Some examples of doubling times for various values of r m . 13.9 0.06 11.6 Logistic Growth Verhulst 1838 recognized that there had to be a maximum amount of food and therefore, a limit to how much a population could grow. The closer a population came to this limit, the more the growth rate would slow, until there was no growth at all. So the maximum growth had to be modified by a factor that would decrease the growth rate with increasing population density. Assumptions of the Logistic Equation Individuals are equal in their reproductive potential.
Reproduction is constant irrespective of climate.
Carrying capacity is constant. The relationship between density and the rate of increase is linear. Each individual has the same effect upon carrying capacity. Modifications of the Logistic To overcome some of the constraints of the assumptions of the logistic equation, we can build time lags into the model. Time lags are ways to make to growth rate of the population respond to some earlier environmental condition rather than to the current condition.