Equilibrium and Fluctuation 343 



sponsible to a greater or lesser degree for the fluctuation in addition 

 to any disturbing influences that may come from the outside. The 

 causes of certain fluctuations can be traced to the reciprocating ef- 

 fects of natality and mortality within the population itself. 



A neat illustration of the mechanisms involved in self-induced fluc- 

 tuations of this sort is found in experiments with laboratory cultures 

 of Daphnia magna (Pratt, 1943). Single females were placed in 

 bottles containing 40 ml of water, and as they and their progeny re- 

 produced parthenogenetically the population in each bottle grew 

 in accordance with the logistic function. The culture medium was 

 renewed each day, insuring ample food supply and removal of me- 

 tabolites, and other external conditions were kept uniform. Follow- 

 ing the initial attainment of maximum size, the population sank to a 

 low ebb and then continued to fluctuate in extreme fashion in spite of 

 constant environmental conditions (Fig. 9.14). The explanation is 



100 



i 80 



60 



e 40 



20 



10 



20 



30 



40 



70 



80 



90 



100 110 



50 60 

 Time in days 

 Fig. 9.14. Changes in the abundance (solid line) of Daphnia magna in a labora- 

 tory culture. The variations in number of births (-•—•) and of deaths ( ) 



that underlie the fluctuations of the population are indicated. (Pratt, 1943.) 



seen in the changes in the birth and death curves indicated in the 

 diagram. Although the number of births declined after the tenth 

 day, young Daphnia continued to be produced for 18 days with the 

 result that more young were added to the population than could sur- 

 vive when they reached adult condition. As overcrowding continued, 

 the death rate rose rapidly and the birth rate dropped to zero. Even 

 after the size of the population was considerably reduced, no repro- 

 duction took place at first and in fact no new young animals appeared 

 until the fortieth day. Animals born in adversity thus did not pro- 

 duce young immediately upon reaching maturity, and the reduction 

 in their reproductive capacity persisted for a long period after fav- 

 orable conditions had been restored. As a consequence the popula- 



