Persistence and Spreading Speeds of Integro-Difference Equations with an Expanding or Contracting Habitat.

We study an integro-difference equation model that describes the spatial dynamics of a species in an expanding or contracting habitat. We give conditions under which the species disperses to a region of poor quality where the species eventually becomes extinct. We show that when the species persists in the habitat, the rightward and leftward spreading speeds are determined by c, the speed at which the habitat quality increases or decreases in time, as well as [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], which are formulated in terms of the dispersal kernel and species growth rates in both directions.

Bifurcations in a discrete time model composed of Beverton-Holt function and Ricker function.

We provide rigorous analysis for a discrete-time model composed of the Ricker function and Beverton-Holt function. This model was proposed by Lewis and Li [Bull. Math.