Self-organization in a simple consumer–resource system, the example of earthworms

Classical predator–prey or host–parasitoid models often lead to spatial self-organization due to local interactions and limited dispersal ability of the resource (prey or host) and consumers (predator or parasitoid). We hypothesized that self-organization may also arise in soil organisms when the resource is passive and has a constant renewal rate. Earthworm density is correlated with soil properties, but soil heterogeneity only explains a small proportion of spatial variations in earthworm densities. We hypothesized that this could be partially due to self-organization. These two hypotheses were tested with an original model parameterized for a savannah earthworm population. The model simulates an earthworm population divided in 1 m2 cells. It is based on the assumption that fine soil aggregates constitute the only limiting resource influencing mortality, fecundity and dispersal and that this resource is renewed according to a constant rate independent of earthworm dynamics. Simulations lead to aggregated spatial distributions when the sensitivity of mortality or fecundity to the availability of the limiting resource is high, and when earthworm mobility is low. Such parameters values are consistent with what is known about earthworm biology. Applicability to different ecological systems and resulting population dynamical properties are discussed.