return to 232 page

Integro-difference equations.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.

##
References

* means required reading

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