Related papers: On a mathematical relation between the Eigen model…
Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with…
We derive and apply a partial differential equation for the moment generating function of the Wright-Fisher model of population genetics.
We consider a hierarchically structured population in which the amount of resources an individual has access to is affected by individuals that are larger, and that the intake of resources by an individual only affects directly the growth…
The drift-barrier hypothesis states that random genetic drift constrains the refinement of a phenotype under natural selection. The influence of effective population size and the genome-wide deleterious mutation rate were studied…
Evolutionary dynamics in an uncorrelated rugged fitness landscape is studied in the framework of Eigen's molecular quasispecies model. We consider the case of strong selection, which is analogous to the zero temperature limit in the…
Eigen's quasi-species model describes viruses as ensembles of different mutants of a high fitness "master" genotype. Mutants are assumed to have lower fitness than the master type, yet they coexist with it forming the quasi-species. When…
In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
The classical approaches to the modeling of sex ratio evolution can be divided into two classes. The first class contains the static strategic models related to the Dusing Fisher Shaw Mohler fitness measure, based on the reproductive value…
We consider an infinitely-many neutral allelic model of population genetics where all alleles are divided into a finite number of classes, and each class is characterized by its own mutation rate. For this model the allelic composition of a…
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 derive new bounds for the condition number of kernel matrices, which we then use to enhance existing non-asymptotic test error bounds for kernel ridgeless regression (KRR) in the over-parameterized regime for a fixed input dimension. For…
We prove that a Moran model converges in probability to Eigen's quasispecies model in the infinite population limit.
Many species reproduce both sexually and asexually producing genetically unique and clonal recruits. The relative contribution of sexual and asexual reproduction is mostly considered a consequence of natural selection, for example,…
The diffusion approximation of the Wright-Fisher model of population genetics leads to partial differentiable equations, the so-called Kolmogorov equations, with an operator that degenerates at the boundary. Standard tools do not apply, and…
Considering the recent experimental discovery of Green et al that present day non-Africans have 1 to 4% of their nuclear DNA of Neanderthal origin, we propose here a model which is able to quantify the interbreeding events between Africans…
Meta-analysis methods have been widely used to combine results from multiple clinical or genomic studies to increase statistical power and ensure robust and accurate conclusion. Adaptively weighted Fisher's method (AW-Fisher) is an…
We consider a multi-colony version of the Wright-Fisher model with seed-bank that was recently introduced by Blath et al. Individuals live in colonies and change type via resampling and mutation. Each colony contains a seed-bank that acts…
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…
Family studies provide an important tool for understanding etiology of diseases, with the key aim of discovering evidence of family aggregation and to determine if such aggregation can be attributed to genetic components. Heritability and…