GENERAL ZOOLOGY 



012345678 

 Units of time 



Fig. 19.6. Comparison of curves describing population growth. A, curve of geometrical 

 progression, a theoretical possibility; B, logistic curve. (From G. L. Clarke, Elements of 

 Ecology, copyright 1954 by John Wiley and Sons, Inc., reprinted by permission.) 



breeding season, if all the offspring survived and reproduced at this rate, the 

 progeny of a single female would number 564,087,257,509,154,652, and 

 would weigh 1,645,254,501,068 pounds. From his studies on pedigreed 

 cultures of Paramecium, Woodruff calculated that during a period of 5 years 

 the number of descendants of a single individual, after 3029 generations, 

 would be represented by 2 raised to the 3029th power. The volume of proto- 

 plasm in all these individuals would be not less than 10^'^'^'^ times that of 

 the earth. 



Needless to say, the growth of populations of organisms under natural 

 conditions is not described by a curve of geometric increase. Instead, it 

 follows a sigmoid curve, often referred to as a logistic curve. The contrast 

 between these two rates of increase, the ideal and the actual, is shown in 

 Figure 19.6. In the logistic curve the rate of increase does not accelerate 

 indefinitely; after a certain point, termed the inflection point, the rate of 

 increase steadily diminishes, and the population thereafter approaches a 

 maximum limit or asymptote. The events described by the logistic curve may 

 be interpreted as follows. In the early stages of population growth, new 

 individuals are added slowly, because the breeding stock is small. As the new 

 individuals reach maturity and begin to add their own progeny to the popula- 



610 



