Related papers: Nonlinear historical superprocess approximations f…
Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical…
Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Here we use phylogenetic Gaussian process regression to model the evolution of simulated function-valued traits. Given…
The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak or…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
We consider branching processes with interaction in continuous time, both with values in the integers and in the reals (in the second case we restrict ourselves to continuous processes), which model the evolution of the size of a…
Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…
Modern generative machine learning models demonstrate surprising ability to create realistic outputs far beyond their training data, such as photorealistic artwork, accurate protein structures, or conversational text. These successes…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
We propose a type-dependent branching model with mutation and competition for modeling phylogenies of a virus population. The competition kernel depends for any two virus particles on the particles' types, the total mass of the population…
In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a…
We consider a model of stationary population with random size given by a continuous state branching process with immigration with a quadratic branching mechanism. We give an exact elementary simulation procedure of the genealogical tree of…
We define symmetric and asymmetric branching trees, a class of processes particularly suited for modeling genealogies of inhomogeneous populations where individuals may reproduce throughout life. In this framework, a broad class of…
We present a genealogy for superprocesses with a non-homogeneous quadratic branching mechanism, relying on a weighted version of the superprocess and a Girsanov theorem. We then decompose this genealogy with respect to the last individual…
Many questions that we have about the history and dynamics of organisms have a geographical component: How many are there, and where do they live? How do they move and interbreed across the landscape? How were they moving a thousand years…
Since the advent of modern bioinformatics, the challenging, multifaceted problem of reconstructing phylogenetic history from biological sequences has hatched perennial statistical and algorithmic innovation. Studies of the phylogenetic…
Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual observed only once, making it impossible to apply traditional…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
Motivated by empirical evidence on the interplay between geography, population density and societal interaction, we propose a generative process for the evolution of social structure in cities. Our analytical and simulation results predict…