MTEXTIFIC AGRICULTURE 



November. 1921 



decrease its eommerc-ial value. While 

 other qualities contribute in a measure, it is 

 the capacity- to yield that largely deter- 

 mines the worth of the common farm crops 

 whose value per unit is low. Consequently 

 this character receives primary considera- 

 tion in crop improvement work. Only 

 such degeneration as impairs this capacity 

 will be considered here but it must be 

 borne in mind that changes may take place 

 that lower commercial value that, perhaps, 

 are not reflected in yield. Our present 

 knowledge regarding mutations is too 

 meagre to settle this point, but there is 

 much evidence to show that a change in a 

 single genetic factor may have a manifold 

 effect upon the body tissues of the or- 

 ganism. Thus the mutation "white eye" 

 in Drosophila is accompanied by a mark- 

 ed decrease in both viability and fecundity. 

 That gross morphological characters may 

 be conditioned by a single factor difference 

 is well established and it has been observed 

 that a change in the germplasm may occa- 

 sion a somatic alteration so slight that it 

 cannot be readily detected. As to the 

 cause and frequenc}- of mutations practic- 

 ally nothing is known since the problem is 

 bound up with the very nature of proto- 

 plasm itself. But the gene has proved to 

 be a relatively stable entity and mutations 

 comparatively infrequent. In his pure 

 lines of beans Johannsen has reported but 

 two among thousands of plants. Plant 

 })reeders are inclined to regard progressive 

 mutations, at least, of too infrequent oc- 

 currence to be of assistance in their opera- 

 tions. * 



It seems quite probable that retrogres- 

 sive mutations such as cause a decrease in 

 chlorophyll production for instance, may 

 take place which impair the plant in its 

 normal metabolic processes. It is reason- 

 able to assume also that disease resistance 

 could be similarly affected. In fact, we 

 have no evidence which indicates that any 

 genetic factor concerned in the determina- 

 tion of a plant's ability to yield, and from 

 the natui-c of the case there nnist be many, 

 is inimuiio from a degressive change. 



■• Environmental influences will, of course, re- 

 sult in fluctuation.'! in yield but the general 

 * Haye.s. H. K. and Garber. R. .T. 1919. Breed- values assigned may be taken as representing 

 ing Small Grains in Minne.sota. Bui. 1S2 Part the average yield determined by repeated trials 

 T. I^niv. of Minn. Apr. Expt. Station. over .m poriod of years. 



Proceeding on the assumption, then, 

 that mutations within pure lines may occa- 

 sionally occur resulting in the segregation 

 of sub-races of an inferior character, what 

 is the effect on the yield of the population 

 in general in succeeding generations! 



The problem may be discussed in gen- 

 eral terms as follows : In a pure line A 

 yielding' at the rate of r bushels per acre, 

 a single individual appears among {n -f- 1) 

 plants, giving rise to a pure line B which 

 is capable of producing (r-s) bushels per 

 acre. In this generation, Avhich we may 

 conveniently call the F^, the ratio of the 

 yield of line A to tjiiat of line B is as nr: 

 (r-s). Assuming complete self-fertiliza- 

 tion and equal viability in both lines, a 

 random sample of the mixture on being 

 sown will give rise to a stand in the ratio 

 of nr plants of line A to (r-s) plants of 

 line B yielding at the rate of r and (r-s) 

 bus. per acre respectively. Thus the ratio 

 of the yield of line A to line B in the F, 

 generation wall be as w-: (r-s)-. It is ob- 

 vious that we have here geometrical series 

 and that in any filial generation p the ratio 

 of yield of A:B is as nr^:{r-s)^. Prom 

 this it ma,y be deduced that for each bushel 

 of seed produced by the plants in B in the 

 pth generation there are n{r/r-s)^ bus. pro- 

 duced b}^ A. We may write the ratio A :B 

 then as nir/r-s)^ :V'. Now since p is a vari- 

 able increasing in magnitude by 1 at each 

 consecutive generation the antecedent in 

 each succeeding ratio will be increased 

 by (r/r-s) while the corresponding conse- 

 quent will always be equal to unity. The 

 terms on all cases being positive the rapid 

 diminution of the proportion of indivi- 

 duals compri.sing line B results. 



To illustrate. If within a pure line X 

 capable of yielding at the rate of 50 bus. 

 per acre a single individual arises in a po- 

 pulation of 101 plants as the result of a 

 degressive mutation, giving rise to a pure 

 line Y with a yielding capacity of 40 bus. 

 per acre the proportions of the crop har- 

 vested resulting from lines X and Y res- 



