An important prediction of several spatio-temporal models of population dynamics is that habitat quality, defined here as the carrying capacity (K) of the environment, should have no influence on the velocity (v) of a population expansion. Using different modelling frameworks: reaction-diffusion equations to stochastic individual based models (IBM), we show that this prediction is far from being generic.

We review known results on theoretical diffusion models, regarding the dependence between K and v for logistic-like growth functions and we derive some additional results for other growth functions (weak or strong Allee effects). We also report some results for equations describing density-dependent dispersal. Then, using discrete space stochastic models, we investigate the dependence between K and v under different assumptions: no Allee effect, weak and strong Allee effects, and positive density-dependent dispersal.

We show that both models lead to an increasing relationship between v and K in the presence of an Allee effect or of positive density-dependent dispersal. This relationship still holds in the IBMs even when there is no Allee effect or positive density-dependant dispersal. This effect is especially strong when K is small (or close to the Allee threshold in the presence of a strong Allee effect), and tends to become less powerful or negligible when K becomes large. Experiments that we have conduced on minute size wasps Trichogramma chilonis in laboratory microcosms confirm the existence of this positive relationship.

Finally, we discuss how this dependence is related to the pulled/pushed nature of the expansion process.