Logistic Curve 337 



will be produced during the second year than during the first. As- 

 suming the same rates of reproduction and mortality, 18 young will 

 be produced, 6 will die, and the total population at the end of the 

 second year will be: 



.Vi + A - M = A'2 



6 + 18 - 6 = 18 

 or 



bNi = N2 



3 X 6 = 18 



If the same rate of increase continues unimpeded, the population will 

 have grown to 54 at the end of the third year, 162 at the end of the 

 fourth year, and so on, as shown in Table 18. The population under 

 these circumstances is exhibiting a geometric or logarithmic increase 

 represented by the equation: 



-IF = ^^^ 



and indicated graphically by curve (A) in Figure 9.11. 



TABLE 18 



Growth of Hypothetical Populations in Which Increase Is 

 (1) Unimpeded and (2) Self-Limited 



Logistic Curve. Since the full biotic potential of a species is not 

 realized under most natural conditions, the population does not in 

 fact increase as fast as it could if its growth were completely unim- 

 peded. However, if the restrictions on increase are density-inde- 

 pendent, and if the natality rate remains above the mortality rate, 

 the population will continue to grow and will increase at an accelerat- 

 ing rate. Nevertheless, the increase in the population will eventually 

 produce conditions harmful to itself— density-dependent factors will 

 come into play. The rate of growth will then be progressively cur- 

 tailed until it reaches zero when the population reaches the largest 

 size possible for it within the area concerned. If the harmful effect 



