In this talk, we consider an Integrodifference model (continuous space, discrete time) for the growth and spread of a plant community in an infinite, one-dimensional heterogeneous environment. We model seed dispersal as a diffusion process, with a spatially dependent deposition rate, and model the population dynamics with spatially dependent growth rates. For the first part of the talk, we will consider the problem of community establishment from an initially localized population. In the second part of the talk, we will consider the case where the environment is favorable for community establishment, and assume that the expanding population evolves into a traveling wave front near the leading edge of the population. For these assumptions, we will derive a dispersion relation for the speed of the wave.