Spatial structure of natural boxwood and the invasive box tree moth can promote coexistence

In the absence of top-down and bottom-up controls, herbivores eventually drive themselves to extinction by exhausting their host plants. Poorly mobile herbivores may experiment only local disappearance, because they can recolonize intact plant patches elsewhere, leaving time to previously over-exploited patches to regrow. However most herbivores such as winged insects are highly mobile, which may prevent the formation of spatial heterogeneity. We test if long-distance dispersal can preclude coexistence using the invasion of box tree moth (Cydalima perspectalis) in Europe as a model system. We build a lattice model and estimate the parameters with a combination of field measurements, experimental data and literature sources. Space corresponds either to a realistic boxwood landscape in the Alps, or to theoretical landscapes of various sizes. We find that both species persist under a large range of realistic parameter values, despite a severe reduction in boxwood biomass, with an alternation of outbreaks and near-to-extinction moth densities. Large landscapes are necessary for coexistence, allowing the formation of spatial structure. Slow plant regrowth combined with long-distance dispersal could drive moths to extinction, because of resources depletion at the global scale even without a complete synchronization of the local dynamics. The spatial dynamics leads to formation of small plant patches evenly distributed in the landscape, because of a combination of local plant dispersal and global indirect competition between plants through their positive effect on moth population size. Coexistence is favoured by such heterogeneous landscapes, because empty patches increase moth mortality during dispersal: the system thus creates its own stability conditions.