ABSTRACT
Clearly overcrowding will reduce the amount of food, as well as tax other resources such as oxygen levels, etc. In the single species model we can add a crowding term, which will result in more deaths with higher numbers of individuals. A simple first assumption might be that the death rate per individual µ, is a function of the population p. That is, we might take µ = µ(p). The simplest form of such a function is linear µ(p) = µp, so that the model becomes
dp
dt = βp− (µp)p. (9.2)
This equation was first introduced by the Dutch mathematical biologist Verhulst in 1837 and has subsequently become known as the logistic equation. The term µp in equation (9.2) simply translates to more deaths occurring when p is large; this is the competition or crowding term.
