A lumped parameter model for acarine predator-prey population interactions

We hereby describe a modelling strategy, based on the implementation of composite models for the numerical simulation of the predator-prey local dynamics. We define a lumped parameter model for the dynamics of the system, where the abundance of the populations are given in terms of their biomass. The model is characterised by bio-ecological parameters (maximum specific rates and conversion factors) and by two functions: the specific growth rate of the prey in absence of predator, and the specific rate of predation, called trophic function. We consider prey growth rates which take into account either undercrowding and overcrowding effects, or only overcrowding effects. We also consider trophic functions depending either on the prey abundance, or on the ratio of the abundance of prey and predator. The responses of the model to different prey growth rates and trophic functions are investigated. Procedures are given for estimating the lumped parameters by means of demographic models of a single species population with stage structure, and formulated in terms of individual life history data. The methodology is applied to a case study of biological control of an acarine population system. Numerical experiments have been performed to illustrate the behaviours of the model with different prey growth and trophic functions. Results of numerical simulations are compared to the dynamics obtained in field experiments. (C) 2003 Elsevier B.V. All rights reserved.