336 Relations within the Species 



distinguished from the question of whether the injiuence of the factor 

 on the population is related to the size of the population. For ex- 

 ample, the winter temperature in most habitats is a density-independ- 

 ent factor since its value is not affected by the number of organisms 

 present, but the effect which the temperature has may or may not be 

 related to the size of a population of animals. In some habitats ex- 

 treme cold will kill the same percentage of a large population as of 

 a small one, with the result that the number of animals succumbing 

 is proportional to abundance. In other instances the habitat will 

 provide adequate shelter (from extreme temperature or other danger) 

 for a small number of animals but inadequate shelter for a large num- 

 ber. As a consequence a much greater fraction of the large popula- 

 tion would be harmed than of the small population. If in another 

 situation a factor killed off a constant number of animals in an area, 

 it would have a greater relative effect on a small population than on 

 a large one. 



Form of Population Growth 



When plants or animals reproduce, they add more individuals to 

 the population, and the enlarged breeding stock then has the capacity 

 to produce a still larger number of progeny. Thus the population 

 tends to grow at an ever-accelerating rate. Sooner or later, however, 

 harmful density-dependent influences begin to take effect. If we 

 assume for a moment that no other interfering factors are present, the 

 growth of the population will follow a mathematically prescribed 

 form. 



Let us take a simple numerical example. Suppose we assume that 

 under the most favorable conditions a certain pair of animals can pro- 

 duce 6 young during a year and that the resulting population suffers 

 a mortality of 2 during the year. We then have: 



A'o + A - M = iVi 

 2+6-2=6 



No 



in which N„ and N, represent the populations at the beginning and 

 at the end of the year, respectively, A is augmentation, M is mortality, 

 and b is the biotic potential or rate of potential increase. At the be- 

 ginning of the second year our sample population stands at 6, and, 

 since there are more individuals to breed, a larger number of progeny 



