What is the essence of the law of independent inheritance of characters?

Independent inheritance (the third law of Mendel). Mendel used homozygous pea plants for dihybrid crossbreeding, differing simultaneously in two pairs of characters. One of the crossed plants had yellow smooth seeds, the other green wrinkled.
All hybrids of the first generation of this cross had yellow smooth seeds. Consequently, the yellow color of the seeds over the green and the smooth form over the wrinkled ones were dominant. Denote the alleles of yellow color A, green – a, smooth shape – B, wrinkled – b. Genes that determine the development of different pairs of characters are called non-allelic and are designated by different letters of the Latin alphabet. In this case, the parent plants have the genotypes AA BB and aabb, and the genotype of the F1 hybrids is AaBb, i.e., it is digeterozygous.
In the second generation, after self-pollination of F1 hybrids, wrinkled and green seeds reappeared in accordance with the law of splitting. The following combinations of characters were observed: 315 yellow smooth, 101 yellow wrinkled, 108 green smooth and 32 green wrinkled seeds. This ratio is very close to 9: 3: 3:
In order to find out how each pair of alleles in the progeny of the diheterozygote behaves, it is advisable to conduct a separate account of each pair of characters – in shape and color of the seeds. Of the 556 seeds Mendel received 423 smooth and 133 wrinkled, as well as 416 yellow and 140 green. Thus, in this case as well, the ratio of dominant and recessive forms for each pair of characters indicates a monohybrid cleavage according to phenotype 3: It follows that the dihybrid cleavage is two independently running monohybrid cleavages that overlap each other.
Observations show that individual pairs of traits behave independently in inheritance. This is the essence of Mendel’s third law – the law of independent inheritance of traits, or independent combination of genes.
It is formulated as follows: each pair of allelic genes (and alternative characters controlled by them) is inherited independently of each other.
The law of independent combination of genes forms the basis of the combinatorial variability observed when crossing in all living organisms. We also note that in contrast to the first Mendel law, which is always true, the second law is valid only for genes localized in different pairs of homologous chromosomes. This is due to the fact that non-homologous chromosomes combine in the cell independently of each other, which was proved not only when studying the nature of inheritance of characters, but also by direct cytological method

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