Influence of spatial patterns on ecological applications of extremal principles

A quite wide number of goal functions, or extremal principles, coming from thermodynamic considerations have been found to direct some ecosystem organisations. These organisations often concern a specific component of the ecosystem: it could be the genetic part for the exergy principle or the atmospheric part for the maximum entropy production. Hence, we can reasonably wonder when investigating an extremal principle: how to estimate it? And in particular: on which part of the system to estimate it? This is an important question, because each component potentially has an influence on the other component entropies and forgetting this influence could lead to inappropriate extremal principle uses. The objective of this study is to focus on the spatial patterns of an ecosystem and to show their impacts on two common extremal principle estimations, namely the maximum exergy and entropy productions. For this purpose, I developed two similar Daisyworlds differing only by their spatial description. The dynamics of daisies and of the planet parameters differs when random (non-spatial) or local (spatial) interactions are assumed. Results indicate that neglecting these spatial patterns in the ecosystem organisation lead to drastic differences on the maximum exergy/entropy values.