144 ECOLOGY AND LIFE HISTORY OF THE COMMON FROG 



just about to arrive. Formally, the multiple correlation coefficient is 

 0-74. The square of this number is a measure of the proportion of the 

 total variance accounted for by the equation, so that 51 per cent of 

 the causes of variation of all kinds have been accounted for. This, 

 however, is an understatement. We know that many of the relations 

 are not linear, and act jointly as well. To construct an equation 

 that takes this into account is impracticable. If it had been possible, 

 there is no doubt that the fit of such an extremely comphcated function 

 would have been better. Now, in many biochemical experiments in a 

 laboratory, the amount of variation not accounted for reaches at 

 least 25 per cent. We really cannot expect that frog-spawn records 

 obtained in the field would be better. Taking all these points into 

 consideration, we must, I think, conclude that the factors controlling 

 the date of spawning have been identified and measured as far as can 

 be reasonably expected. This is not to say that the equation is the last 

 word on the subject. On the contrary, the latitude and longitude 

 factors almost certainly are merely "dustbins" into which have been 

 throv^oi any effects correlated with latitude and longitude that have 

 not otherwise been considered. For example, the longitude effect is, 

 I think, probably of geological origin, but I have no numerical values 

 for this, and cannot think of any way of getting any. I have already 

 said that the latitude effect probably includes length of day, which 

 cannot be used, and I have not considered even bright sunshine in 

 more than one month, Mi. Finally, if the algal hypothesis is true, the 

 whole equation could be replaced by one factor, an event in the hfe of 

 a plant or plants. 



In my view, the principal value of the equation is that it shows the 

 independence of the various factors. It is, for example, not now possible 

 to argue that the effect of rain is really due to the temperatures 

 associated with rain, for all the necessary allowances have been made. 

 Moreover, this has been done not by bringing in any information from 

 outside the data, but solely from within, as if we knew nothing except 

 these figures. 



The coefficients in the equation give no easy idea of the importance 

 of the various factors, or of the closeness of the correlation between 

 any of them, considered alone, and the spawn date. The usual way of 

 testing for such correlations is to compute partial correlation coefficients, 

 as was done in 1935, but, with data so voluminous as these, the opera- 

 tion is excessively laborious, and an alternative was used. Table 7 



