Related papers: Autonomous models on a Cayley tree
A general procedure to formulate asexual (unstructured, deterministic) population dynamical models resulting from individual pairwise interactions is proposed. Individuals are characterized by a continuous strategy that represents all their…
The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…
The investigation of leaf-level traits in response to varying environmental conditions has immense importance for understanding plant ecology. Remote sensing technology enables measurement of the reflectance of plants to make inferences…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
The most general local Markovian stochastic model is investigated, for which it is known that the evolution equation is the Fokker-Planck equation. Special cases are investigated where uncorrelated initial states remain uncorrelated.…
We present a generalized dynamical mean-field approach for the nonequilibrium physics of a strongly correlated system in the presence of a time-dependent external field. The Keldysh Green's function formalism is used to study the…
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…
In this paper we consider the 2-component reaction-diffusion model that was recently obtained by a systematic reduction of the 3-component Gilad et al. model for dryland ecosystem dynamics. The nonlinear structure of this model is more…
A new family of tree models is proposed, which we call "differential trees." A differential tree model is constructed from multiple data sets and aims to detect distributional differences between them. The new methodology differs from the…
Spontaneous emission and Lamb shift of atoms in absorbing dielectrics are discussed. A Green's-function approach is used based on the multipolar interaction Hamiltonian of a collection of atomic dipoles with the quantised radiation field.…
A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For…
We analyze a model of interacting agents (e.g. prebiotic chemical species) which are represended by nodes of a network, whereas their interactions are mapped onto directed links between these nodes. On a fast time scale, each agent follows…
We consider the population dynamics of a set of species whose network of catalytic interactions is described by a directed graph. The relationship between the attractors of this dynamics and the underlying graph theoretic structures like…
We consider the set of random Bienaym\'e-Galton-Watson trees with a bounded number of offspring and bounded number of generations as a statistical mechanics model: a random tree is a rooted subtree of the maximal tree; the spin at a given…
We consider large but finite systems of identical agents on the line with up to next nearest neighbor asymmetric coupling. Each agent is modelled by a linear second order differential equation, linearly coupled to up to four of its…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
Evolutionary transitions among ecological interactions are widely known, although their detailed dynamics remain absent for most population models. Adaptive dynamics has been used to illustrate how the parameters of population models might…
We study the discretization of a linear evolution partial differential equation when its Green function is known. We provide error estimates both for the spatial approximation and for the time stepping approximation. We show that, in fact,…
The model of interaction between learning and evolutionary optimization is designed and investigated. The evolving population of modeled organisms is considered. The mechanism of the genetic assimilation of the acquired features during a…
Species distribution models usually attempt to explain presence-absence or abundance of a species at a site in terms of the environmental features (socalled abiotic features) present at the site. Historically, such models have considered…