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The current paper is concerned with the existence of spreading speeds andlinear determinacy for two species competition systems with nonlocal dispersalin time and space periodic habitats. The notion of spreading speed intervalsfor such a system is first introduced via the natural features of spreadingspeeds. The existence and lower bounds of spreading speed intervals are thenestablished. When the periodic dependence of the habitat is only on the timevariable, the existence of a single spreading speed is proved. It also showsthat, under certain conditions, the spreading speed interval in any directionis a singleton, and, moreover, the linear determinacy holds.

Spreading Speeds and Linear Determinacy for Two Species Competition Systems with Nonlocal Dispersal in Periodic Habitats