To study tri-trophic systems composed of plants, prey and predatory mites, we proposed a continuous model of partial differential equations. Using a discrete space, we introduce the finite difference equations and implement in space by using Runge-Kutta methods. By describing how the spatial patterns appear and evolve, we aim to figure out how cheating plants appear and survive in Nature.
Different from the honest plants which shout to attract predatory mites when they are under attack of herbivores, cheaters send chemical volatiles to call predators even when they are not in danger. All mathematical models in literature predict the extinction of such cheating plants as soon as predators learn to avoid them, what does not happen in Nature. |
Our preliminary results show that space is responsible for the persistence of cheaters. This finding not only agrees with experimental data but confirms the importance of spatial modelling in Biology.
This work is carried out in collaboration with Dr Arne Janssen and Dr Maarten Boerlijst (University of Amsterdam), Dr Katerina Stankova (Maastricht University) and Dr Minus van Baalen (cole Normale Superieure, Paris). Two papers reporting the scientific optimal control conclusions and the spatial pattern are being written. Using the same numerical and analytical techniques, we will focus on different prey-predator systems. All new results will be tested by using experimental from researches carried out at Institute for Biodiversity and Ecosystem Dynamics of the University of Amsterdam. |