Related papers: Mobility promotes and jeopardizes biodiversity in …
We propose a minimal off-lattice model of living organisms where just a very few dynamical rules of growth are assumed. The stable coexistence of many clusters is detected when we replace the global restriction rule by a locally applied…
Cooperative mutualism is a major force driving evolution and sustaining ecosystems. Although the importance of spatial degrees of freedom and number fluctuations is well-known, their effects on mutualism are not fully understood. With range…
We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with…
We study the rock-paper-scissors game in structured populations, where the invasion rates determine individual payoffs that govern the process of strategy change. The traditional version of the game is recovered if the payoffs for each…
Global, population-wide oscillations in models of cyclic dominance may result in the collapse of biodiversity due to the accidental extinction of one species in the loop. Previous research has shown that such oscillations can emerge if the…
In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyze how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes…
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…
The prototype of a cyclic dominant system is the so-called rock-scissors-paper game, but similar relation among competing strategies can be identified in several other models of evolutionary game theory. In this work we assume that a…
The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…
In a static environment, optional participation and a local agglomeration of cooperators are found to be beneficial for the occurrence and maintenance of cooperation. In the optional public goods game, the rock-scissors-paper cycles of…
Natural ecosystems, in particular on the microbial scale, are inhabited by a large number of species. The population size of each species is affected by interactions of individuals with each other and by spatial and temporal changes in…
Population diversity is crucial in evolutionary algorithms to enable global exploration and to avoid poor performance due to premature convergence. This book chapter reviews runtime analyses that have shown benefits of population diversity,…
Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
In apparent contradiction to competition theory, the number of known, co-existing plankton species far exceeds their explicable biodiversity - a discrepancy termed the Paradox of the Plankton. We introduce a new game-theoretic model for…
We study the biodiversity problem for resource competition systems with extinctions and self-limitation effects. Our main result establishes estimates of biodiversity in terms of the fundamental parameters of the model. We also prove the…
Cyclic dominance of competing species is an intensively used working hypothesis to explain biodiversity in certain living systems, where the evolutionary selection principle would dictate a single victor otherwise. Technically the…
Iterated games provide a framework to describe social interactions among groups of individuals. Recent work stimulated by the discovery of "zero-determinant" strategies has rapidly expanded our ability to analyze such interactions. This…
Rock-Paper-Scissors (RPS), a game of cyclic dominance, is not merely a popular children's game but also a basic model system for studying decision-making in non-cooperative strategic interactions. Aimed at students of physics with no…