112 



by dividing the whole developmental period 

 by the number of days (or hours) taken for 

 its completion; they represent the reciprocal 

 of the fraction of the whole development 

 that takes place in a day (or an hour). 

 Practically, the medial temperatures are 

 those at which the increase in rate of devel- 

 opment is directly proportional to the rise in 

 temperature, i.e., to the region expressed 

 by a straight line in the temperature veloc- 

 ity curves shown in Figure 17. Develop- 

 mental units can be used to demonstrate 

 that the rate of development under variable 



ANALYSIS OF THE ENVIRONMENT 



environmental or in organismic units, tem- 

 peratirre summation, in the present sense, 

 finds its mathematical formulation in th& 

 equations of Sanderson and Peairs and of 

 Krogh, and their modifications. 



Supporting evidence for the validity of 

 the concept of temperature summation is to 

 be found in the work of many biologist? 

 who have studied a wide variety of organ- 

 isms, both under natural conditions and in 

 the laboratory; special attention has been 

 paid to the length of life histories of insects. 

 The straight-line portions of the preceding 



.14 



.12 



.10 



.08 



.06 



.04 



.02 



r — 7^/T" 



/ / Y 



_A —^ ;f 



10 



15 



20 



25 30 



TEMPERATURE c! 



35 



Fig. 18. Comparison of the rates of development of each stage of the Japanese beetle: P, 

 Pupa; £, egg; 1, 2, and 3 represent respective larval instars. ( Redrawn from Ludwig. ) 



field conditions approaches expectations 

 based on the theory of temperature summa- 

 tion and on laboratory experience with 

 controlled temperatures. When summed for 

 a given process, the total number of such 

 units for completion of the process in 

 question is a more refined expression than 

 that given by the thermal constant obtained 

 from the summation of day-degrees (Shel- 

 ford, 1929, p. 368). Whether measured in 



temperature-velocity curves all imply that 

 temperature summation is relatively accu- 

 rate within the indicated medial tempera- 

 tures. Similar data from one more set of 

 experiments are summarized in Figure 18, 

 for the developing Japanese beetle, Popillia 

 japonica. This is a good final test case for 

 several reasons. Data for eggs and pupae 

 fit the theory rather well. Those for larval 

 stages show irregularities produced, in part 



