.
Examples of Law of Independent Assortment -
The law of independent assortment applies well to most plants and animals, but only to those genes which occur on non-homologous autosomal chromosomes. Here, following dihybrid crosses of guinea pigs and Drosophila can be considered as the examples for law of independent assortment in animals. 1. When a black short haired guinea pig (BB SS, the black colour and short hairs dominate over brown colour and longhairs respectively) and a brown, long-haired- guinea pig (bb ss) are mated, the BB SS individuals produce gametes all of which are BS. The bb ss guinea pigs produce only bs gametes. Each gamete contains one and only one of each kind of gene. The union of BS gametes and bs gametes yields F1 heterozygous, black, short haired individuals with the genotype of Bb Ss.
However, when two of the F1 individuals are mated each produces four kinds of gametes in equal numbers-BS, Bs, bS, bs. These gametes unite to produce 16 combinations in F1 in the phenotypic ratio of 9 black, short haired: 3 black, long haired: 3 brown, short haired: 1 brown, long haired or 9 : 3 : 3 : I. The results of this cross have been represented by following diagram.
However, when two of the F1 individuals are mated each produces four kinds of gametes in equal numbers-BS, Bs, bS, bs. These gametes unite to produce 16 combinations in F1 in the phenotypic ratio of 9 black, short haired: 3 black, long haired: 3 brown, short haired: 1 brown, long haired or 9 : 3 : 3 : I. The results of this cross have been represented by following diagram.
The results of this cross clearly show that the segregation of the B-b genes is independent of the segregation of the S-s genes.
Methods of Determination of Allelic Combinations of Gametes of Homozygous and Heterozygous Individuals -
For every mono-, di-, or polyhybrid crosses one has to determine the genotype of different kinds of gametes of an experimental organism. By various crosses, now it has become clear that
(1) a homozygote always produces single type of gametes;
(2) a monohybrid produces two types of gametes;
(3) a dihybrid produces four types of gametes; in equal number. Thus, an increase in numbers of a pairs of alleles in a hybrid, enlarges the possibility, probability or chance for new types of allelic combination as has been tabulated in following.
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