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The coupling between evolutionary and ecological changes (eco-evolutionary dynamics) has been shown to be relevant among diverse species, and is also of interest outside of ecology, i.e. in cancer evolution. These dynamics play an important…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
Methods for predicting the probability and timing of a species' extinction are typically based on a combination of theoretical models and empirical data, and focus on single species population dynamics. Of course, species also interact with…
In this paper we explore the life expectancy limits by based on the stochastic modeling of mortality and applying the first exit or hitting time theory of a stochastic process. The main assumption is that the health state or the "vitality",…
Ageing phenomena are observed in a large variety of dynamical systems exhibiting a slow relaxation from a non-equilibrium initial state. Ageing can be characterised in terms of the linear response R(t,s) at time t to a local perturbation at…
Ageing in systems without detailed balance is studied in bosonic contact and pair-contact processes with Levy diffusion. In the ageing regime, the dynamical scaling of the two-time correlation function and two-time response function is…
Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual observed only once, making it impossible to apply traditional…
A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…
Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death…
Survival analysis, or time-to-event modelling, is a classical statistical problem that has garnered a lot of interest for its practical use in epidemiology, demographics or actuarial sciences. Recent advances on the subject from the point…
We consider continuous time random walks (CTRW) and discuss situations pertinent to aging. These correspond to the case when the initial state of the system is known not at preparation (at $t=0$) but at the later instant of time $t_1>0$…
Aging, the process of growing old or maturing, is one of the most widely seen natural phenomena in the world. For the stochastic processes, sometimes the influence of aging can not be ignored. For example, in this paper, by analyzing the…
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator…
This topic review communicates working experiences regarding interaction of a multiplicity of processes. Our experiences come from climate change modelling, materials science, cell physiology and public health, and macroeconomic modelling.…
The evolutionary biology of aging is fundamental to understanding the mechanisms of aging and how to develop anti-aging treatments. Thus far most evolutionary theory concerns the genetics of aging with limited physiological integration.…
The number of recurrent events before a terminating event is often of interest. For instance, death terminates an individual's process of rehospitalizations and the number of rehospitalizations is an important indicator of economic cost. We…
We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies…
This chapter reviews some aspects of the theory of age-structured models of populations with finite maximum age. We formulate both the renewal equation for the birth rate and the partial differential equation for the age density, and show…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…