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High-diversity assemblages are very common in nature, and yet the factors allowing for the maintenance of biodiversity remain obscure. The competitive exclusion principle and May's complexity-diversity puzzle both suggest that a community…

The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…

Many patterns have been uncovered in complex systems through the application of concepts and methodologies of complex networks. Unfortunately, the validity and accuracy of the unveiled patterns are strongly dependent on the amount of…

Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…

The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…

The properties of competition models where all individuals are identical are relatively well-understood; however, juveniles and adults can experience or generate competition differently. We study here less well-known structured competition…

The myriad microscopic interactions among the individual organisms that constitute an ecological system collectively give rise, at the macroscopic scale, to evolutionary trends. The ability to detect the directionality of such trends is…

Cooperation and competition coexist and coevolve in natural and social systems. Cooperation generates resources, which in turn, drive non-cooperative competition to secure individual shares. How this complex interplay between cooperation…

The pursuit of highest payoffs in evolutionary social dilemmas is risky and sometimes inferior to conformity. Choosing the most common strategy within the interaction range is safer because it ensures that the payoff of an individual will…

Given the importance of clusters to the fields of cosmology and galaxy evolution, it is critical to understand how the cluster detection process affects (biases) ones scientific conclusions derived from a given cluster sample. I review the…

Network science plays an increasingly important role to model complex data in many scientific disciplines. One notable feature of network organization is community structure, which refers to clusters of tightly interconnected nodes. A…

This paper follows the recent history of automated beauty competitions to discuss how machine learning techniques, in particular neural networks, alter the way attractiveness is handled and how this impacts the cultural landscape. We…

Many organisms live in populations structured by space and by class, exhibit plastic responses to their social partners, and are subject to non-additive ecological and fitness effects. Social evolution theory has long recognized that all of…

Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the…

In the last years, a remarkable theoretical effort has been made in order to understand stability and complexity in ecological communities. The non-random structures of real ecological interaction networks has been recognized as one key…

Ecologists have long suspected that species are more likely to interact if their traits match in a particular way. For example, a pollination interaction may be more likely if the proportions of a bee's tongue fit a plant's flower shape.…

Environmental variation can play an important role in ecological competition by influencing the relative advantage between competing species. Here, we consider such effects by extending a classical, competitive Moran model to incorporate an…

I prove that competitive market outcomes require computational intractability. If P = NP, firms can efficiently solve the collusion detection problem, identifying deviations from cooperative agreements in complex, noisy markets and thereby…

A social network is often divided into many factions. People are friends within each faction, while they are enemies of the other factions, and even my enemy's enemy is not necessarily my friend. This configuration can be described in terms…

Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…