Related papers: Stochastic dynamics for adaptation and evolution o…
Speciation is of fundamental importance to understanding the huge diversity of life on Earth. In contrast to current phenomenological models, we develop a biophysically motivated approach to study speciation involving the co-evolution of…
We study distributed agreement in microbial distributed systems under stochastic population dynamics and competitive interactions. Motivated by recent applications in synthetic biology, we examine how the presence and absence of direct…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
In this paper we prove the convergence to the stochastic Burgers equation from one-dimensional interacting particle systems, whose dynamics allow the degeneracy of the jump rates. To this aim, we provide a new proof of the second order…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
Phenotypes of individuals in a population of organisms are not fixed. Phenotypic fluctuations, which describe temporal variation of the phenotype of an individual or individual-to-individual variation across a population, are present in…
We seek models for the genotype evolution of agricultural animals, animals involved in primary production processes. Classical models for genotype evolution have tended to be very simple in order that analytic methods may be employed in…
We investigate a selection-mutation model for the dynamics of technological innovation,a special case of reaction-diffusion equations. Although mutations are assumed to increase the variety of technologies, not their average success…
Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic…
It has been recently shown that the exponential growth rate of a population of bacterial cells starting from a single cell shows transient oscillations due to early synchronized bursts of division. These oscillations are enhanced by cell…
We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…
We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown' effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a…
Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An…
Cell migration is a fundamental process involved in physiological phenomena such as the immune response and morphogenesis, but also in pathological processes, such as the development of tumor metastasis. These functions are effectively…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…
The most frequently used in physical application diffusive (based on the Fokker-Planck equation) model leans upon the assumption of small jumps of a macroscopic variable for each given realization of the stochastic process. This imposes…
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.…
In this article, a stochastic individual-based model describing Darwinian evolution of asexual, phenotypic trait-structured population, is studied. We consider a large population with constant population size characterised by a resampling…