Cooperation, optimal density and low density thresholds: yet another modification of the logistic model

Abstract

A modification of the logistic model is proposed which incorporates the principles of optimal density and cooperation. Three components have been added defining effectivity, "saturation" and exponentiality of cooperation. By adequate choice of constants a wide array of population characteristics may be represented including threshholds of growth. The main application of the model concerns, low density problems such as colonization and extinction.

Single-species Models of the Allee Effect: Extinction Boundaries, Sex Ratios and Mate Encounters

“…Various mechanisms such as the need of a minimal group size necessary to successfully raise offspring, produce seeds, forage, and/or sustain predator attacks, or enhanced genetic inbreeding at low population sizes have been proposed as potential sources of the Allee effect (Jacobs, 1984;Lamont et al, 1993;Saether et al, 1996;Courchamp et al, 1999a;. However, the most cited potential source of the Allee effect is doubtlessly the difficulty in finding mates in small/sparse, sexually reproducing populations (Ehrlich & Roughgarden, 1987;Levitan et al, 1992;Groom, 1998;Kindvall et al, 1998;Wells et al, 1998, and others).…”

“…Models suitable for ''general'' use should, in our opinion, include at least the ES and US scenarios. Model (8) of Jacobs (1984) is probably the most flexible one but contains many parameters and is strongly nonlinear. Model (6) provides a more-or-less direct transition from the logistic growth to a model with the Allee effect.…”

“…Model (8) proposed by Jacobs (1984) combines, to some extent, features of heuristic approach with biological reasoning. It treats the Allee effect and negative density dependence separately and may combine them in a wide range of biologically plausible relationships; on the other hand, the model is quite complicated.…”

Effects of prey over–undercrowding in predator–prey systems with prey-dependent trophic functions

“…Also the models listed in [15] (except one, namely [27]), for a single species dynamics, simulate the Allee effect in the same way. In all these models the growth function G(x) can be expressed as…”

A host–parasitoid system with predation-driven component Allee effects in host population

“…Empirical evidence of Allee effects has been reported in many natural populations including plants [19], insects [32], marine invertebrates [47], birds and mammals [6]. Various mechanisms at low population sizes, such as the need of a minimal group size necessary to successfully raise offspring, produce seeds, forage, and/or sustain predator attacks, or enhanced genetic inbreeding have been proposed as potential sources of the Allee effect [5,24,33,44,46]. There is a clear distinction between the component Allee effect and the strong Allee effect [46].…”