SOME OP THE PRINCIPLES OP PLANT- BREEDING 



65 



bearded wheat be fertilized with its own pollen and 

 that 100 egg-cells be fertilized with 100 pollen- 

 grains of the same hybrid. There are two kinds of 

 egg-cells produced, some with potentialities of the 

 bald wheat and some with potentialities of the 

 bearded wheat, and the same is true of the pollen- 

 grains. Taking the egg-cells and pollen-grains 

 without selection, therefore, we would expect to 

 have of the egg-cells 50 with bald potentialities 

 and 50 with bearded potentialities. In the pollen- 

 grains also we would expect to have 50 with bald 

 potentialities and 50 with bearded potentialities. 

 If these are brought together, allowing the law of 

 chance to govern the union, the probability is that 

 we would have 25 bald uniting with 25 bald; 25 

 bald uniting with 25 bearded ; 25 bearded uniting 

 with 25 bald, and 25 bearded uniting with 25 

 bearded. Representing the bald potentialities by B 

 and the bearded potentialities by b, we have the 

 following formulae, which explain the probable 

 unions graphically (and this is what is known as 

 Mendel's law): — 



One Hundred Egg-cells by One Hundred 

 Sperm-cells. 



ocD N^ ocD _ ocTjp / (Theso do not contain potentlali- 

 ZbH X -ibB - Zt>iia -J^ tiesof b.andwillreproducetrue.) 



(These are hybrids so far as this 

 character -pair is concerned, — 

 exactly the same as in the first 

 generation, and contain poten- 

 tialities of both B and b. These 

 will not reproduce true to type, 

 and will break up like second- 

 generation hybrids.) 



(These do not contain the poten- 

 tialities of B, and will reproduce 

 true.) 



25B X 25b = 25Bb 



2Bb X 25B = 25bB 



25b X 25b = 25bb 



"This formula for the hybrids," writes Bailey, 

 "is Mendel's law. In words, it may be expressed 

 as follows: Differentiating characters in plants 

 reappear in their purity and in mathematical reg- 

 ularity in the second and succeeding hybrid off- 

 spring of these plants ; the mathematical law is 

 that each character separates in each of these 

 generations in one-fourth of the progeny and 

 thereafter remains true." 



The above illustration will explain the law of 

 .'3egregation, and probable ratio of recombination 

 when hybrids are inbred with their own pollen, 

 and when only one pair of characters is considered. 

 When an egg-cell with bald potentialities unites 

 with a sperm-cell with bald potentialities, this 

 gives rise to a pure germ-cell containing only bald 

 potentialities, and the progeny in subsequent gen- 

 erations will breed true so far as this character is 

 concerned. Also when the egg-cell with bearded 

 potentialities unites with a sperm-cell with bearded 

 potentialities, the result is a pure germ-cell con- 

 taining only bearded potentialities, and the progeny 

 would reproduce true, so far as this character is 

 concerned, in subsequent generations. In the other 

 two cases where, in fecundation, germs with bald 

 potentialities unite with germs with bearded poten- 

 tialities, giving the combinations Bb and bB, which 



S5 



amount to the same thing, we have in reality 

 hybrids exactly the same as in the first generation, 

 and the progeny from these in the next generation 

 behave exactly the same as did the first-generation 

 hybrids in the second generation. In such a case 

 as this, where one of the characters, as the bald 

 head, is strong and dominant, all combinations that 

 contain the potentialities of this character, whether 

 pure or mixed, show this character only. Thus, in 

 the above table the 25bb would come with bearded 

 heads, while the 75 of other combinations would 

 have bald heads. To determine which of these 75 

 heads are the combination Bb, that is bald with 

 bearded, and which BB, that is bald with bald, 

 would require the growing of progeny, to deter- 

 mine which were reproduced true to type. The 

 ratio of the combinations, it will be noticed, is IBB 

 to 2Bb to Ibb. While in certain hybrids of parents 

 possessing two opposed parental characters this 

 ratio of probabilities is not produced, if large num- 

 bers are used the ratio will be found in many cases 

 with little deviation. A sufficiently large number 

 of cases have now been carried out with various 

 plants and animals to place the conclusion beyond 

 question. We do not know, however, how many 

 characters follow Mendel's law, and are not yet 

 entirely certain whether those character-pairs that 

 sometimes follow the law of segregation always 

 follow it. 



The individuals of the second generation which 

 contain the potentialities of both characters of the 

 pair, if self -fertilized or bred with similar indi- 

 viduals containing the potentialities of both char- 

 acters, exhibit in the third generation exactly the 

 same nature that first-generation hybrids exhibit 

 in the second generation. The two potentialities 

 are commingled in their cells, and to all intents 

 and purposes they are exactly the same as first- 

 generation hybrids. When such self -fertilized hy- 

 brids are grown they give again, in the third gene- 

 ration, the regular Mendelian proportion of IBB to 

 2Bb to Ibb. Here the individuals containing only 

 potentialities of one character, that is, BB and bb, 

 would come true to these characters in succeeding 

 generations, while those individuals containing the 

 potentialities of both characters, Bb, would be ex- 

 pected to appear again in the fourth generation in 

 similar proportions. 



When we deal with more than one character- 

 pair the matter becomes complicated, but will 

 become clearer on careful study. If we combine 

 with the above characters the character of hairy 

 (H) and smooth (s) chaflf in the head, and remember 

 that the potentialities of these two characters in 

 the hybrids segregate exactly as in the case of 

 bald and bearded heads, we can foretell what will 

 occur. In this case, the hairy chaff is the strong 

 dominant character, as in the first - generation 

 hybrids of hairy with smooth sorts the chaflf is 

 always or very generally hairy. We would thus 

 represent these characters by H, for the hairy or 

 dominant character, and s for the smooth or reces- 

 sive character. In this character-pair we would 

 expect a splitting and segregation to have occurred 

 in the formation of the germ-cells of the fiist-gen- 



