The Background
Gregor Mendel analyzed the pattern of inheritance of seven pairs of contrasting traits in the domestic pea plant. He did this by cross-breeding dihybrids; that is, plants that were heterozygous for the alleles controlling two different traits.
Example
Producing dihybrids (F1)
He mated a variety that was pure-breeding (hence homozygous) for round (RR), yellow (YY) seeds with one that was pure-breeding for wrinkled (rr), green (yy) seeds. All the offspring (F1) produced from this mating were dihybrids; that is, heterozygous for each pair of alleles (RrYy). Furthermore, all the seeds were round and yellow, showing that the genes for round and yellow are dominant.
Mating the dihybrids to produce an F2 generation
Mendel then crossed these dihybrids. If it is inevitable that round seeds must always be yellow and wrinkled seeds must be green, then he would have expected that this would produce a typical monohybrid cross: 75% round-yellow; 25% wrinkled-green. But, in fact, his mating generated seeds that showed all possible combinations of the color and texture traits.
9/16 of the offspring were round-yellow
3/16 were round-green
3/16 were wrinkled-yellow, and
1/16 were wrinkled-green
Finding in every case that each of his seven traits was inherited independently of the others, he formed his “second rule“ the Rule of Independent Assortment:
The inheritance of one pair of factors (genes) is independent of the inheritance of the other pair.
Today we know that this rule holds only if two conditions are met:
the genes are on separate chromosomes or
the genes are widely separated on the same chromosome.
Mendel was lucky in that every pair of genes he studied met one requirement or the other.
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