Answer and Explanation:
The exposed example refers to a population that exhibits a logistic growth model. Population growth depends on density, the natality and mortality rate depends on the population size, which means that there is no independence between population growth and population density.
When a population grows in a limited space, density rises gradually and eventually affects the multiplication rate. The population's per capita growth rate decreases as population size increases. The population reaches a maximum point delimited by available resources, such as food or space. This point is known as the carrying capacity, K.
K is a constant that coincides with the size of the population at the equilibrium point when the natality rate and the mortality rate get qual to each other.
If the population size, N, is inferior to K (N<K) the population can still grow. When N approximates to K, the population´s growth speed decreases. When N=K, the population reaches equilibrium, and when N is superior to K (N>K) the population must decrease in size because there are not enough resources to maintain that size.
The sigmoid curve represents the logistic growth model. At the beginning population grow slowly. In the exposed example this occurred when the small group of 10 foxes moved to the new environment, starting a new population. In the second stage, the population size increases rapidly. Probably this happened when foxes reached a number of 40 individuals. And finally, slow and gradually, the population reaches the equilibrium point, K, which depends on resource availability. This point belongs to the stage where food starts to become harder to find, and much of the living space is occupied.
As the foxes population in the exposed example is still growing but in a decreased rate, we could assume that this population is reaching its carrying capacity, but it is not there yet. This population is reaching the top of the sigmoid curve. N is approximating to K, and the population´s growth speed decreases.