METHODS l8l 



useful to make some comments upon it. The authors have found that 

 by using the total rainfall of the previous season as one independent 

 variable in a multiple regression equation, and the density of the 

 parental population as the other independent variable, a multiple 

 correlation coefficient as high as 0-89 was obtained. It is now possible 

 in this area to make a prediction of a locust outbreak with high 

 accuracy as soon as the July records are available, even though the 

 outbreak will not occur until the following year. The economic value 

 of tliis work needs no words of mine to emphasize, and I confine 

 myself to the principles that are of equal scientific importance, whether 

 they are applied to frogs, cuckoos or to locusts. 



On p. 193 I point out that the criticisms sometimes advanced 

 against the use of measurements of weather from distant weather 

 stations — that the weather there is not that at the point where the 

 animals live — is based on a misconception about the nature of the 

 statistical approach. This does not require absolute accuracy and we 

 can get along very well with less than perfect data, if we cannot have 

 just what we would like. Now, Gunn and Symmons did not even use 

 rain gauges — they used the height of a river to indicate approximately 

 the amount of rain in the river basin. The next point to note is that 

 the records they used extended over only ten years, which supports 

 my suggestion that valuable information can come from quite short 

 series of observations, if only the right methods of analysis are used. 

 It was a hypothesis directly obtained from the field, followed by 

 correct analytical methods that led to success. There were no vast 

 masses of undigested data, and no conjectural mathematical models. 



Guim and Symmons have, of course, had some good fortune in 

 finding that only two independent factors give them the accuracy they 

 need. As they themselves point oiit, other species may not prove so 

 simple. These might yield to the methods of this chapter or of 

 Chapter 8. 



A few historical comments may be of interest. So far as I know, the 

 first use of multiple regression analysis to predict the date of an event 

 in the life of an animal was in my paper of 1935- Davidson and 

 Andrewartha (1948) used a similar tecliniquc in their study of popu- 

 lation fluctuations in an insect. WilHams (195 1) proposed the use of 

 the analysis of variance in the study of phenological data, but did not 

 use it for this purpose. Moran (1953), studying the Canadian Lynx 

 cycle, stated that multiple regression analysis would give the answer, 



