Population growth regulated by intraspecific competition for energy or time: Some simple representations

An examination is made of some of the ways populations can grow in response to changes in their own density. Under two different assumptions on birth and death rates, models for single-species population growth that incorporate intraspecific competition by interference but not exploitation are of logistic form. Where an individual's net energy input from feeding is inversely proportional to population size, population growth follows a convex curve, whether interference is included or not. Data of Smith (1963) on Daphnia populations are fit well by this kind of curve. Combination of the two kinds of growth can produce S-shaped curves whose inflection is displaced from that value—half the carrying capacity—given by the logistic; an upward displacement is favored by a high ratio of metabolic and replacement costs to feeding input. Inflection points from real curves are much more often higher than expected from the logistic. Nonmonotonic growth curves can arise when there is instantaneous feedback between consumers and resource availability; certain of these equations are of logistic or convex form at equilibrium. The possible effect of r- and K-selection on the biological parameters, such as feeding efficiency, used to construct the monotonie equations is discussed, and the equations are extended to 2-species competition. Table III characterizes some simple single-species growth curves.