Coevolution of competing systems: local cooperation and global inhibition

摘要

Using a set of heterogeneous competing systems with intra-system cooperation and inter-system aggression, we show how the coevolution of the system parameters (degree of organization and conditions for aggression) depends on the rate of supply of resources ˙S . The model consists of a number of units grouped into systems that compete for the resource S; within each system several units can be aggregated into cooperative arrangements whose size is a measure of the degree of organization in the system. Aggression takes place when the systems release inhibitors that impair the performance of other systems. Using a mean field approximation we show that i) even in the case of identical systems there are stable inhomogeneous solutions; ii) a system steadily producing inhibitors needs large perturbations to leave this regime; and iii) aggression may give comparative advantages. A discrete model is used in order to examine how the particular configuration of the units within a system determines its performance in the presence of aggression. We find that full-scale, one sided aggression is only profitable for less-organized systems, and that systems with a mixture of degrees of organization exhibit robustness against aggression. By using a genetic algorithm we find that, in terms of the full-occupation resource supply rate ˙SF , the coevolution of the set of systems displays the following behavior: i) for ˙S < ˙SF /10 aggressions are irrelevant and most systems exhibit a high degree of organization; ii) For ˙SF /10 < ˙ S < ˙SF /3 aggressions are frequent, making systems with a low degree of organization competitive; iii) for ˙SF /3 < ˙S < ˙SF /2 the systems display global evolutive transitions between periods of calm (few aggressions and high degree of organization) and periods of belligerence (frequent aggressions and low degree of organization); iv) for ˙S > ˙SF /2 the periods of aggression becomes progressively rarer and shorter. Finally, when ˙S approaches ˙SF the selection pressure on the cooperativity and the aggression between systems disappears. This kind of model can be useful to analyse the interplay of the cooperation/competition processes that can be found in some social, economic, ecological and biochemical systems; as an illustration we refer to the competition between drug-selling gangs.