226 L. B. SLOBODKIN 



As the number of animals in the population declines, the size distribution 

 shifts until all of the animals are of reproductive size. Before this, ovaries 

 have begun to reappear. Young animals are now produced, resulting in an 

 increase of population size and a new peak in numbers. This may be followed 

 by a numerical decline. If only adult animals survive, the fluctuation will be 

 repeated. Fluctuation in number and size distribution may persist throughout 

 the history of the population. Occasionally, however, a population may 

 come to a continuous size distribution, with a preponderance of large 

 animals, but at least some smaller animals present at all times. Populations 

 of this sort are numerically constant unless environmental changes occur. 



The number of animals in a population that is not fluctuating is a linear 

 function of food supply. The total nitrogen content of Daphnia populations 

 is also a linear function of food supply. In the case o£ Daphnia, therefore, the 

 only significant population interactions between the animals are those that 

 alter the food supply for each animal. We can ignore metabolites, condition- 

 ing, cannibahsm, etc. 



If a Daphnia population is subjected to predation, population size is reduced, 

 and the amount of food ingested by the population may decrease. The 

 reproductive rates and growth rates of the survivors increase. These effects 

 depend on the kinds of animals that are removed as well as on the rate of 

 predation. 



We will defme F (fishing rate) as the fraction ((number of animals removed 

 per unit time) divided by (number of animals born per unit time)). This 

 differs from most definitions of predation rates but it is very simple for 

 analytic purposes. 



F refers to the rate of taking animals but does not specify the kind of 

 animals removed. For example, if F for a particular population has been set 

 at 25 per cent, the number of animals removed as yield would be one- 

 quarter of the number born. The yield animals might be either new-born 

 or adults or any other category. The kind of animal taken, as well as P, must 

 be specified, to unequivocally describe a predation procedure. 



If young animals are preferentially removed from Daphnia pulex popula- 

 tions the steady state size of the residual populations (P^) and the mean yield 

 per unit time are both linearly related to food supply. Fig. i shows the 

 relation between population size per unit food and F. Fig. 2 shows the 

 relation between yield of young animals per unit food and F. 



The relation between Pp and F can be adequately expressed by the 

 equation : 



