I40 ANIMAL AGGREGATIONS 



metabolic products are removed by the periodic changes of the flour. 

 The equilibrium is apparently based upon a competition between 

 adults and larvae, as is shown by the fact that in one 1 6-gram en- 

 vironment the number of adults was accidentally reduced on the 

 seventy-eighth day of the experiment and was never returned to its 

 place in the geometric series, while the number in its total popula- 

 tion — eggs, larvae, pupae, and adults — did so return. 



Following current tendencies. Chapman interprets his findings in 

 terms of a mathematical formula, C = Bp{R), when C is the concen- 

 tration of insects, R is the environmental resistance, and Bp is the 

 biotic potential, which he defines as the mean maximum rate of re- 

 production in a given period under given conditions. Substituting 

 and solving, we find : 



^^ (43-97X8.4). 25 ^^ ^ 

 43-97 



The concentration of insects per gram of flour is 43.97. The aver- 

 age number of eggs laid per day in these experiments is 8.4, and one- 

 fourth of the population are egg-producing females. The formula so 

 given represents the state of equilibrium only. 



The work we have been discussing summarizes the effect of the 

 environmental factors associated with crowding upon the total popu- 

 lation. The work which deals most directly with the harmful effects 

 of crowding on length of life is that of Drzewina and Bohn. In con- 

 nection with their studies on the relation existing between mass of 

 toxic liquids and the contained mass of animals, Drzewina and Bohn 

 have found that many cases of protection are furnished by increasing 

 the numbers of animals present in the same solution. These wifl be 

 reported later. In some instances they record the opposite results 

 (i92i(^, 1922). 



When KCl was used as a toxic agent with cultures of Convoluta, a 

 smaU marine planarian, other things being equal, those in the solu- 

 tion containing the larger number died first. Similar relations hold 

 when the same number of individuals are placed in differing amounts 

 of the same strength of KCl solution: those in the smaller amount of 

 liquid die more rapidly. The fresh-water planarian Polycelis nigra 



