306 



POPULATIONS 



V. Extinction: the passing out of the 

 population 



VI. Special cases. Accentuated, sudden 

 changes in growth form that depart 

 radically from the patterns in I-V: 



A. Population "spurts" 



B. Population "crashes" 



The first five relations defined are shown 

 in Figure 96, in which growth form is 

 stylized for purposes of clarity. Observed 

 population growth, as we shall see, fre- 

 quently falls well beyond the limits of the 

 curves shown. In fact, the periods them- 

 selves must not be understood as actually 

 sharply defined.** As we shall soon show, 



the species— or it can be true at the level 

 of certain species population subgroups and 

 not for others. This is to be expected. 



Despite obvious objections that can be 

 raised to Figure 96 and the ideas it sum- 

 marizes, the fact that a few growth forms 

 describe the major trends that essentially 

 all populations follow during their total life 

 history has both a technical and an inter- 

 pretative value. 



APPLICATIONS 



THE PERIOD OF POSITIVE GROWTH 



The growth curve that represents this 

 period is usually sigmoid or S-shaped in 



TIME SCALE 

 Fig. 96. Stylized representation of the various phases of population growth form. 



the variability in growth of populations can 

 be considerable. Also, some populations 

 have their abscissal or time axis greatly ex- 

 aggerated. Thus, although it is the excep- 

 tion rather than the rule, it is not unknown 

 in nature for a group to reach an equilib- 

 rium that is rather closely maintained for 

 extended periods of time. This can be true 

 at the species level— i.e., for all members of 



' In embryogeny, for example, we speak 

 of the blastula and the gastrula as if they were 

 temporally discrete units. This is convenient 

 and from that point of view necessary, but 

 obviously not rigorous, since cleavage stages 

 merge inperceptibly into the blastula and the 

 blastula into the gastrula. 



form. This imphes merely that initial growth 

 is slow, intermediate growth more rapid, 

 and later growth slow again. The situation 

 is well described by the logistic curve, the 

 applications of which to population data are 

 many. In the last chapter the rationale of 

 the curve was briefly presented. Now we 

 wish to provide actual illustrations drawn 

 from the population literature. This shows 

 how widely the logistic has been applied, 

 permits a judgment to be formed about the 

 goodness of fit of the curve to actual data 

 and provides an adequate summary of a 

 segment of the growth form, the period of 

 positive growth. 



