Related papers: Scaling in a continuous time model for biological …
This paper investigates the connection between discrete and continuous models describing prion proliferation. The scaling parameters are interpreted on biological grounds and we establish rigorous convergence statements. We also discuss,…
We study the long-time behaviour of phenotype-structured models describing the evolutionary dynamics of asexual species whose phenotypic fitness landscape is characterised by multiple peaks. First we consider the case where phenotypic…
Assuming the deleterious mutations in the Penna ageing model to affect mainly the young ages, we get an enhanced mortality at very young age, followed by a minimum of the mortality, and then the usual exponential increase of mortality with…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
We study the growth rate of a cell population that follows an age-structured PDE with time-periodic coefficients. Our motivation comes from the comparison between experimental tumor growth curves in mice endowed with intact or disrupted…
The long-time dynamics of the 1D contact process suddenly brought out of an uncorrelated initial state is studied through a light-cone transfer-matrix renormalisation group approach. At criticality, the system undergoes ageing which is…
This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of…
The possible coexistence of one host, one aggressive parasite and one non-lethal parasite is simulated using the Penna model of biological ageing. If the aggressive parasites survive the difficult initial times where they have to adjust…
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…
We obtain scaling limit results for asymmetric trap models and their infinite volume counterparts, namely asymmetric K processes. Aging results for the latter processes are derived therefrom.
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.…
As the global population continues to age, there is an increasing demand for ways to accurately quantify the biological processes underlying aging. Biological age, unlike chronological age, reflects an individual's physiological state,…
We consider several one-species population dynamics model with finite and infinite carrying capacity, time dependent growth and effort rates and solve them analytically. We show that defining suitable scaling functions for a given time, one…
We consider an interacting particle Markov process for Darwinian evolution in an asexual population with non-constant population size, involving a linear birth rate, a density-dependent logistic death rate, and a probability $\mu$ of…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
We solve a lifecycle model in which the consumer's chronological age does not move in lockstep with calendar time. Instead, biological age increases at a stochastic non-linear rate in time like a broken clock that might occasionally move…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…
We first review an approach that had been developed in the past years to introduce concepts of "bivariate ageing" for exchangeable lifetimes and to analyze mutual relations among stochastic dependence, univariate ageing, and bivariate…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…