Revealing the effect of a hidden dimension on slug spatial distributions in arable fields

The movement and spatial distribution of the grey field slug (Deroceras reticulatum) in arable fields are investigated in ongoing interdisciplinary research motivated by the concept of targeted pesticide application in the population of slugs. The previous work suggested an explanation for the self-organized formation of a heterogeneous (patchy) spatial population distribution of slugs due to their density-dependent movement on the soil surface. This article reports new results of the study in which a vertical movement feature has been added to the baseline two-dimensional mathematical and computational model to see how it may contribute to the appearance and disappearance of slug patches in arable fields. A model of spatio-temporal dynamics of vertical movement is presented in the paper and correlation between spatial distributions of the slug population on and under the soil surface is investigated. It is explained how the probabilities of upward and downward movement in the new three-dimensional model impact the formation and stability of patchy spatial patterns overground and underground. It is suggested that the vertical movement of the slugs should be taken into account when evaluating the efficiency of pesticide application.