We analyze traveling front solutions for a class of reaction-transport Lattice Models (LMs) in order to claim their interest on the description of biological invasions. As lattice models are spatially discrete models, we address here the problem of invasions trough patchy habitats, where every node in the lattice represents a different patch. Distributed generation times for the individuals are considered, so that different temporal patterns can be studied. Specifically, we explore some examples of seasonal and nonseasonal patterns which may be of ecological interest. The main advantage of the LMs described here is that a direct correspondence between these discrete models and a mesoscopic description of Continuous-Time Random Walks (CTRW) can be found. This point is of great importance, since many times one needs analytical expressions to support or validate numerical results, or vice versa. Finally, that correspondence allows us to provide a discussion about some general aspects of reaction-dispersal models. © 2008 Society for Mathematical Biology.
- Traveling fronts