Competition in a system of Brownian particles: Encouraging achievers.

We introduce and analytically and numerically study a simple model of interagent competition, where underachievement is strongly discouraged. We consider N≫1 particles performing independent Brownian motions on the line. Two particles are selected at random and at random times, and the particle closest to the origin is reset to it.

Fluctuations and first-passage properties of systems of Brownian particles with reset.

We study, analytically and numerically, stationary fluctuations in two models involving N Brownian particles undergoing stochastic resetting in one dimension. We start with the well-known reset model where the particles reset to the origin independently (model A). Then we introduce nonlocal interparticle correlations by postulating that only the particle farthest from the origin can be reset to the origin (model B).

Phase Transition in a Non-Markovian Animal Exploration Model with Preferential Returns.

We study a non-Markovian and nonstationary model of animal mobility incorporating both exploration and memory in the form of preferential returns. Exact results for the probability of visiting a given number of sites are derived and a practical WKB approximation to treat the nonstationary problem is developed. A mean-field version of this model, first suggested by Song et al.

Big-data approaches lead to an increased understanding of the ecology of animal movement.

Understanding animal movement is essential to elucidate how animals interact, survive, and thrive in a changing world. Recent technological advances in data collection and management have transformed our understanding of animal "movement ecology" (the integrated study of organismal movement), creating a big-data discipline that benefits from rapid, cost-effective generation of large amounts of data on movements of animals in the wild. These high-throughput wildlife tracking systems now allow more thorough investigation of variation among individuals and species across space and time, the nature of biological interactions, and behavioral responses to the environment.

Extinction risk of a metapopulation under bistable local dynamics.

We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics includes deterministic bistability. Mixing between patches is shown to dramatically influence the population's viability. We demonstrate that slow migration always increases the population's global extinction risk compared to the isolated case, while at fast migration synchrony between patches minimizes the population's extinction risk.

Population extinction under bursty reproduction in a time-modulated environment.

In recent years nondemographic variability has been shown to greatly affect dynamics of stochastic populations. For example, nondemographic noise in the form of a bursty reproduction process with an a priori unknown burst size, or environmental variability in the form of time-varying reaction rates, have been separately found to dramatically impact the extinction risk of isolated populations. In this work we investigate the extinction risk of an isolated population under the combined influence of these two types of nondemographic variation.