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Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible…

A population of heterogenous agents compeeting through a minority rule is investigated. Agents which frequently loose are selected for evolution by changing their strategies. The stationary composition of the population resulting for this…

We introduce and solve analytically a model for the development of disparate social classes in a competitive population. Individuals advance their fitness by competing against those in lower classes, and in parallel, individuals decline due…

Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general…

Adaptive control in biological systems, such as intestinal immunity, remains poorly understood despite detailed knowledge of underlying regulatory networks. We propose an alternative framework based on stochastic martingale turnover, in…

The hierarchical topology is a common property of many complex systems. Here we introduce a simple but generic model of hierarchy growth from the bottom to the top. Therein, two dynamical processes are accounted for: agent's promotions to…

The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of…

In complex ecological communities, species may self-organize into clusters or clumps where highly similar species can coexist. The emergence of such species clusters can be captured by the interplay between neutral and niche theories. Based…

Competition for a limited resource is the hallmark of many complex systems, and often, that resource turns out to be the physical space itself. In this work, we study a novel model designed to elucidate the dynamics and emergence in complex…

We explore the evolution of cooperation in the framework of the evolutionary game theory using the prisoner's dilemma as metaphor of the problem. We present a minimal model taking into account the growing process of the systems and…

We explain how hierarchical organization of biological systems emerges naturally during evolution, through a transition in the units of individuality. We will show how these transitions are the result of competing selective forces operating…

Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two…

A dynamical model for the distribution of resources between competing agents is studied. While global competition leads to the accumulation of all the resources by a single agent, local competition allows for a wider resource distribution.…

We introduce a minimal model of multilevel selection on structured populations, considering the interplay between game theory and population dynamics. Through a bottleneck process, finite groups are formed with cooperators and defectors…

Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality…

We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…

The study of the evolution of cooperative behaviours --which provide benefits to others-- and altruism --which provides benefits to others at a cost to oneself-- has been on the core of the evolutionary game theoretical framework since its…

Time evolutions of number of cities, population of cities, world population, and size distribution of present languages are studied in terms of a new model, where population of each city increases by a random rate and decreases by a random…

Quantifying the spatial organization of human settlements is fundamental to understanding the complexity of urban systems. However, the quantitative patterns of the distribution of villages, towns, and cities that lie between random and…

We demonstrate diversification rather than optimisation for highly interacting organisms in a well mixed biological system by means of a simple model and reference to experiment, and find the cause to be the complex network of interactions…