Related papers: The statistical mechanics of a polygenic character…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is…
In population genetics, extant samples are usually used for inference of past population genetic forces. With the Kingman coalescent and the backward diffusion equation, inference of the marginal likelihood proceeds from an extant sample…
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…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
The theory of life history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens in both epidemic and endemic situations. This framework, however, relies on the assumption that pathogen populations are…
In evolutionary game theory, an important measure of a mutant trait (strategy) is its ability to invade and take over an otherwise-monomorphic population. Typically, one quantifies the success of a mutant strategy via the probability that a…
In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by…
Recruitment dynamics, or the distribution of the number of offspring among individuals, is central for understanding ecology and evolution. Sweepstakes reproduction (heavy right-tailed offspring number distribution) is central for…
We consider population dynamics as implemented by the cloning algorithm for analysis of large deviations of time-averaged quantities. Using the simple symmetric exclusion process as a prototypical example, we investigate the convergence of…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Stochastic mechanics is based on the hypothesis that all matter is subject to universal modified Brownian motion. In this report, we calculated probability density distributions using concepts of stochastic mechanics independent of…
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…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
Natural selection and random drift are competing phenomena for explaining the evolution of populations. Combining a highly fit mutant with a population structure that improves the odds that the mutant spreads through the whole population…
The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…
It is generally accepted that populations are useful for the global exploration of multi-modal optimisation problems. Indeed, several theoretical results are available showing such advantages over single-trajectory search heuristics. In…
We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0,1,...,L} and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation…
The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and…
Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…