In order to deal with the inhomogeneous nature of the environment, formulation based on lattice models and metapopulation models are commonly used in mathematical ecology. These models are analyzed by a numerical method such as Individual based model and by a theoretical method such as pair approximation. On the other hand, in the field of chemistry it is well known that a theoretical framework based on Fractal reaction is efficient in dealing with the chemical reactions in inhomogeneous medium[1]. This theory is effective when the movements of the reactants exhibit a peculiar behavior termed anomalous diffusion. It has been found recently that the movements of some walking insects shows an anomalous diffusion[2]. Given these results, we propose a new theoretical framework in mathematical ecology; application of Fractal reaction theory to population dynamics in inhomogeneous environment. We would like to discuss the effectiveness of this theoretical framework through an application to a plant pest disease model.

1. Kopelman, Science vol.241 pp.1620-1626 (1988)

2. Vinatier et al., Animal Behaviour vol.80 pp.221-229 (2010)