Page:Popular Science Monthly Volume 67.djvu/206

From the facts that cross-bred animals form sexual elements (or gametes) of two sorts, and that the two sorts are equally numerous, it follows that among their offspring dominant and recessive individuals will occur in definite proportions. It has been found by experiment that when two cross-bred (or hybrid) dominant animals are mated together, the offspring consist of a mixture of dominant with recessive individuals in approximately the proportions, three dominant to one recessive. Further, when a hybrid dominant is mated with a recessive animal, half the offspring are hybrid dominants, half recessives. These proportions of necessity result, provided neither sort of gamete has greater affinity for one kind than for the other. For consider all the possible unions between two sets of gametes each $D$ and $R$ (the case in which two hybrid dominants are bred together):

${\begin{array}{rcl}D&{\text{and}}&R\end{array}}$

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⋮⁠⋱⋰⁠⋮

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${\begin{array}{rcl}D&{\text{and}}&R\end{array}}$

$\underbrace {DD+2D(R)} _{3}+{\underset {1}{RR}}$

They are 1 $DD$, 2 $DR$ and 1 $RR$, or three unions involving the $D$ character to one involving the $R$ character only; hence three dominant individuals will be produced to one recessive. Further, one of the three dominants ($DD$) will be pure, while the other two are hybrid in character. Recessive individuals are, however, necessarily pure and breed true inter se. Thus, smooth-coated guinea-pigs produce only smooth-coated offspring, albinos only albino offspring, and long-haired ones only long-haired offspring, when mated to animals like themselves. The reason for this will be clear if we return to the illustration with the glass plates. Pairs of transparent plates can be separated only into transparent pieces, and these can be recombined only into transparent pairs.

With the dominant offspring of hybrids, however, the case is different. Only pure dominants ($DD$) will breed true when mated inter se; hybrid dominants ($DR$) will continue to give a mixed progeny. For pairs of opaque plates, when separated, can be recombined only into opaque pairs; but pairs composed each of an opaque and a transparent plate, when separated, may be recombined either into opaque pairs or into transparent pairs, the chance frequencies of the two sorts of combination being as three to one.

Accordingly, any pair of recessive individuals may form the beginning of a pure race of recessives, but in starting a pure race of dominants we must test each animal used, to make sure that it does not