Goal functions for the development of natural systems

Le Chatelier's principle in replicator dynamics

The Le Chatelier principle states that physical equilibria are not only stable, but they also resist external perturbations via short-time negative-feedback mechanisms: a perturbation induces processes tending to diminish its results. The principle has deep roots, e.g., in thermodynamics it is closely related to the second law and the positivity of the entropy production. Here we study the applicability of the Le Chatelier principle to evolutionary game theory, i.e., to perturbations of a Nash equilibrium within the replicator dynamics. We show that the principle can be reformulated as a majorization relation. This defines a stability notion that generalizes the concept of evolutionary stability. We determine criteria for a Nash equilibrium to satisfy the Le Chatelier principle and relate them to mutualistic interactions (game-theoretical anticoordination) showing in which sense mutualistic replicators can be more stable than (say) competing ones. There are globally stable Nash equilibria, where the Le Chatelier principle is violated even locally: in contrast to the thermodynamic equilibrium a Nash equilibrium can amplify small perturbations, though both types of equilibria satisfy the detailed balance condition.

A thermodynamic perspective on food webs: quantifying entropy production within detrital-based ecosystems

Because ecosystems fit so nicely the framework of a "dissipative system", a better integration of thermodynamic and ecological perspectives could benefit the quantitative analysis of ecosystems. One obstacle is that traditional food web models are solely based upon the principles of mass and energy conservation, while the theory of non-equilibrium thermodynamics principally focuses on the concept of entropy. To properly cast classical food web models within a thermodynamic framework, one requires a proper quantification of the entropy production that accompanies resource processing of the food web. Here we present such a procedure, which emphasizes a rigorous definition of thermodynamic concepts (e.g. thermodynamic gradient, disequilibrium distance, entropy production, physical environment) and their correct translation into ecological terms. Our analysis provides a generic way to assess the thermodynamic operation of a food web: all information on resource processing is condensed into a single resource processing constant. By varying this constant, one can investigate the range of possible food web behavior within a given fixed physical environment. To illustrate the concepts and methods, we apply our analysis to a very simple example ecosystem: the detrital-based food web of marine sediments. We examine whether entropy production maximization has any ecological relevance in terms of food web functioning.

Gaia as a complex adaptive system

We define the Gaia system of life and its environment on Earth, review the status of the Gaia theory, introduce potentially relevant concepts from complexity theory, then try to apply them to Gaia. We consider whether Gaia is a complex adaptive system (CAS) in terms of its behaviour and suggest that the system is self-organizing but does not reside in a critical state. Gaia has supported abundant life for most of the last 3.8 Gyr. Large perturbations have occasionally suppressed life but the system has always recovered without losing the capacity for large-scale free energy capture and recycling of essential elements. To illustrate how complexity theory can help us understand the emergence of planetary-scale order, we present a simple cellular automata (CA) model of the imaginary planet Daisyworld. This exhibits emergent self-regulation as a consequence of feedback coupling between life and its environment. Local spatial interaction, which was absent from the original model, can destabilize the system by generating bifurcation regimes. Variation and natural selection tend to remove this instability. With mutation in the model system, it exhibits self-organizing adaptive behaviour in its response to forcing. We close by suggesting how artificial life ('Alife') techniques may enable more comprehensive feasibility tests of Gaia.