Related papers: Stochastic Physics, Complex Systems and Biology
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
All living things exhibit adaptations that enable them to survive and reproduce in the natural environment that they inhabit. From a biological standpoint, it has long been understood that adaptation comes from natural selection, whereby…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
Finite-size fluctuations arising in the dynamics of competing populations may have dramatic influence on their fate. As an example, in this article, we investigate a model of three species which dominate each other in a cyclic manner.…
I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations…
Control of the living cell functions with remarkable reliability despite the stochastic nature of the underlying molecular networks -- a property presumably optimized by biological evolution. We here ask to what extent the property of a…
Life can be viewed as a localized chemical system that sits on, or in the basin of attraction of, a metastable dynamical attractor state that remains out of equilibrium with the environment. Such a view of life allows that new living states…
We argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics.…
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.…
In biology and ecology, individuals or communities of individuals living in unpredictable environments often alternate between different evolutionary strategies to spread and reduce risks. Such behavior is commonly referred to as…
Behavioural differences may arise in the absence of genetic or environmental variation. Chaotic dynamics may influence behavioural development, and so this among-individual variation. We discuss methods and experimental designs to test this…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
We study a stochastic two-species chemical reaction system with two mechanisms. One mechanism consists of chemical interactions which govern the overall drift of species amounts in the system; the other mechanism consists of resampling,…