142 ECOLOGY AND LIFE HISTORY OF THE COMMON FROG 



existence of a light effect. It should be added that the impossibility 

 of using day length as a factor does not imply that it is not acting. 

 On the contrary, it is almost certainly adding its effects to those that 

 can be studied, and it is only the properties of the solar system that 

 have technically interfered with its direct investigation. 



Altitude 



In places that are Hable to have orographical rain, that is rain caused 

 by hills lying in the path of wet winds, it was found in the 1935 paper 

 that there was a tendency for spawning to be earhest at about 800 feet. 

 At altitudes lower and higher than this, dates were later. Paris (1944) 

 confirmed this by observations on a hill in Ireland, and found in a 

 series of ponds that there was an early point at 600 feet. I suggested 

 that this was due to a point of balance between the increase of rain with 

 altitude, and the decrease in temperature. Dr. J. Glasspoole pointed 

 out to me that these are the altitudes with minimum fog, and in view 

 of the hght effect, this suggestion should not be overlooked. Perhaps 

 both are acting. 



In other parts of the country, not only are these effects much smaller 

 or non-existent, but there are not many observers hving at such 

 altitudes. The result of this is that in the larger investigation of 1956-8 

 no significant correlations with altitude were found — the effects were 

 swamped by the numerous observations from areas where nothing of 

 the kind could be expected. 



Regression Methods 



These diagrams, although very illuminating, are theoretically liable 

 to a disadvantage, for each contains the influences of the other factors. 

 This effect is not so great as it would be if all the correlations were 

 large, as is explained in Chapter 10, but it was nevertheless felt desirable 

 to use another method to prove the independence of the various 

 factors. It would be possible to remove the effect of the other factors 

 from each diagram, but on this large scale, the process is excessively 

 laborious ; it would probably have taken years. 



The method adopted is standard statistical practice : multiple linear 

 regression analysis. The fmal result is that each factor appears free 

 from the effects of every other factor as a coefhcient in an equation. 



If the variables are denoted as follows, the equation can be set out 

 concisely. 



