Related papers: Evolution Equation of Phenotype Distribution: Gene…
The evolution of dispersal is a classical question in evolutionary ecology, which has been widely studied with several mathematical models. The main question is to define the fittest dispersal rate for a population in a bounded domain, and,…
We introduce a model of biological evolution where species evolve in response to biotic interactions and a fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective…
We study the evolution leading to (or regressing from) a large fluctuation in a Statistical Mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables $n_m$…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
The number of substitutions (of nucleotides, amino acids, ...) that take place during the evolution of a sequence is a stochastic variable of fundamental importance in the field of molecular evolution. Although the mean number of…
Genomic evolution can be viewed as string-editing processes driven by mutations. An understanding of the statistical properties resulting from these mutation processes is of value in a variety of tasks related to biological sequence data,…
The relationship between genotype and phenotype plays a crucial role in determining the function and robustness of biological systems. Here the evolution progresses through the change in genotype, whereas the selection is based on the…
We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time…
We consider the asymptotic behaviour of the fluctuation process for large stochastic systems of interacting particles driven by both idiosyncratic and common noise with an interaction kernel \(k \in L^2(\R^d) \cap L^\infty(\R^d)\). Our…
In this work, the dynamics of fluctuations in gene expression time series is investigated. By using collected data of gene expression from yeast and human organisms, we found that the fluctuations of gene expression level and its average…
Phoneme frequency distributions exhibit robust statistical regularities across languages, including exponential-tailed rank-frequency patterns and a negative relationship between phonemic inventory size and the relative entropy of the…
We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…
The evolution model with parallel mutation-selection scheme is solved for the case when selection is accompanied by base substitutions, insertions, and deletions. The fitness is assumed to be either a single-peak function (i.e., having one…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a $\bbT_d^+$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain…
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…
Phenotypic plasticity and its evolution may help evolutionary rescue in a novel and stressful environment, especially if environmental novelty reveals cryptic genetic variation that enables the evolution of increased plasticity. However,…