Related papers: Adaptation in a stochastic multi-resources chemost…
In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (competition or predation), the long term behavior of this…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
In many complex systems, the dynamical evolution of the different components can result in adaptation of the connections between them. We consider the problem of how a fully connected network of discrete-state dynamical elements which can…
Biological populations are subject to fluctuating environmental conditions. Different adaptive strategies can allow them to cope with these fluctuations: specialization to one particular environmental condition, adoption of a generalist…
A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on behaviour of locusts. It exhibits nontrivial…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…
We study the adaptation dynamics of an initially maladapted asexual population with genotypes represented by binary sequences of length $L$. The population evolves in a maximally rugged fitness landscape with a large number of local optima.…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
The Crump-Young model consists of two fully coupled stochastic processes modeling the substrate and microorganisms dynamics in a chemostat. Substrate evolves following an ordinary differential equation whose coefficients depend of…
We study a model of a multi-species ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law…
Stochastic phenotype switching has been suggested to play a beneficial role in microbial populations by leading to the division of labour among cells, or ensuring that at least some of the population survives an unexpected change in…
In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…
The intensification and increased frequency of weather extremes is emerging as one of the most important aspects of climate change. We use Monte Carlo simulation to understand and predict the consequences of variations in trends (i.e.,…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
Complex change is often described as "evolutionary" in economics, policy, and technology, yet most system dynamics models remain constrained to fixed state spaces and equilibrium-seeking behavior. This paper argues that evolutionary…
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous…
This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here we consider species assembly models where the population dynamics is kept far from fixed points through the…
The multiple knapsack problem (MKP) generalizes the classical knapsack problem by assigning items to multiple knapsacks subject to capacity constraints. It is used to model many real-world resource allocation and scheduling problems. In…
Given an endogenous timescale set by invasion in a constant environment, we introduced periodic temporal variation in competitive superiority by alternating the species' propagation rates. By manipulating habitat size and introduction rate,…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…