Related papers: Two-timescale evolution on a singular landscape
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
The Wright-Fisher diffusion is a fundamentally important model of evolution encompassing genetic drift, mutation, and natural selection. Suppose you want to infer the parameters associated with these processes from an observed sample path.…
Dynamical mechanisms that can stabilize the coexistence or diversity in biology are generally of fundamental interest. In contrast to many two-strategy evolutionary games, games with three strategies and cyclic dominance like the…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
Our motivation comes from the large population approximation of individual based models in population dynamics and population genetics. We propose a general method to investigate scaling limits of finite dimensional population size Markov…
Kramer's theory of activation over a potential barrier consists in computing the mean exit time from the boundary of a basin of attraction of a randomly perturbed dynamical system. Here we report that for some systems, crossing the boundary…
We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
Stochastic vegetation-water dynamical systems play a pivotal role in ecological stability, biodiversity, water resource management, and adaptation to climate change. This research proposes a machine learning-based method for analyzing rare…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the…
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a…
We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-)steady state…
Extinction times in resampling processes are fundamental yet often intractable, as previous formulas scale as $2^M$ with the number of states $M$ present in the initial probability distribution. We solve this by treating multinomial updates…
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook…
A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths --- the rare trajectories that transit between the folded and unfolded ensembles --- using only thermodynamic information, such as a…
Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
This paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to…
In large but finite populations, weak demographic stochasticity due to random birth and death events can lead to population extinction. The process is analogous to the escaping problem of trapped particles under random forces. Methods…