Now, supposing that instead of one, there are two characteristics that are in antagonism; in that case, we have the occurrence of double hybridism (dihybridism).
Let us take the strains of peas already considered, but let us choose for observation the character of their seed. One of the plants has round seed and yellow cotyledons; and the other angular seed and green cotyledons. These two characteristics, therefore, are both inherent in the seed; condition of surface (rough, smooth), and colour (green, and yellow).
After fertilisation, Mendel's first law, that of the prevalence of the dominant character, will operate, and all the plants of the first generation will have round seed and yellow cotyledons. Hence these are the dominant characteristics, which we will represent by capital letters: R (round), Y (yellow), to distinguish them from the recessive characteristics, which we will designate with small letters: a (angular), and g (green).
According to Mendel's hypothesis, all these hybrids with round seed and yellow cotyledons, contain sexual cells of opposite potentialities, numerically equal and corresponding to the antagonistic characters of the parent plants. That is, they must have in their pollen grains and their ovarian cells all the possible combinations of their different potentialities.
They should produce in equal quantities:
| pollen grains (P) with | round | seed and | yellow | cotyledons: | R Y |
| " | " | green | " | R g | |
| angular | " | yellow | " | a Y | |
| " | " | green | " | a g | |
| ovarian cells (O) with | round | " | yellow | " | R Y |
| " | " | green | " | R g | |
| angular | " | yellow | " | a Y | |
| " | " | green | " | a g |
The total number of combinations that may result is sixteen; that is, each one of the four combinations of pollen may unite with any one of the ovarian cells; thus constituting four groups of four. And these groups represent the combinations (of pollen and ova) capable of producing individuals:
| R Y - R Y = R Y | a Y - R Y = R Y |
| R Y - R g = R Y | a Y - R g = R Y |
| R Y - a Y = R Y | a Y - a Y = a Y |
| R Y - a g = R Y | a Y - a g = a Y |
| R g - R Y = R Y | a g - R Y = R Y |
| R g - R g = R g | a g - R g = R g |
| R g - a Y = R Y | a g - a Y = a Y |
| R g - a g = R g | a g - a g = a g |
Fig. 8.