A Verhulst-Pearl logistic growth pattern is

In nature, no population of any species has unlimited resources to allow exponential growth. Individuals compete for limited resources. As a result, the 'fittest' person will eventually survive and reproduce. When a population grows in a habitat with limited resources, it goes through a lag phase, then acceleration and deceleration phases, and eventually an asymptote, which occurs when the population density meets the carrying capacity. 

A sigmoid curve is formed when N is plotted against time (t). This type of population growth is called a Verhulst-Pearl Logistic Growth and since most animal populations have finite growth resources that eventually run out, the logistic growth model is thought to be more realistic.