It is possible for one plant to have all of these dominant characters or all of the recessive ones, or part of one kind and part of the other. The inheritance formula of a plant having all seven of the dominant characters is ABCDEFG; of one having all of the recessive characters abcdefg. When two such plants are crossed the inheritance formula of the hybrid is AaBbCcDdEeFfGg, and since the dominant and recessive characters (or rather determiners of characters) represented by these seven pairs of letters separate in the formation of the gametes, and since each separate determiner may be associated with either member of the other six pairs, the number of possible combinations of these determiners in the gametes is (2)7 or 128. That is, in this case 128 kinds of germ cells may be produced, each having a different inheritance formula; and since each of these 128 kinds of male germ cells may unite with any one of the 128 kinds of female germ cells, the number of possible combinations is (128)2 or 16,384, which represents the number of combinations of these characters which are possible in the F2 generation. Every one of these more than sixteen thousand genotypes may be represented by various combinations of the letters ABCDEFG and abcdefg.
When many characters are concerned it is difficult to remember what each letter stands for, and consequently it is customary in such cases to designate characters by the initial letter in the name of that character. By this form of short hand one can show in a graphic way the possible segregations and combinations of hereditary units in gametes and zygotes through successive generations, and as a result many modern works on Mendelian inheritance look like pages of algebraic formulæ.
Some progress has been made, as was pointed out in the last lecture, in identifying certain structures of the germ cells with certain hereditary units, but quite irrespective of what these units may be and where they may be located it is possible, by means of the Mendelian theory of segregation of units in the germ cells and of chance combinations of these in fertilization to predict the number of genotypes and phenotypes which may be expected as the result of a given cross.
4. Presence and Absence Hypothesis.—Mendel spoke of the presence of contrasting or differentiating characters in the plants which he crossed, such as round or wrinkled seeds, tall or short stems, etc. Many other writers regard these contrasting characters as positive and negative expression of a single character, and consequently they speak of the presence or absence of single characters; thus round seeds are due to the presence of a factor for roundness (A) while wrinkled seeds are characterized by the absence of that factor (a). Round seeds are wrinkled seeds plus the factor for roundness. Most of the phenomena of Mendelian inheritance are more simply stated in terms of presence or absence of single characters than in terms of contrasting characters.
