384 



POPULATIONS 



The findings are partially depicted in 

 Figure 135 and can be summarized ia 

 Salt's words as follows: 



"As the density of parasites in a fixed popu- 

 lation of hosts is increased, more and more 

 superparasitism occurs, and the following 

 effects on the populations are observed: 



related to a theoretical model, is afforded 

 by the paper of DeBach and Smith (1941) 

 Though quite different in conception, botn 

 approaches are productive. 



DeBach and Smith used as a mathemati- 

 cal model of host-parasite interactions sev- 

 eral equations developed by Nicholson and 



100 



I 5 10 25 



DENSITY OF PARASITES PER iOO HOSTS 



50 



Fig. 135. The effect of increasing density of parasites upon the population of host (Sitotroga 

 cerealella) and parasite (Trichogramma evanescens) . I, parasite progeny; II, hosts escaped; 

 and III, hosts that gave neither larvae nor parasite progeny. (After Salt.) 



•'(1) 



'(2) 



•(3) 

 '(4) 



The number of hosts that escape 

 steadily decreases; but even at high 

 densities of parasites some hosts oc- 

 casionally escape. 



The number of hosts that die without 

 yielding either hosts or parasites 

 steadily increases. 



The number of parasite progeny 

 reaches a maximum and then decreases. 

 The number of progeny of the in- 

 dividual parasites steadily decreases. 



"(5) An increasing proportion of the emer- 

 gents are imperfectly developed. 



"(6) An increasing proportion of the emer- 

 gents are males ' ( p. 375 ) . 



Salt's study is purely experimental and 

 is concerned with an intensive analysis of 

 the reproduction and development of the 

 parasite population under known controlled 

 conditions. An investigation typifying a 

 different approach, one concerned with 

 host-parasite growth trends as these are 



Bailey (1935) that are not overcomplex 

 and that can be numerically applied to ex- 

 perimental data. Nicholson and Bailey 

 postulated that if P„ and Hn stand for the 

 population density of parasites and hosts, 

 respectively, at the nth generation; that if 

 the parasite has a specific searching abil- 

 ity* of a; that if these parasites search 

 among host progeny whose initial popula- 

 tion density is /H„, where / is the host's 

 power of increase, then the final density 

 of the host population is 



H„+i = fHne-P° 

 * "a" can be solved by this equation 



Hn + l 



- loge 



fH„ 



P„ 



and / was arbitrarily, yet reasonably, assiimed 

 to have the constant value 2. 



