EquiUbrunn and Fluctuation 341 



observed when a bare area is invaded, when a new species is intro- 

 duced, or when a check holding a species to a low number is sud- 

 denly removed. Aside from these special situations the changes ob- 

 served in population size involve the action of both density-dependent 

 and density-independent factors usually long after the original growth 

 of the population. In both laboratory cultures and in natural habi- 

 tats, after the initial attainment of maximal size, a population will 

 ( 1 ) maintain itself at about the same level for a long period, ( 2 ) 

 decline and eventually become extinct, or (3) fluctuate regularly or 

 irregularly. 



If the population approaches its asymptote in such a way that the 

 supply of food, and other necessities, and the removal of harmful by- 

 products keeps pace with growth, then the population will maintain 

 itself at or near this equilibrium level {A=: M) until outside condi- 

 tions are altered. Under these circumstances the reproductive rate 

 may be high or low, but, as long as it is exactly offset by mortality, 

 the population size will not change. Nevertheless the magnitude of 

 A and M may exert an important ecological effect on evolution. If 

 A is very large, as is true of many invertebrate animals, the accom- 

 panying high mortality will generally take place when the progeny 

 are young and usually before reproduction has occurred. On the 

 other hand, if A and M are small, a much larger proportion of the 

 young animals may live long enough to reproduce before they are 

 eliminated from the population. In the former circumstance, most 

 of the mutations appearing in the population will be lost, but in the 

 latter case a larger percentage will be retained long enough to affect 

 the next generation. We find that the possible effect of this difference 

 corresponds to the generally more rapid evolution of mammals, for 

 example, than that of invertebrates. 



In other populations the harmful conditions that were produced by 

 increasing numbers and that brought the growth of the population to 

 a stop may progressively intensify. Under these circumstances the 

 greater and greater scarcity of food, the accumulation of metabolites, 

 or other inimical change will cause a decline in the population either 

 immediately or after a period of time. If the changes in the environ- 

 ment brought about by overcrowding are irreversible, extinction of 

 the population will eventually follow. This result is commonly seen 

 in laboratory cultures of bacteria, Protozoa, and other organisms. In 

 nature a similar fate may overtake a population developing on a small 

 island as a result of the introduction of breeding stock by natural 

 processes of dispersal or by man. Rats, goats, rabbits, or other ani- 

 mals, escaped from explorers' ships or introduced by colonists, often 



