At dihybrid crossing each couple of signs in posterity gives 54 splittings independently from each other. At the same time in F2 the posterity as purely parental type, and with a new combination of signs is formed. So, in G. Mendel's experience seeds yellow smooth and green wrinkled had the initial forms of peas, and in F2 not only the combination of signs, as at parents, but also a plant with yellow wrinkled and green smooth seeds is received. G. Mendel came to a similar conclusion in the analysis of genotypes of posterity in F2. Having analysed all possible phenotypes of posterity, he came to a conclusion that in the genetic relation the posterity of phenotypic classes is not uniform. In particular, three of four phenotypic classes represent set of several genotypic classes in certain numerical ratios:
phenotypic classes genotypic class
The elementary mathematical analysis showed that the splitting formula which is experimentally calculated by it on a genotype at dihybrid crossing is equal to 1: 2: 1: 2: 4: 2: 1: 2: 1 also represents result of an independent combination of genotypes at two monohybrid crossings (1: 2: 1) × (1: 2: 1) or (1: 2: 1) 2. In other words each couple of signs behaves among generations independently from each other therefore among posterity there are individuals with a new combination of signs not only on a phenotype, but also on a genotype. In the form of genetic record it will look so:
(1АА : 2Аа : 1аа) × (1ВВ : 2Вв : 1вв) =
1ААВВ : 2АAВв : 1АAвв : 2АаВВ : 4АаВв : 2Аавв : 1ааВВ : 2ааВв : 1аавв.
Splitting on a genotype in F2 when crossing two diheterozygotes of АаВв × АаВв can be shown also by means of Punnett square (tab. 1) lattice which gives the evident image of a free combination of gametes among themselves therefore there are 16 various genotypic classes. A feast close examination of a lattice it is visible that genotypic classes form the combinational row consisting of 9 members (genotypes).
The table 1 Splitting on a genotype in F2 when crossing diheterozygotes АаВв × АаВв
At dihybrid crossing 16 genotypic classes forming 9 genotypes that also proves existence of an independent combination of signs (alleles) when forming posterity of F2 are formed. This phenomenon reflects the 3-rd law of Mendel – the law of independent inheritance of signs or otherwise an independent combination of genes.
The essence of the 3-rd law of G. Mendel consists in the following: each couple of alternative signs among generations behaves independently from each other therefore among posterity organisms with new combinations of signs appear.
The principle of equiprobable distribution of prepotent and recessive alleles at formation of gametes at F1 hybrids is the cornerstone of the 3-rd law of G. Mendel. In case of a diheterozygote of AaBb we deal with two couples of alternative signs (four alleles А, а и В, в) which are in pairs distributed between gametes with identical probability.
Therefore, splitting of prepotent and recessive alleles of each of genes will be equal:
(А : а) и (В : в).
Using the 3-rd law of G. Mendel, it is possible to write down a formula of probabilistic distribution of alleles between gametes as follows:
(А : а) × (В : в) = АВ : Ав : аВ : ав.
Verification of this assumption was made by G. Mendel with use of the analyzing crossing (АаВв × аавв) in which the ratio of phenotypic classes has to reflect a ratio of types of gametes of hybrids of F1:
АаВв × аавв
1АаВв : 1Аавв : 1ааВв : 1аавв
In one of the cases of analyzing crossing, it received the following ratios of phenotypes of seeds at plants: 31 round yellow (АаВв), 26 round green (Аавв), 27 wrinkled yellow (ааВв) and 26 wrinkled green (аавв).