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Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Numerical studies of the May-Leonard model for cyclically competing species exhibit spontaneous spatial structures in the form of spirals. It is desirable to obtain a simple coarse-grained evolution equation describing spatio-temporal…
The existence and uniqueness of a global positive solution is proven for the system of stochastic differential equations describing a nonautonomous stochastic density dependent predator-prey model with Holling-type II functional response…
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions…
This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…
A non-Markovian stochastic predator-prey model is introduced in which the prey are immobile plants and predators are diffusing herbivors. The model is studied by both mean-field approximation (MFA)and computer simulations. The MFA results a…
We study a stochastic predator-prey model on a square lattice, where each of the six species has two superior and two inferior partners. The invasion probabilities between species depend on the predator-prey pair and are supplemented by…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
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 computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…
This paper investigates the long-term dynamics of a reaction-diffusion predator-prey system subject to random environmental fluctuations modeled by Markovian switching. The model is formulated as a hybrid system of partial differential…
In mathematical modeling, several different functional forms can often be used to fit a data set equally well, especially if the data is sparse. In such cases, these mathematically different but similar looking functional forms are…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
The classic Rosenzweig-MacArthur predator-prey model has been shown to exhibit, like other coupled nonlinear ordinary differential equations (ODEs) from ecology, worrying sensitivity to model structure. This sensitivity manifests as…