Related papers: Understanding evolutionary and ecological dynamics…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…
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…
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
Species subject to predation and environmental threats commonly exhibit variable periods of population boom and bust over long timescales. Understanding and predicting such behavior, especially given the inherent heterogeneity and…
Eco-evolutionary game dynamics which characterizes the mutual interactions and the coupled evolutions of strategies and environments has been of growing interests in very recent years. Since such feedback loops widely exist in a range of…
A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or…
The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…
Eco-evolutionary dynamics, or eco-evolution for short, are thought to involve rapid demography (ecology) and equally rapid phenotypic changes (evolution) leading to novel, emergent system behaviours. This focus on contemporary dynamics is…
On infinitesimally short time interval various processes contributing to population change tend to operate independently so that we can simply add their contributions (Metz and Diekmann (1986)). This is one of the cornerstones for…
The purpose of this roadmap article is to draw attention to a paradigm shift in our understanding of evolution towards a perspective of ecological-evolutionary feedback, highlighted through two recent highly simplified examples of rapid…
It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…
Logistic equations play a pivotal role in the study of any non linear evolution process exhibiting growth and saturation. The interest for the phenomenology, they rule, goes well beyond physical processes and cover many aspects of ecology,…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
A general stochastic maximum principle is proved for optimal controls of semilinear stochastic evolution equations. Stochastic evolution operators, and the control with values in a general set enter into both drift and diffusion terms.
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We consider the dynamics of a 1D system evolving according to a deterministic drift and randomly forced by two types of jumps processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously…
The evolutionary edit distance between two individuals in a population, i.e., the amount of applications of any genetic operator it would take the evolutionary process to generate one individual starting from the other, seems like a…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
In the work two ways of evolutionary interpretation of entropy model for correspondence matrix calculation are proposed. Both approaches based on the stochastic chemical kinetic evolution under the detailed balance condition. The first…