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We consider the one-dimensional driven ABC model under particle-conserving and particle-non-conserving processes. Two limiting cases are studied: (a) the rates of the non-conserving processes are vanishingly slow compared with the…
Biological aging is characterized by an age-dependent increase in the probability of death and by a decrease in the reproductive capacity. Individual age-dependent rates of survival and reproduction have a strong impact on population…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
Species evolution is essentially a random process of interaction between biological populations and their environments. As a result, some physical parameters in evolution models are subject to statistical fluctuations. In this paper, two…
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic…
Higher dimensional space-time models provide us an alternative interpretation of nature, and give us different dynamical aspects than the traditional four-dimensional space-time models. Motivated by such recent interests, especially for…
Gene regulatory networks exhibit hierarchical organization across scales; capturing this structure mathematically requires a metric that distinguishes regulatory influence at each level. We show that the ultrametric of the $p$-adic integers…
Darwin introduced the concept of the "living fossil" to describe species belonging to lineages that have experienced little evolutionary change, and suggested that species in more slowly evolving lineages are more prone to extinction (1).…
The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a…
We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many…
We investigate the non-linear evolution of matter perturbations in $f(R)$ models with the Chameleon screening mechanism. The novel feature of our investigation is an iterative solution for the non-linear equation for the scalar field $\chi…
The universal genetic code presents a fundamental paradox in molecular biology. Recent advances in synthetic biology have demonstrated that the code is remarkably flexible--organisms can survive with 61 codons instead of 64, natural…
Eco-evolutionary dynamics is crucial to understand how individuals' behaviors and the surrounding environment interplay with each other. Typically, it is assumed that individuals update their behaviors via linear imitation function, i.e.,…
We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…
Non-selective effects, like genetic drift, are an important factor in modern conceptions of evolution, and have been extensively studied for constant population sizes. Here, we consider non-selective evolution in the case of growing…
We consider Ewens random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$ and to study the asymptotic behaviour as $n\to\infty$. We obtain very precise information on the joint distribution of…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
Life uses non-equilibrium mechanisms to create ordered structures not attainable at equilibrium; the resulting order is assumed to provide functional benefits that outweigh costs of time and energy needed by these mechanisms. Here, we show…
Developmental constraints have been postulated to limit the space of feasible phenotypes and thus shape animal evolution. These constraints have been suggested to be the strongest during either early or mid-embryogenesis, which corresponds…
The prevalence of neutral mutations implies that biological systems typically have many more genotypes than phenotypes. But can the way that genotypes are distributed over phenotypes determine evolutionary outcomes? Answering such questions…