POPULATION FACTORS AND SELECTED POPULATION PROBLEMS 



385 



The number of hosts eliminated by the 

 parasites (P„) is equal to fH.^—H„^i. Since 

 it is assumed that for each host destroyed, 

 a mature parasite is produced in the next 

 generation, it follows that the number of 

 parasites present in the next generation is 

 given by the equation 



Pn + l = fHn — Hd+1 



DeBach and Smith attempted to set up 

 somewhat oversimplified but controlled ex- 

 periments designed to test these equations 

 numerically. They used as the host the 

 common housefly {Musca domestica), and 

 as the parasite, Mormoniella vitripennis, a 

 hymenopteran that invades the fly pupae. 

 The details of the experimental design, pro- 

 cedures, and findings do not concern us 

 here. Our concern hes only in reporting the 

 agreement (or lack of it) between theo- 

 retical and observed population curves. 



The experiments ran for seven genera- 

 tions and are summarized in Figure 136. 



the theoretical conclusions of Nicholson 

 and Bailey ('35)." It is of course unfor- 

 tunate that the study was not carried on 

 for thirteen, instead of seven, generations 

 so that the confluence of the two curves 

 dming the most crucial period could have 

 been observed as the oscillation built up 

 and then fell. 



The summary of DeBach and Smith is 

 of considerable general interest. They 

 state: 



"An almost universal characteristic of animal 

 populations is their tendency to fluctuate about 

 a mean density. These fluctuations or oscilla- 

 tions are in great part the result of regular 

 changes which take place in the physical en- 

 vironment, such as variations in weatlier. But 

 many students of populations, particularly those 

 interested in the use of mathematical analysis, 

 have postulated that osciUations are also in- 

 herent in the interaction of an animal popula- 

 tion and that of a specific enemy or disease and 

 would take place even in a physically constant 

 environment ... So far as the experiments [re- 



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GENERATIONS 

 ' ( Fig. 136. Interactions between populations of the parasite, Mormoniella vitripennis, and 

 •''the host, Musca domestica, in seven successive generations. Solid lines, observed; broken lines, 

 _ calculated. (After DeBach and Smith.) 



The coordinates are population density as 

 the ordinate and generations as the ab- 

 scissa. The figure graphs both host and 

 parasite population curves; the broken fines 

 are those derived by solution of the equa- 

 tions; while the solid lines represent the 

 experimental data. In forming a judgment 

 of the goodness of fit DeBach and Smith 

 say, "so far as the data of this experiment 

 go, they follow with remarkable fidehty 



ported in the paper] have gone, they lend 

 strong support to the idea that population 

 oscillations are inherent in the host-parasite or 

 predator-prey interaction. Further study is 

 necessary for complete verification of this 

 theory" (pp. 368-369). 



Attention should be directed to Varley's 

 (1947) contribution to this problem, un- 

 fortunately published too late for adequate 

 treatment here. Varley observed natural 



