New models for seed dispersal and competition between plant species ar
e formulated and analyzed. The models are integrodifference equations,
discrete in time and continuous in space, and have applications to an
nual and perennial species. The spread or invasion of a single plant s
pecies into a geographic region is investigated by studying the travel
ling wave solutions of these equations. Travelling wave solutions are
shown to exist in the single-species models and are compared numerical
ly. The asymptotic wave speed is calculated for various parameter valu
es. The single-species integrodifference equations are extended to a m
odel for two competing annual plants. Competition in the two-species m
odel is based on a difference equation model developed by Fakes and Ma
iler [26]. The two-species model with competition and dispersal yields
a system of integrodifference equations. The effects of competition o
n the travelling wave solutions of invading plant species is investiga
ted numerically.