This paper studies concentration (i.e. inequality) aspects of the functions of Zipf and of Lotka. Since both functions are power laws (i.e. they are – mathematically the same) it suffices to develop one concentration theory for power laws and apply it twice for the different interpretations of the laws of Zipf and Lotka. After a brief repetition of the functional relationships between Zipf’s la...

Based on the law of mass action (and its microscopic foundation) and mass conservation, we present here a method to derive consistent dynamic models for the time evolution of systems with an arbitrary number of species. Equations are derived through a mechanistic description, ensuring that all parameters have ecological meaning. After discussing the biological mechanisms associated to the logis...

Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model...

May’s celebrated theoretical work of the 70’s contradicted the established paradigm by demonstrating that complexity leads to instability in biological systems. Here May’s randommatrix modelling approach is generalized to realistic large-scale webs of species interactions, be they structured by networks of competition, mutualism or both. Simple relationships are found to govern these otherwise ...

We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but few for their stochastic counterparts. The food chain we analyze consists of one prey and [Formula: see text] predators. The jth predator eats the [Formula:...