228 



SCIENCE 



[N. S. Vol. XXVIII. No. 712 



hundredth part of a per cent, in this ratio 

 — i. e., if on the average one more in- 

 dividual ia ten thousand should come to 

 maturity— this would result in nearly- 

 tripling the numbers of individuals veithin 

 a hundred generations, and one tenth of 

 one per cent, augmentation— i. e., if one 

 more in a thousand should survive— would 

 be an increase in numbers amounting in 

 the same period to nearly fourteen thou- 

 sand fold. 



DISTURBING, CONTRIBUTING AND EFFECTIVE 

 FACTORS 



The various causes of death may be 

 classed into two groups; first, those that 

 destroy all insects in a certain condition or 

 position, irrespective of the numbers pres- 

 ent (for instance, frost, which might kill 

 the same proportion whether there was but 

 one to the acre or a hundred thousand) ; 

 and second, those that are more and more 

 efScient as the numbers increase. This is 

 true in general of predaeeous and parasitic 

 insects and of disease^. Causes of death of 

 the first class will aid in maintaining the 

 balance in an insect to the extent they are 

 uniform in their action, the regularly re- 

 curring winter, for instance; but are 

 usually erratic and disturbing rather than 

 balancing. Those of the second category, 

 however, all tend towards balance and 

 their efficiency is attested by the approxi- 

 mate balance maintained in nature. 

 Probably in all eases numerous parasites 

 and predators and other factors of this 

 same class contribute to form the control- 

 ling environment of an injurious species, 

 and each factor has a difi:erent potentiality. 

 Those of the second category can be further 

 subdivided into two classes, the contribu- 

 tory and the effective. In the former class, 

 the efficiency increases with the increase of 

 the host, but not in a sufficient ratio to 

 ever overtake it. Thus with the host at 

 one hundred per acre it may destroy one 



third, at two hundred four ninths, at four 

 hundred thirteen twenty-sevenths, etc., 

 never reaching fifty per cent. Any series 

 that does not ultimately pass the percent- 

 age of normal death rate is incapable of 

 itself diminishing the numbers of its host. 

 Its only effect is in slowing down the rate 

 of increase until some effective factor be- 

 comes operative or until a disturbing factor 

 like frost produces a general destruction. 



The effective class of factors is that in 

 which the ratio finally reaches one hundred 

 per cent. Thus with the host at one hun- 

 dred per acre it may destroy say one 

 half, at two hundred three quarters, at 

 four hundred, seven eighths, etc.; finally 

 reaching a fraction so large that only 

 those survive that are necessary to main- 

 tain the species. 



Every factor of this class has its par- 

 ticular point of balance. One may over- 

 take the host at two hundred per acre and 

 another only at two million per acre, but 

 both be finally efficient. To a member of 

 this class of checking factors, Mr. Elwood 

 Cooper, the former Horticultural Commis- 

 sioner of California, would apply the term 

 "the true parasite," and those alone he 

 would consider worthy of importation. 



To determine at any time the status of 

 an insect we should have to know the per- 

 centage of efficiency of each factor under 

 the existing numerical prominence of the 

 host and in order to prognosticate the 

 future we should need to know the ratio of 

 increased or decreased efficiency of each 

 under the changed numbers of the host. 



None of these factors can ever be deter- 

 mined with any great degree of accuracy 

 because they are each involved in as com- 

 plicated a system of interrelations and in 

 many cases the efficiency of a check against 

 any one insect is profoundly influenced by 

 the ups and downs of numerous other in- 

 sects that serve as alternate hosts. 



The complication of the subject indeed is 



