Previously, we talked about some modifications of the basic model for spatial spread, but kept within the framework of the diffusion equation approach. Here, we ask ourselves what happens if we change our basic model and make it discrete in time -- can we get different results? We look at the spatial spread question first, picking up from the Shigesada et al. example of last time. We then look at the implications of this approach for other questions. In particular, integro-difference equations have been used to model stage-structured populations, and are known as integral-projection models.
Persistence of Transients in Spatially Structured Ecological Models (in Reports) Alan Hastings, Kevin Higgins Science, New Series, Vol. 263, No. 5150. (Feb. 25, 1994), pp. 1133-1136.
VanKirk, RW; Lewis, MA. Integrodifference models
for persistence in fragmented habitats.
BULLETIN OF MATHEMATICAL BIOLOGY, JAN, 1997, V59(N1):107-137.
* Rees M, Childs DZ, Ellner SP (2014) Building integral projection models: a user's guide. Journal of Animal Ecology
Ellner SP, Rees M (2006) Integral projection models for species with complex demography. The American Naturalist 167:410-428
* means required reading