CERTAIN DEMOGRAPHIC BACKGROUNDS FOR POPULATION STUDIES 301 



This figure shows clearly that the mutation 

 "vestigial" affects the form of the life curve 

 exhibited by the population just as it af- 

 fects the wing size of an individual fly. 

 Whereas the wild type flies approach more 

 closely the physiological or right-angled 

 curve, the mortality of vestigial flies results 

 in a curve form that is lower through early 

 middle life and then stretches out into a 

 long tail during old age. It should be re- 

 membered, of course, that the abscissa of 

 this graph is a relative and not an absolute 

 scale. Actually, the wild type Drosophila 

 have a longer life duration than do the 

 mutants. 



Categories of Survivorship Curves 



Pearl (1940) makes the interesting point 

 that the form taken by population mortality 

 varies with the species, as would be ex- 

 pected, but that, as might not be expected, 

 these "forms" fall into three general groups. 

 This can be seen in Figure 93, in which Ij. 

 is plotted against age expressed on a rela- 

 tive scale. There is considerable confluence 

 between individual curves within each of 

 the three categories. Pearl designates 

 Group A as the rectangular; Group B, the 

 intermediate; and Group C, the diagonal 

 type. 



The rectangular pattern, which inciden- 

 tally is the closest approach to the physio- 

 logical curve, describes a situation in which 

 all the individuals of a cohort are born at 

 the same time, live with a minimum of 

 mortality for a considerable period of their 

 life, and then die off rapidly. For the three 

 examples presented (the rotifer Proales, 

 starved wild Drosophila, starved vestigial 

 Drosophila), the upper limit of the life 

 span stands to the mean duration of life 

 rouehly as 140:100 in terms of relative age. 



The intermediate pattern is typified bv 

 the roach Blatta orientalis, the mouse, and 

 wild tvpe Drosophila melanogaster. Here 

 the dying off begins slowly at first, then 

 attains its m.aximum rate, and finally slows 

 down: the curve stretches out because of 

 the abilitv of a few individuals to outlive 

 considerably their companions. The upper 

 limit of the life span stands to the mean as 

 185:100. 



The diagonal pattern is illustrated by 

 the mortality of vestigial Drosophila, Hydra, 

 and the slug;, Deroceras a^reste — (Agrioli- 

 max aqrestis). In this form the death rates 

 are approximately constant until extreme 



old age is attained. There is also a large 

 ratio of total life span to mean life duration. 

 This, for the three species, is about 300: 

 100. 



There is, as Pearl recognizes, a fourth 

 logical possibility as regards the l^ curve. 

 This is another rectangular curve inverse in 

 form to the one discussed. It is sometimes 

 called the "positive skew" rectangular type 

 in contradistinction to the "negative skew." 

 For this curve there would exist an explo- 

 sive mortality in early life followed by a 

 lingering of the few survivors for a con- 

 siderable period. No actual illustration of 

 this curve can be provided at this time, 

 although it seems likely that certain species 

 must have this form of mortality, as, for 

 example. May fly imagoes. Probably the 

 closest known approach (actually not very 

 close) is derived from the life table for the 

 human population of India. There, a great 

 infant mortality eliminates a sizable com- 

 ponent during the first year of life. The 

 mean duration of life is also low.* 



It has seemed of some importance to de- 

 scribe these types of survivorship curves. In 

 the first place, the fact that organisms can 

 be differentiated into groups according to 

 the form of their mortality suggests an eco- 

 logical principle of some significance. 

 Secondly, as life tables accumulate for var- 

 ious species it will be technically useful to 

 know into which group the particular or- 

 ganism falls. 



The Logistic Curve 



One of the most active, and in some 

 ways polemic, areas of population biology 

 has centered for the past twenty years 

 around the development and application of 

 the logistic curv^e to the growth of popula- 

 tions (see section on History p. 61). In 

 this chapter it is our purpose to discuss 

 briefly certain of the basic assumptions 

 underlying this curve, assumptions which 

 the ecologist should imderstand and then 

 evaluate for himself. The next chapter on 

 Population Growth-Form contains a num- 

 ber of illustrations of the curve applied to 



• On the basis of old statistics ( 1901 to 

 1910) for India assembled by Glover (1921). 

 it can be shown that of an initial population of 

 100,000 males, about 45,000 die during the first 

 five years of life; 50,000 by the tenth year; 

 and 85,000 by the fifty-fifth year! Comparable 

 figures for, say, Swedish males are (approxi- 

 mately) 13,000; 15,000; and 38,000. 



