相关论文: Age-structured Trait Substitution Sequence Process…
In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
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…
We consider a metapopulation made up of $K$ demes, each containing $N$ individuals bearing a heritable quantitative trait. Demes are connected by migration and undergo independent Moran processes with mutation and selection based on trait…
The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary…
Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick-von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in [1,2]. Here we develop…
Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multi-mutation leaps, that is, several mutations…
Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference…
We consider Markov jump processes describing structured populations with interactions via density dependance. We propose a Markov construction with a distinguished individual which allows to describe the random tree and random sample at a…
Although the concepts of age, survival and transit time have been widely used in many fields, including population dynamics, chemical engineering, and hydrology, a comprehensive mathematical framework is still missing. Here we discuss…
A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The…
We propose a predator-prey model with an age-structured predator population that exhibits a functional role reversal. The structure of the predator population in our model embodies the ecological concept of an "ontogenetic niche shift," in…
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…