108 



ANALYSIS OF THE ENVIRONMENT 



1935; Krogh, 1914a) (see Fig. 16), so that 

 the expression becomes: 



V = tk + c 



If graphed, the equation yt = r gives 



a rectangular hyperbola, the reciprocal of 

 which is a straight hne that theoretically 

 intercepts the temperature axis at zero; the 

 value of c in the modified formula shows 

 the shift of the intercept. 



TEMPERATURE 



Fig. 16. A generalized time-temperature hy- 

 perbola and its straight-line reciprocal. (Re- 

 drawn from Belehradek. ) 



This statement of the case means that the 

 velocity of the process under consideration 

 is a linear function of temperature, a rela- 

 tionship that has been found to hold for 

 many physiological events that have ecolog- 

 ical significance. This is by no means a 

 perfect working tool. It is most useful when 

 few measurements are available at tempera- 

 tures some distance apart. This makes the 

 Sanderson-Peairs-Krogh formula serviceable 

 for field workers who need to make an 

 approximation of the length of various 

 developmental stages at different times of 

 the year. 



When the effects of temperatures closely 

 spaced along the whole range of effective 

 temperatures are examined, the resulting 

 velocity curve remains Unear only at inter- 

 mediate points. Near the ecological zero for 

 the reaction (s), the effect of a degree rise 

 in temperature is greater, and near the up- 

 per temperature limit it is less than at the 

 intermediate points. A more or less sigmoi- 

 dal curve results (see Fig. 17), the form 

 of which is not given by the equation. 



In summary, we are forced to the con- 

 clusion that, despite a great mass of work 

 by ecologists and physiologists, there is as 

 yet no generaUzed expression for the known 

 relations throughout the range of effective 

 temperatures that is soUdly based on 

 theory. A new approach may be necessary 

 in order to express mathematically the sub- 

 tility of the effect of temperature on the 

 rate of Hving processes. Even an approxi- 

 mate solution of the problem may depend 

 on accumulation of more complete knowl- 

 edge of temperature relations of enzyme 

 systems. The difficulties involved are in- 

 creased by the readiness with which organ- 

 isms acclimate to temperature, and accUma- 

 tization has ecological impUcations with 

 both ontogenetic and evolutionary values. 

 For example: There are five species of Rana 

 in the eastern United States and Canada. 

 The species whose range extends farthest 

 north, R. sylvatica, tolerates lower tempera- 

 tures, breeds earher in the season, and has 

 the most rapid rate of development at a 

 given temperature. Similar relations hold 

 with regard to the rate of development of 

 Ambystoma (Moore, 1939) and various 

 other aquatic animals, both fresh-water and 

 marine. It follows that the rate of metabo- 

 Usm in animals of the colder waters is not 

 necessarily retarded as would be inferred 

 from temperature formulae. 



The different chemo-biological tempera- 

 ture formulae have received attention from 

 ecologists and others out of proportion to 

 their proved usefulness; even so, they are 

 suggestive. The known importance of tem- 

 perature upon such processes as the rate of 

 egg laying, of development, and of death 

 of insects, among others, indicates tha* 

 velocities dependent on temperature affect 

 population ecology as well as the ecology 

 of individuals. The probable significance of 

 favorable temperatures in relation to out- 

 breaks of insect plagues and the useful- 

 ness, here as elsewhere in ecology, of an 

 approach to mathematical formulations are 

 reasons for continued preoccupation with 

 these problems. 



VARYING TEMPERATURES 



The most densely inhabited portions of 

 the earth's biosphere have daily or seasonal 

 fluctuations in temperature or both. Many 

 well-occupied habitats, on the other hand, 

 have nearly or quite constant temperatures 

 the year around. Even under arid condi- 



