Wild species populations are known to exhibit a wide range of spatiotemporal dynamics. We are using mathematical modelling to investigate why biological populations show a variety of spatiotemporal dynamics, more commonly associated with chemical and physical systems, such as travelling waves, spirals and chaos. We aim to make our state of the art mathematical techniques understandable and available to biologists generally.
Two tools have been developed to accompany our recent publications, these are:
We have also written an online tutorial for calculating the absolute stability of travelling in the Lambda-Omega equations which can be found by clicking here.
- Maria Bruna, Jonathan Chapman, and Matthew J Smith, Model reduction for slow-fast stochastic systems with metastable behaviour, in Journal of Chemical Physics, American Institute of Physics, April 2014.
- Gian Marco Palamara, Gustav W. Delius, Matthew J. Smith, and Owen L. Petchey, Predation effects on mean time to extinction under demographic stochasticity, in Journal of Theoretical Biology, Elsevier, June 2013.
- Robin Freeman, Ben Dean, Holly Kirk, Kerry Leonard, Richard A Phillips, Chris M Perrins, and Tim Guilford, Predictive ethoinformatics reveals the complex migratory behaviour of a pelagic seabird, the Manx Shearwater, in Journal of the Royal Society Interface, Royal Society, March 2013.
- Raul Garcia-Valdes, Miguel A Zavala, Migueal B Araujo, and Drew W Purves, Chasing a moving target: projecting climate change-induced shifts in non-equilibrial tree species distributions, in Journal of Ecology, British Ecological Society, January 2013.
- Jonathan A. Sherratt and Matthew J. Smith, Transition to Spatiotemporal Chaos Via Stationary Branching Shocks and Holes, in Physica D: Nonlinear Phenomena, Elsevier, 2012.
- Jonathan A. Sherratt, Matthew J. Smith, and Jens D. M. Rademacher, Patterns of sources and sinks in the complex ginzburg-landau equation with zero linear dispersion, in SIAM Journal of Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2010.
- Matthew J. Smith, Jens D. M. Rademacher, and Jonathan A. Sherratt, Absolute stability of wavetrains can explain spatiotemporal dynamics in reaction-diffusion systems of lambda-omega type, in SIAM Journal of Applied Dynamical Systems, 8(3), 1136-1159, 27 August 2009.
- Sherratt JA, Smith MJ, and Rademacher JDM, Spatiotemporal Dynamics in Ecology: Insights from Physics, in Proc 16th Int. Cong. Math. Phys. , vol. 651, August 2009.
- Jonathan A. Sherratt, Matthew J. Smith, and Jens D.M. Rademacher, Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion, in Proceedings of that National Academy of Sciences of the United States of America, 106(27), pp. 10890-10895, 7 July 2009.
- Matthew Smith, Jonathan Sherratt, and Xavier Lambin, The effects of density dependent dispersal on the spatiotemporal dynamics of cyclic populations, in Journal of Theoretical Biology, Elsevier, 21 September 2008.