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Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…
This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic…
Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
In this study, a new and natural way of constructing a stochastic Susceptible-Infected-Susceptible (SIS) model is proposed. This approach is natural in the sense that the disease transmission rate, $\beta$, is substituted with a generic,…
Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple…
We study the discrete-time dynamical systems associated to a stage-structured wild and sterile mosquito population. We describe all fixed points of the evolution operator (which depends on five parameters) of mosquito population and show…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition…
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…
We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly…
Synchronous dynamic systems are well-established models that have been used to capture a range of phenomena in networks, including opinion diffusion, spread of disease and product adoption. We study the three most notable problems in…
This article considers the stochastic optimal control of discrete-time linear systems subject to (possibly) unbounded stochastic disturbances, hard constraints on the manipulated variables, and joint chance constraints on the states. A…
To study population dynamics, ecologists and wildlife biologists use relative abundance data, which are often subject to temporal preferential sampling. Temporal preferential sampling occurs when sampling effort varies across time. To…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
In a wide variety of natural systems, closely-related microbial strains coexist stably, resulting in high levels of fine-scale biodiversity. However, the mechanisms that stabilize this coexistence are not fully understood. Spatial…
Most climate trend studies analyze long-term trends as a proxy for climate dynamics. However, when examining seasonal data, it is unrealistic to assume that long-term trends remain consistent across all seasons. Instead, each season likely…
The maintenance of diversity, the `commonness of rarity', and compositional turnover are ubiquitous features of species-rich communities. Through a minimal model, we consider how these features reflect the interplay between environmental…
In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive…