(theta)
in which case the model is called the theta-logistic)
The original logistic equation assumes that each organism has an equal opportunity to acquire the disputed resources and that the relationship between the realized per-capita rate of change and population density is linear. There are situations, however, when the relationship is not expected to be linear as, for example, when social behavior determines the outcome of the interaction.
The problem of nonlinearity in the logistic R-function
can be accommodated by the addition of another parameter, the
coefficient of curvature, QP (sometimes
the coefficient is symbolized by (theta)
in which case the model is called the theta-logistic)
or
When QP = 1 the R-function is linear (b, figure below), when QP < 1 it is concave (the slope of the function decreases with density) (a, see figure), and when QP > 1 it is convex (the slope becomes steeper as density rises) (c, figure below). In situations where intentional intraspecific competition is occurring, as in territorial animals for example, we would expect QP to be greater than unity because competition should become more fierce near to carrying capacity.
©1997 Alan A. Berryman