Abstract
Finding general patterns in the expansion of natural populations is a major challenge in ecology and invasion biology. Classical spatio-temporal models predict that the carrying capacity (K) of the environment should have no influence on the speed (v) of an expanding population. We tested the generality of this statement with reaction-diffusion equations, stochastic individual-based models, and microcosms experiments with Trichogramma chilonis wasps. We investigated the dependence between K and v under different assumptions: null model (Fisher-KPP-like assumptions), strong Allee effects, and positive density-dependent dispersal. These approaches led to similar and complementary results. Strong Allee effects, positive density-dependent dispersal and demographic stochasticity in small populations lead to a positive dependence between K and v. A positive correlation between carrying capacity and propagation speed might be more frequent than previously expected, and be the rule when individuals at the edge of a population range are not able to fully drive the expansion.
Highlights
Peer Community Journal is a member of the Centre Mersenne for Open Scientific Publishing http:// www.centre-mersenne.org/
We investigate this hypothesis by analyzing propagation dynamics in presence of three factors known to penalize colonization success in small populations: strong Allee effects, positive density-dependent dispersal and demographic stochasticity
In order to disentangle the effect of the carrying capacity from the effect of the per capita growth rate, we propose a new form for the growth function f : (4)
Summary
Peer Community Journal is a member of the Centre Mersenne for Open Scientific Publishing http:// www.centre-mersenne.org/. A direct consequence is that the speed of range expansion does not depend on the carrying capacity K It is fully determined by the intrinsic growth rate and the diffusion coefficient leading to simple formulas. Several empirical observations were not consistent with such predictions, in particular in presence of demographic properties like the Allee effect (Liebhold et al, 1992; Neubert and Caswell, 2000; Okubo et al, 1989) In such cases, it appeared that population propagation was not entirely driven by individuals at the edge of the range. We could expect a positive relationship between carrying capacity and propagation speed We investigate this hypothesis by analyzing propagation dynamics in presence of three factors known to penalize colonization success in small populations: strong Allee effects, positive density-dependent dispersal and demographic stochasticity. The experimental study is made on a parasitoid wasp in laboratory microcosms, for which we establish that positive density-dependent dispersal occurs
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