Related papers: Survival in the replicator model: Dynamics and sta…
We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we…
We study the statistics of ecosystems with a variable number of co-evolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly…
Modern ecology has re-emphasized the need for a quantitative understanding of the original 'survival of the fittest theme' based on analyzis of the intricate trade-offs between competing evolutionary strategies that characterize the…
The problem of multi-agent learning and adaptation has attracted a great deal of attention in recent years. It has been suggested that the dynamics of multi agent learning can be studied using replicator equations from population biology.…
The eco-evolutionary dynamics of species are fundamentally linked to the energetic constraints of its constituent individuals. Of particular importance is the interplay between reproduction and the dynamics of starvation and recovery. To…
This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…
We present a non-equilibrium statistical mechanics description of rank abundance relations (RAR) in random community models of ecology. Specifically, we study a multi-species replicator system with quenched random interaction matrices. We…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
In this paper, we study a special case of the invasion fitness matrix in a replicator equation: the invader-driven case. In this replicator, each species is defined by its unique active invasiveness potential (initial growth rate when…
We analyze from basic physical considerations the Darwinian competition for reproduction (evolutionary dynamics) of strategists in a Public Goods Game, the archetype for $n$-agent (group) economical and biological interactions. In the…
We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (e.g. adult, juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the…
The study of interactions between multiple species in an ecosystem is an active and impactful direction of inquiry. This is true in particular for fragile systems in which even small perturbations of their functional parameters can produce…
We consider a continuum version of a previously introduced and numerically studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve by an optimization process in a rugged fitness landscape and die due to their…
We consider the general properties of the replicator dynamical system from the standpoint of its evolution and stability. Vector field analysis as well as spectral properties of such system has been studied. Lyaponuv function for…
Ecological networks describe the interactions between different species, informing us of how they rely on one another for food, pollination and survival. If a species in an ecosystem is under threat of extinction, it can affect other…
We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…
We study the spatial rock-paper-scissors model, where resource competitors' cyclic dominance impacts organisms' energy levels. Our model assumes that failed selection interactions can lead to energy loss, reducing the chances of success in…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
A new model ecosystem consisting of many interacting species is introduced. The species are connected through a random matrix with a given connectivity. It is shown that the system is organized close to a boundary of marginal stability in…