Spatially-explicit matrix models: A mathematical analysis of stage-structured integrodifference equations.

• Author(s) / Creator(s)

  • Lewis, Mark A.
  • Lutscher, F.

• This paper is concerned with mathematical analysis of the ‘critical domain-size’ problem for structured populations. Space is introduced explicitly into matrix models for stage-structured populations. Movement of individuals is described by means of a dispersal kernel. The mathematical analysis investigates conditions for existence, stability and uniqueness of equilibrium solutions as well as some bifurcation behaviors. These mathematical results are linked to species persistence or extinction in connected habitats of different sizes or fragmented habitats; hence the framework is given for application of such models to ecology. Several approximations which reduce the complexity of integrodifference equations are given. A simple example is worked out to illustrate the analytical results and to compare the behavior of the integrodifference model to that of the approximations.

• Date created

  2004-01-01

• Subjects / Keywords

  • Bifurcation analysis
  • Habitat fragmentation
  • Integrodifference equations
  • Critical domain size
  • Stage structure

• Type of Item

  Article (Published)

• DOI

  https://doi.org/10.7939/R3Q82W

• License

  © 2004 Springer. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.