Reaction-diffusion equations are a trusted modeling framework for the dynamics of

biological populations in space and time, and their traveling wave solutions are interpreted as the

density of an invasive species that spreads at constant speed. Even though certain species can

significantly alter their abiotic environment for their benefit, and even though some of these so-called

“ecosystem engineers” are among the most destructive invasive species, most models neglect this

feedback. Here, we extended earlier work that studied traveling waves of ecosystem engineers with

a logistic growth function to study the existence of traveling waves in the presence of a strong Allee

effect. Our model consisted of suitable and unsuitable habitat, each a semi-infinite interval, separated

by a moving interface. The speed of this boundary depended on the engineering activity of the species.

On each of the intervals, we had a reaction–diffusion equation for the population density, and at the

interface, we had matching conditions for density and flux. We used phase-plane analysis to detect and

classify several qualitatively different types of traveling waves, most of which have previously not been

described. We gave conditions for their existence for different biological scenarios of how individuals

alter their abiotic environment. As an intermediate step, we studied the existence of traveling waves

in a so-called “moving habitat model”, which can be interpreted as a model for the effects of climate

change on the spatial dynamics of populations.