Contents

• Contents
• Lab 1 - Introducing MATLAB
  • Goals
  • Introducing the Software
• Lab 2 - Dispersal
  • Goals
  • Probability and Dispersal in One Space Dimension
  • Probability and Dispersal in Two Space Dimensions
• Lab 3 - Implementing an Integro-Difference Model
  • Goals
  • Enhanced Nicholson-Bailey Model
  • Matlab Implementation of the Simplest IDE
  • An Integro-Difference Approach to Nicholson-Bailey
  • Spatially Structured Environments
• Lab 4 - Boundaries, Chemotaxis and Student Case Studies
  • Goals
  • Reflecting and Absorbing Boundary Conditions
  • A Model for Chemo-Taxis
• Bibliography

On-Line Appendix of MATLAB Scripts

• ballspore.m -- script simulating ballistic dispersal of a fungus in one dimension.
• turchtax.m -- script implementing an IDE emulation of the effects of differential motility on aggregation (described by Turchin et. al., 1998).
• malthus.m -- script implementing the simplest IDE: Malthusian growth with dispersal in one dimension.
• nbspace.m -- script implementing Enhanced Nicholson-Bailey model with dipsersla in two dimensions.
• rockies.m -- script generating a two-dimensional random field with perscribed correlation structure.
• bcs.m -- script using reflections in one dimension to implement boundary conditions.
• bc2d.m -- script using reflection technique in two dimensions to do mixed absorbing/reflecting boundaries (for a ripple dispersal).
• chemotax2.m -- script implementing chemotactic response following Powell et. al., 1998.

Distributed in Class Reader:

• Getting Started with MATLAB. (green)

• Kot, M., 1992. ``Discrete-time travelling waves: Ecological examples,'' Journal of Mathematical Biology 30: 413-436. (yellow)

• Holmes, E.E., M.A. Lewis, J.E. Banks and R.R. Veit, 1994. ``Partial differential equations in ecology: spatial interactions and population dynamics,'' Ecology 75: 17-29 (from the special issue Space, the Final Frontier for Theoretical Ecology). (pink)

• Neubert, M.G., M. Kot and M.A. Lewis, 1995. ``Dispersal and pattern formation in a discrete time predator-prey model,'' Theoretical Population Biology 48: 7-43. (yellow)

• Allen, J.C., C.C. Brewster and D.H. Slone, 2001. ``Spatially explicity ecological models: a spatial convolution approach,'' Chaos, Solitons and Fractals 12: 333-347. (blue)

• Powell, J.A. and N.E. Zimmermann, 2001. ``Multi-Scale Analysis of Seed Dispersal and the Resolution of Reid's Paradox,'' submitted to Ecology, August, 2000. (white)