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This publication reviews the framework of abstract competition, which is aimed at studying complex systems with competition in their generic form. Although the concept of abstract competition has been derived from a specific field -…
Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where…
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…
The dynamics leading to extinction or coexistence of competing species is of great interest in ecology and related fields. Recently a model of intra- and interspecific competition between two species was proposed by Gabel et al. [Phys. Rev.…
We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
A simple cellular automata model for a two-group war over the same territory is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are…
Seasonality frequently occurs in population models, and the corresponding seasonal patterns have been of great interest to scientists. This paper is concerned with traveling waves to a time-periodic bistable Lotka-Volterra competition…
We study communities emerging from generalised random Lotka--Volterra dynamics with a large number of species with interactions determined by the degree of niche overlap. Each species is endowed with a number of traits, and competition…
Ecological trade-offs between species are often invoked to explain species coexistence in ecological communities. However, few mathematical models have been proposed for which coexistence conditions can be characterized explicitly in terms…
This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…
The role of skill (fitness) and luck (randomness) as driving forces on the dynamics of resource accumulation in a myriad of systems have long puzzled scientists. Fueled by undisputed inequalities that emerge from actual competitions, there…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
There are clear benefits associated with a particular consumer choice for many current markets. For example, as we consider here, some products might carry environmental or `green' benefits. Some consumers might value these benefits while…
The maintenance of diversity, the `commonness of rarity', and compositional turnover are ubiquitous features of species-rich communities. Through a minimal model, we consider how these features reflect the interplay between environmental…
Cooperation and competition are fundamental forces shaping both natural and human systems, yet their interplay remains poorly understood. The Prisoner's Dilemma Game (PDG) has long served as a foundational framework in Game Theory for…
We investigate extinction dynamics in the paradigmatic model of two competing species A and B that reproduce (A-->2A, B-->2B), self-regulate by annihilation (2A-->0, 2B-->0), and compete (A+B-->A, A+B-->B). For a finite system that is in…
Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the…
We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…
We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might…