Source-sink dynamics explains the co-existence of the invasive pest Dryocosmus kuriphilus and its biological control agent Torymus sinensis across French Eastern Pyrenees.

Biological invasions have become a major cause of ecological and economic costs in many (agro-)ecosystems. Understanding the regulation of their local dynamics by resources limitation and natural enemies, i.e. bottom-up and top-down determinants, through inherently heterogenous environments stands as a critical challenge to provide efficient risk assessments and management measures. Here, we propose an unprecedented integrative modelling approach based on a spatial extension of the seminal Nicholson-Bailey model parameterized by a comprehensive field assessment of all the bottom-up and top-down determinants affecting the spread of a worldwide invasive pest, Dryocosmus kuriphilus, in 23 natural chestnut tree populations of the French Eastern Pyrenees. The analysis of the within-site dynamics allowed to quantify the spatial heterogeneity in the two types of regulatory forces across the study area, and to identify 16/23 sites where the control agent, Torymus sinensis, is expected to persist and control the invasive pest. The comparison of these predictions with the levels of D. kuriphilus hyperparasitism by T. sinensis, observed in all 23 forest sites, suggested hidden source-sink dynamics within the study area. The investigation of such dynamics by the coupling of any two local dynamics predicted in each of the 23 sites showed that i) low rates of D. kuriphilus and T. sinensis dispersal lead to a synchronization to the dynamic expected in the site with the highest chestnut tree frequency, while ii) higher rates typically allow for a stable equilibrium. Those predictions provide quantitative evidences for the persistence of T. sinensis in the 7 predicted sink sites sustained by its local 16 source populations. Dispersal then tends to homogenize the local efficiencies of the control agent while decreasing its global impact on the pest invasion. Overall, this pioneer spatial modelling of D. kuriphilus - T. sinensis interaction suggests that both introduced species are likely to persist in the European forest environments in a co-invasion scenario.