316 THE AMERICAN NATURALIST [Vol.LVI 



the several arrays, it still seems probable from mere in- 

 spection of the general surface that the regression is 

 non-linear. This idea is strengthened by examination 

 of the regression line itself, shown in Fig. 1. 



It is seen from this diagram that, neglecting the great 

 dip of the line at density 55 which is consequent upon a 

 very small array with large probable error, the general 

 sweep of the curve indicates an optimum density (great- 

 est mean duration of life) in the general region of 35 to 

 45 flies per bottle, with a decline on either side of that 

 point, but falling lower on the side of high densities 

 than on that of low. 



From this table we have the following constants: 



r = — .0511 ± .0068, 

 V = .2443 ± .0064. 



There can be no question that the regression is non- 

 linear. Blakeman's (43) criterion has the following 

 value : 



f=z .0571 ±.0031. 



It must therefore be concluded that the regression is 

 significantly skew. 



The correlation between duration of life and density 

 of population in the case of the Sepia stock is shown in 

 Table II. 



