Dipartimento di Agraria, Università di Napoli Federico II, Via Università 100, 80055 Portici (NA), firstname.lastname@example.org
mathematical modelling; complex systems; hybrid model; applied ecology
Differential equations (ODE and PDE) have long been used to model biological and environmental systems; however, classical differential models could became unsuitable to deal with complex natural systems, in which a large number of factors interact at different spatial and temporal scales (Gross, 1997).
Individual-Based Modelling (IBM) is a bottom-up approach that starts with the ’parts’ (i.e. individuals/agents) of a system (i.e. population) and then tries to understand how the system’s properties emerge from the interactions among these parts (Grimm, 1999).
The IBM approach is useful when individual-scale processes are important to explain the behaviour of a system accurately. The structure of IBMs feels closer to what can be observed (and measured) in reality, and, in many cases, IBMs are capable of simulating population-scale phenomena in a more understandable manner through a limited set of rules dictating the life of individuals. So building an IBM consists in isolating the major algorithmic rules that all individuals follow, and also in defining variable properties that will introduce the heterogeneity between individuals that is often necessary to reproduce the dynamics of the entire system.
Moreover differential equations and Individual-Based Modelling have usually been considered as exclusive alternatives instead of synergistic tools. Recently was pointed out the usefulness of merging the two paradigms inside of a hybrid modelling framework to handle some ecological systems and population dynamics (Vincenot, 2011).
In this talk, an overview will be given to Individual-Based and hybrid modelling approaches with some applications to environmental systems and population dynamics.
Gross L., 1997. Computational ecology: environmental problem solving for the new millennium, SIAM news 9
Grimm, V. 1999. Ten years of individual-based modelling in ecology: what have we learned and what could we learn in the future?. Ecological Modelling 115:129-148.
Vincenot C., Giannino F., Rietkerk M., Moriya K., Mazzoleni S., (2011) Theoretical considerations on the combined use of System Dynamics and individual-based modeling in ecology, Ecological Modelling, Volume 222, Issue 1, 10, pp. 210-218.