Delay differential equation modelling of the slug deroceras reticulatum, an agricultural pest.

Schley, D. and Bees, M.A. (2003) Delay differential equation modelling of the slug deroceras reticulatum, an agricultural pest. Ecological Modelling, 162 (3), 177-198. (doi:10.1016/S0304-3800(02)00358-7).

Abstract

Slugs are devastating agricultural and horticultural pests. However, their population dynamics are not well understood and this hinders the construction of efficient control strategies. This is especially true with organic farming for which biological controls are preferred. Moreover, the dominant species, Deroceras reticulatum, does not follow a regular annual life cycle, as do the majority of the other slug species. Its dominance may be associated with this fact. In this paper, we investigate whether mechanisms associated with the slugs’ time-delayed population dynamics are responsible for the large variations in numbers, with particular emphasis on their sensitivity to environmental conditions. In order to do this, several versions of a non-autonomous delay differential equation model are developed in which we highlight some of the contentious issues in slug modelling. Analyses of the models are combined with numerical experiments using parameters based upon controlled laboratory experiments. In the absence of seasonal forcing, we find that the delay term may be neglected in the simplest models. However, the presence of a predator dramatically increases the impact of the delay term and may drive a delay induced instability. Notably, we find that in all cases the delay term is of considerable qualitative importance in models which incorporate seasonal fluctuations. We highlight the fact that the models are capable of producing a large range of solution behaviour and, furthermore, discuss the conditions for, and thus the likelihood of their relevance.

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