The local dynamics of a tri-trophic system

A lumped parameter model to describe the local dynamics of a tri-trophic ch ain (resource, herbivore, carnivore) is presented. The time evolution of th e system is determined by ordinary differential equations and written in te rms of normalized biomass of the three levels of the chain. In these equati ons we have introduced bio-ecological parameters (specific rates, conversio n factors) and two parameters p and q which measure the efficiency of the i nteraction processes (e.g. predation processes). A stability and persistenc e analysis of the solutions to these equations has been performed by assumi ng that: (i) the bio-ecological parameters are given tin other work we sugg est procedures to estimate them from individual data and demographic models ); (ii) the function determining the growth of the first level and the func tional responses of the second and third levels to the abundances of the fi rst and second levels, respectively, are characterized only by a shape of f unctional response and not by analytical expressions; and (iii) by consider ing the behavioural parameters p and q as bifurcation parameters. The regio ns in the (p, q) plane of existence and stability of the non-negative stead y states, and those of persistence and limit cycles of the system are deter mined. Results of numerical simulations are shown. (C) 2001 Elsevier Scienc e B.V. All rights reserved.