Related papers: On mathematical theory of selection: Continuous ti…
We review the statistical mechanics approach to the study of the emerging collective behavior of systems of heterogeneous interacting agents. The general framework is presented through examples is such contexts as ecosystem dynamics and…
We study the limit of many small mutations of a model of population dynamics. The population is structured by phonological traits and is spatially inhomogeneous. The various sub-populations compete for the same nutrient which diffuses…
Our research is concerned with studying behavioural changes within a dynamic system, i.e. health care, and their effects on the decision-making process. Evolutionary Game theory is applied to investigate the most probable strategy(ies)…
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.…
The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
Cumulants and moments are closely related to the basic mathematics of continuous and discrete selection (respectively). These relationships generalize Fisher's fundamental theorem of natural selection and also make clear some of its…
The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
We study a continuous-time dynamical system that models the evolving distribution of genotypes in an infinite population where genomes may have infinitely many or even a continuum of loci, mutations accumulate along lineages without…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
Accurate modeling of opinion dynamics has the potential to help us understand polarization and what makes effective political discourse possible or impossible. Here, we use physics-based methods to model the evolution of political opinions…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference…
To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the…
Many analyses of resource-allocation problems employ simplistic models of the population. Using the example of a resource-allocation problem of Marecek et al. [arXiv:1406.7639], we introduce rather a general behavioural model, where the…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
Selection, the tendency of some traits to become more frequent than others in a population under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social…