brates, and even lower vertebrates like fish, 

 produce more than a million fertilized eggs 

 annually. Higher vertebrates, especially birds 

 and mammals, do not produce so many eggs, 

 but these animals provide more care for the 

 developing young, so that a larger propor- 

 tion of the offspring can survive. Probably 

 the slowest multiplication rate is that of the 

 elephant. This animal begins to breed at the 

 age of 20 and continues until 60, producing 

 an average of six calves during the reproduc- 

 tive period. Even at this exceedingly slow 

 rate, ;'/ every elephant survived, the descend- 

 ants of a single pair would number more 

 than 18,000,000 in 750 years; and in three 

 or four additional centuries, the earth could 

 provide "standing room only, for elephants 

 only." 



These facts are summarized by realizing 

 that every kind of organism, whether its 

 multiplication rate is slow or fast, tends to 

 increase in geometrical progression: n, n 2 , n s , 

 . . . etc. where n is the average number of 

 offspring per individual parent per genera- 

 tion, and the exponential numbers designate 

 the sequence of the generations. Graphically 

 this relation is shown by curve A in Figure 



Nafural Selection; Origin of Species - 539 



28-1, which is often called the curve of com- 

 pound interest, or the growth curve. In this 

 natural type of multiplication, the rate of 

 increase grows greater and greater as the 

 population increases. Accordingly, if all the 

 offspring survived and reproduced, every 

 species, even those with the slowest natural 

 rates of reproduction, eventually would in- 

 crease until it covered the earth, and this 

 eventuality would be fulfilled within a rela- 

 tively short time in relation to terrestrial 

 history. 



Limits of Population Increases. Obviously, 

 plant and animal populations do not actually 

 increase in this manner, for they are limited 

 by the food supply and by a number of other 

 environmental conditions. This limitation is 

 illustrated by the lower curve in Figure 28-1, 

 which shows the actual multiplication of 

 yeast cells in a definitely limited amount of 

 nutrient. Initially the actual growth curve 

 follows the theoretical growth curve very 

 closely, but soon the rate of increase falls off, 

 and finally the number of cells reaches a 

 constant value beyond which there is no 

 further increase. Under comparable condi- 

 tions, a population of any species behaves 



500 



400 



300 



200 



100 



THEORETICAL RATE 



OF MULTIPLICATION 



WITH UNLIMITED 



SPACE AND FOOD 



J L 



ACTUAL RATE OF MULTIPLICATION 



IN A DEFINITELY LIMITED AMOUNT 



OF NUTRIENT SOLUTION 



DAYS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 



Fig. 28-1. Multiplication of yeast cells: abscissas, time in days; ordinates, num- 

 ber of cells (in millions). 



