OCTOBEK 14, 1910] 



SCIENCE 



523 



ity in the number of ovules per locule and per 

 fruit are somewliat more complicated than 

 those for mean number, so the reader need not 

 be burdened with details. 



On the whole it seems that the variability 

 of the matured fruits is less than that of the 

 original series of ovaries before elimination 

 has taken place. In the 1906 series, where we 

 are working with ovaries in different stages 

 of development, there seems to be a steady de- 

 crease in the variability as we pass from the 

 youngest to the oldest. 



In the 1908 collections the eliminated or- 

 gans also seem to be less variable than the 

 original series. Probably this means that 

 those which develop to maturity came largely 

 from the upper end of the original range of 

 variation, while those which fail came chiefly 

 from the lower end. Obviously the variability 

 of a part of a population selected towards a 

 particular mean or type can not equal that of 

 the whole population. 



Changes in Mean Radial Asymmetry due to 

 Selective Elimination. — In a fruit of Staphy- 

 lea the numbers of ovules may be the same in 

 all three cells or differ from locule to locule. 

 Opening the compartments quite at random — 

 there being no external characteristic to indi- 

 cate any difference in them — one may find 

 such numbers of ovules as 



11— 11— 11 

 10—11—10 

 8—10— 9 

 9— 9—11 

 9— 7—10 

 and so on. 



Now we may consider a fruit in which the 

 ovules are distributed equally among the three 

 locules as radially symmetrical with resp.ect 

 to number of ovules per locule; such are 

 fruits of the type 8-8-8, 9-9-9, 11-11-11. 

 Ovaries with one locule differing from the 

 others by a single ovule, e. g., 9-8-9, are 

 somewhat radially asymmetrical, while those 

 with all three locules with different numbers 

 of ovules, for instance 9-8-7, are more so. 



As a measure of this radial asymmetry we 

 may take the mean square deviation of the 



number of ovules per locule from the mean 

 number in the whole fruit. For a fruit of the 

 type 



(a) (6) (c) 

 7 — 8 — 6 



the mean number per locule is 7 and we have : 



(A — a)- = 



(A — 6)^=1 Coefficient of asymmetry 



(A — c)-=i\ V2/3 = .81f)5 



For an ovary of the formula 7-8-7, A = 7.333,, 

 (A — a) = -H .3333, {A — V) = — .6666, 

 (A— c)= + .3333, and the coefficient of 

 asymmetry is 



A 



,3333= H- .6666= -f .3333= 

 -3 =-*'l^- 



The asymmetries of the fruits studied in 

 1908 ranged from .0000 to 2.1602. To de- 

 termine whether there is a selective elimina- 

 tion depending upon the radial asymmetry of 

 the fruit as just defined, we obtain the co- 

 efficient for each individual ovary and com- 

 pare the means of those in the eliminated 

 series with those which develop to maturity. 

 Diagram 2 constructed in the same manner 

 as that for the means shows the result for the 

 individual trees. The arrows show that in 

 seven cases the mean asymmetry is greater 

 after elimination has taken place, while in 

 twenty-one cases it is less. The two trans- 

 verse lines show that for the grand totals 

 there is a very decided reduction in asym- 

 metry as we pass from the eliminated to the 

 matured ovaries. Statistically the differences 

 are: 



Mean asymmetry of eliminated ovaries 



= .4515 ± .0051 



Mean asymmetry of matured ovaries 



= .3724 ± .0045 



Reduction in asymmetry by selective elimination 



= .0791 ± .0068 



Absolutely the difference is not large, but 

 relatively it appears that there has been a re- 

 duction of (.0791 X-100)/.4515 = 17.5 per 

 cent. The difference is more than ten times 

 its probable error and highly reliable. 



For the developing ovaries taken in 1906 



