Statistical mechanics and stability of a model eco-system

Abstract

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally direct competitive or co-operative interaction between species may occur through a random coupling matrix. We compute the order parameters of the system in a fixed point regime, and identify the onset of instability and compute the phase diagram. We focus on the effects of variability of resources, direct interaction between species, co-operation pressure and dilution on the stability and the diversity of the ecosystem. It is shown that resources can be exploited optimally only in absence of co-operation pressure or direct interaction between species.

23 pages, 13 figures; text of paper modified, discussion extended, references added

References in corpus (9)

• Statistical mechanics of complex networks
• Neutral Theory and Relative Species Abundance in Ecology
• Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model
• A mean field stochastic theory for species-rich assembled communities
• Continuum time limit and stationary states of the Minority Game
• Species Abundance Patterns in Complex Evolutionary Dynamics
• Random replicators with asymmetric couplings
• Dynamics of random replicators with Hebbian interactions
• Adapting to heterogeneous comfort levels

Cited by in corpus (7)

• Dynamically evolved community size and stability of random Lotka-Volterra ecosystems
• Phase transition to chaos in complex ecosystems with non-reciprocal species-resource interactions
• Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems
• Ecological communities from random generalised Lotka-Volterra dynamics with non-linear feedback
• Competitive exclusion and Hebbian couplings in random generalised Lotka-Volterra systems
• Path-integral solution of MacArthur's resource-competition model for large ecosystems with random species-resources couplings
• Demographic noise in complex ecological communities