Related papers: When Can The Discrete Moran Process May Bereplaced…

We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J. Appl. Prob. 39 (2002), 38-54) and Taylor…

We establish an explicit rate of convergence for some systems of mean-field interacting diffusions with logistic binary branching towards the solutions of nonlinear evolution equations with non-local self-diffusion and logistic mass growth,…

New ideas and technologies adopted by a small number of individuals occasionally spread globally through a complex web of social ties. Here, we present a simple and general approximation method, namely, a message-passing approach, that…

We consider a discrete model of population with interaction where the birth and death rates are non linear functions of the population size. After proceeding to renormalization of the model parameters, we obtain in the limit of large…

We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…

Evolution occurs in populations of reproducing individuals. In stochastic descriptions of evolutionary dynamics, such as the Moran process, individuals are chosen randomly for birth and for death. If the same type is chosen for both steps,…

Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion…

Diffusion models have become a standard approach for generative modeling in continuous domains, yet their application to discrete data remains challenging. We investigate why Gaussian diffusion models with the DDPM solver struggle to sample…

We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…

Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A…

The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation…

Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective advantage over…

We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…

The Moran process, as studied by [Lieberman, E., Hauert, C. and Nowak, M. Evolutionary dynamics on graphs. Nature 433, pp. 312-316 (2005)], is a stochastic process modeling the spread of genetic mutations in populations. In this process,…

Under natural assumptions a Feller type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved…

We study the fixation and stationary behavior of the Lambda-Wright-Fisher process with parent-independent mutation and finitely many types, a jump-diffusion model for allele frequency dynamics in large populations with potentially large…

Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…

We consider a stochastic model describing a constant size $N$ population that may be seen as a directed polymer in random medium with $N$ sites in the transverse direction. The population dynamics is governed by a noisy traveling wave…

Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where…