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Evolution in finite populations is often modelled using the classical Moran process. Over the last ten years this methodology has been extended to structured populations using evolutionary graph theory. An important question in any such…
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…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the Kimura Equation. In this formalism, the central component is the fitness potential, from which we obtain…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
We study a population model of fixed size undergoing strong selection where individuals accumulate beneficial mutations, namely the Moran model with selection. In a specific setting with strong selection, Schweinsberg showed that the…
In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion…
The goal of cancer genome sequencing projects is to determine the genetic alterations that cause common cancers. Many malignancies arise during the clonal expansion of a benign tumor which motivates the study of recurrent selective sweeps…
We derive and apply a partial differential equation for the moment generating function of the Wright-Fisher model of population genetics.
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
Models of ordering dynamics allow to understand natural systems in which an initially disordered population homogenizes some traits via local interactions. The simplest of these models, with wide applications ranging from evolutionary to…
We study competition between two biological species advected by a compressible velocity field. Individuals are treated as discrete Lagrangian particles that reproduce or die in a density-dependent fashion. In the absence of a velocity field…
Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic…
We present an novel framework for efficiently and effectively extending the powerful continuous diffusion processes to discrete modeling. Previous approaches have suffered from the discrepancy between discrete data and continuous modeling.…
We consider two processes that have been used to study gene duplication, Watterson's [Genetics 105 (1983) 745--766] double recessive null model and Lynch and Force's [Genetics 154 (2000) 459--473] subfunctionalization model. Though the…
Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…
Diffusion is a commonly used technique for spreading information from point to point on a graph. The rationale behind diffusion is not clear. And the multi-types Galton-Watson forest is a random model of population growth without space or…
In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has…