Comparison of spatially implicit and explicit approaches to model plant infestation by insect pests

Spatial heterogeneities have been explored in many different ways in population dynamic models. We investigate here the way in which space should be considered in the dynamics of an aphid–parasitoid system in a melon greenhouse, in order to plan a biological control program at a wide scale. By comparing a non-spatial model with a spatially explicit model (a lattice one), we show a strong difference between predictions and we thus confirm that it is essential to take space into account in such closed and structured environments when describing the spatial heterogeneities observed in the field. The way in which space should be considered in such system is tested by comparing the spatially explicit model with a new implicit approach, which describes the level of plant infestation by a continuous variable corresponding to the number of plants with a given density of pests at a given time. When the explicit model needs as many equations as plants in the greenhouse, our novel approach has only a partial differential equation. We infer from the comparisons between the two spatial models that the predicted host–parasitoid dynamics are similar under most conditions. Some differences occur when local dispersal (considered only in the explicit model) is high and it can have a strong impact on population dynamics but does not change the conclusions for crop protection. We conclude that the new spatially implicit model thus generate relevant predictions with a more synthetic formalism than the common plant-by-plant model and it will thus be more adapted to test biological control strategies at a higher scale than the greenhouse.