Related papers: Error Threshold of Fully Random Eigen Model
Paired estimation of change in parameters of interest over a population plays a central role in several application domains including those in the social sciences, epidemiology, medicine and biology. In these domains, the size of the…
We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the…
We study general properties of the leading eigenvalue $\overline{w}(q)$ of Eigen's evolutionary matrices depending on the probability $q$ of faithful reproduction. This is a linear algebra problem that has various applications in…
Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges…
We investigate random feature models in which neural networks sampled from a prescribed initialization ensemble are frozen and used as random features, with only the readout weights optimized. Adopting a statistical-physics viewpoint, we…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
Which factors govern the evolution of mutation rates and emergence of species? Here, we address this question using a first principles model of life where population dynamics of asexual organisms is coupled to molecular properties and…
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…
We describe a stochastic birth-and-death model of evolution of horizontally transferred genes in microbial populations. The model is a generalization of the stochastic model described by Berg and Kurland and includes five parameters: the…
Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can…
We explore some aspects of the relationship between biological evolution processes and the mathematical theory of records. For Eigen's quasispecies model with an uncorrelated fitness landscape, we show that the evolutionary trajectories…
While Neutral Theory famously describes the number of discrete genetic differences in populations, we consider the number of genetic backgrounds under which such differences are observed - setting limits to the generalizability of their…
We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a…
This paper introduces a martingale that characterizes two properties of evolving forecast distributions. Ideal forecasts of a future event behave as martingales, sequen- tially updating the forecast to leverage the available information as…
We study a model of species survival recently proposed by Michael and Volkov. We interpret it as a variant of empirical processes, in which the sample size is random and when decreasing, samples of smallest numerical values are removed.…
This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…
Survival models capture the relationship between an accumulating hazard and the occurrence of a singular event stimulated by that accumulation. When the model for the hazard is sufficiently flexible survival models can accommodate a wide…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…