Alternatives to Lotka-Volterra competition: Models of intermediate complexity

Abstract

A family of one-level differential-equation competition models in which two populations are limited by the energy flowing into the system generates the following results. For competitors on the same and only resource: 1) Purely exploitative competition leads to exclusion; which species wins depends on relative abilities to appropriate and extract energy from the resource, and the relative death and maintenance rates. 2) If conspecific interference (e.g., deaths or energy loss from fighting, cannibalism, or display) is sufficiently high relative to abilities to exploit the common resource, competition for the same resource can lead to coexistence. 3) If heterospecific interference is sufficiently high relative to abilities to exploit the common resource, competition for the same resource can lead to a priority effect, in which the outcome depends on initial population sizes. 4) Depending on whether situation (2) or (3) prevails, an increase in the amount of the common resource can convert an outcome in which one species always wins into one giving coexistence (2) or a priority effect (3). 5) If species are similar to one another in their abilities to appropriate and extract energy from the common resource and show reciprocity in intererence costs, competition can have multiple outcomes; either one species wins or the species coexist, depending on initial values. For competition on the same resource, but with each species monopolizing an exclusive resource as well: 1) Purely exploitative competition always leads to a unique point coexistence. 2) If interference is added to the system described in (1), two points of coexistence, separated by a saddle (an “unstable equilibrium”) are possible. This is favored by a) a small yield from the exclusive resources relative to the common one; and b) strong interspecific relative to intraspecific interference.