Related papers: Competition among alliances of different sizes
Competing strategies in an evolutionary game model, or species in a biosystem, can easily form a larger unit which protects them from the invasion of an external actor. Such a defensive alliance may have two, three, four or even more…
The self-protection of alliances against external invaders is a key concept behind the maintenance of biodiversity in the face of natural selection. But since these alliances, which can be formed by different numbers of competitors, can…
In a diverse population, where many species are present, competitors can fight for surviving at individual and collective levels. In particular, species, which would beat each other individually, may form a specific alliance that ensures…
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
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…
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…
We study a set of six-species ecological models where each species has two predators and two preys. On a square lattice the time evolution is governed by iterated invasions between the neighboring predator-prey pairs chosen at random and by…
The role of species interactions in controlling the interplay between the stability of an ecosystem and its biodiversity is still not well understood. The ability of ecological communities to recover after a small perturbation of the…
The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a model ecosystem of sessile and mutually excluding organisms competing for space [Mathiesen et al. Phys. Rev.…
As a generalization of the 3-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated…
Relations among species in ecosystems can be represented by complex networks where both negative (competition) and positive (mutualism) interactions are concurrently present. Recently, it has been shown that many ecosystems can be cast into…
Mutualistic interactions, which are beneficial for both interacting species, are recurrently present in ecosystems. Observations of natural systems showed that, if we draw mutualistic relationships as binary links between species, the…
This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…
Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we…
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…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
A model of six-species food web is studied in the viewpoint of spatial interaction structures. Each species has two predators and two preys, and it was previously known that the defensive alliances of three cyclically predating species…
Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous…