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We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
We investigate the thermodynamics as well as the population dynamics of ecosystems based on a stochastic approach in which the number of individuals of the several species of the ecosystem are treated as stochastic variables. The several…
Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In…
We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly…
This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes…
Many driven systems alternate between bursts of activity and quiescence and can become trapped in an absorbing state, such as complete inactivity in reaction-diffusion processes or extinction in predator-prey dynamics. It is generally…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
Isolated populations ultimately go extinct because of the intrinsic noise of elementary processes. In multi-population systems extinction of a population may occur via more than one route. We investigate this generic situation in a simple…
Many types of bacteria can survive under stress by switching stochastically between two different phenotypes: the "normals" who multiply fast, but are vulnerable to stress, and the "persisters" who hardly multiply, but are resilient to…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…
We study the interplay between synchronization and extinction of a species. Using a general model we show that under a common external forcing, the species with a quadratic saturation term in the population dynamics first undergoes spatial…