How does exponential growth differ from logistic growth? R‐selected species have exponential growth rates, whereas K‐selected species always experience logistic growth. Exponential growth occurs when the population is at its biotic potential, whereas logistic growth is limited by the carrying capacity of the environment. Exponential growth is expressed as doubling time, whereas logistic growth is expressed as a percentage change. Exponential growth occurs when a population is very large, whereas logistic growth occurs when a population is at its minimum viable number. Exponential growth results in a J‐shaped curve, whereas logistic growth results in an S‐shaped curve.

Exponential growth occurs when the population is at its biotic potential, whereas logistic growth is limited by the carrying capacity of the environment.

Explanation:  

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.

This model is based on unlimited resource availability which means that there is no effect depending on density. There is no competition for resources. Natality and mortality rate do not depend on density. There is a constant growth rate per capita and it is proportional to the population size.

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