Anomalous kinetics of a three-species food chain with spatial heterogeneity

In classic kinetics, reactants are based on homogeneous distributions and the expected reaction order is given through differential rate equation. However, spatial heterogeneity is an important consideration in the dynamics of interacting species. Therefore, it is necessary to investigate the multi-species kinetics on heterogeneous space via the traditional theory of chemical kinetics. In this paper, by means of cellular automata simulations, we explored anomalous kinetics of a three-species food chain on four regimes of spatial heterogeneity. The results show that as spatial heterogeneity increases, reaction order becomes increasingly anomalous. Because of local dispersal, reaction order estimates are less than the expected value of 1.0 on a homogeneous lattice. This result verifies previous theories. We also obtain some different results. On the percolation maps, reaction order estimates for consumers are lower than for basal species and predators. While on gradient percolation maps and blocks surfaces, reaction order estimates for consumers and predator more than for basal species when p-value greater than 0.7. Moderate patch connectivity on roads surfaces (i.e. 0.56 <; p <; 0.89) made the results like those caused by patchy aggregation. From the view of ecology, spatial heterogeneity has an important influence on the sensitivity of fecundity to the population density (i.e. reaction order). Large spatial heterogeneity will decrease the sensitivity, which means that it will increase the extinction risk of species.