arXiv subjects

Priscilla E. Greenwood

Publications and source records attributed to Priscilla E. Greenwood.

10 recordsLinked to original sources

arXiv2026

Heavy-Tailed Dispersal Kernels from Stopped Subdiffusive Fractional Brownian Motion

Subdiffusive fractional Brownian motions produce localized aggregation when particles are stopped at exponentially distributed times. In applications where clumping and long-distance dispersal events are observed simultaneously, such as in some instances of seed dispersal, this model fails to describe the tails of the data. The resulting redistribution kernel has only an exponentially decaying tail, whereas a heavier tail is needed for modeling the long-distance dispersal observed. Here we propose a model in which subdiffusive particles stop at exponentially distributed times, but with a rate parameter that is Gamma distributed. This heterogeneity in stopping rates causes the density of final radial positions to have a heavy-tailed distribution. Our model retains the strong localized clumping characteristic of subdiffusive fractional Brownian motion while simultaneously generating the heavy tails required for realistic long-distance dispersal.

cond-mat.stat-mech↗

arXiv2026

Intermittent precipitation and spatial Allee effects drive irregular vegetation patterns in semiarid ecosystems

Vegetation in semi-arid ecosystems frequently organizes into spatially heterogeneous mosaics that regulate ecosystem functioning, productivity, and resilience. These patterns arise from local biological interactions, including facilitation among neighboring plants and competition for limiting resources. Classical theoretical approaches have attributed such organization to scale-dependent feedbacks, predicting regular spatial patterns and abrupt transitions to collapse. However, growing empirical and theoretical evidence reveal that environmental variability and demographic stochasticity can fundamentally reshape spatial organization, driving irregular clusters, dynamic mosaics, and gradual rather than catastrophic vegetation declines. In drylands, rainfall variability is a dominant source of environmental forcing: precipitation typically occurs in short, irregular pulses that transiently enhance survival and recruitment before competitive interactions again dominate. Near persistence thresholds, ecosystem dynamics are therefore governed not only by average climatic conditions but also by the timing and spatial coincidence of favorable events. Under these conditions, positive density dependence and local facilitation can critically determine whether vegetation patches persist, expand, or collapse. Here, we develop an individual-based model that integrates intermittent precipitation with local Allee effects to examine how stochastic rainfall shapes spatial organization and persistence. We show that the interaction between pulsed resource availability and density-dependent survival generates irregular cluster structures and strongly modulates extinction risk, with resilience emerging from local spatial covariance and neighborhood density rather than from total biomass alone. These results highlight the importance of individual-level, stochastic processes in determining ecosystem resilience.

q-bio.PE↗

arXiv2026

Designing a Resilient Allee-Ornstein-Uhlenbeck model

In stochastic population dynamics, stochastic wandering can produce transition to an absorbing state. In particular, under Allee effects, low densities amplify the possibility of population collapse. We investigate this in an Allee-Ornstein-Uhlenbeck (Allee-OU) model, that couples a bistable Allee growth equation, with demographic noise, and environmental fluctuations modeled as an Ornstein-Uhlenbeck process. This process replaces the bifurcation parameter of the deterministic Allee effect equation. In the model, small noise may induce escape from the safe basin around the positive equilibrium toward extinction. We construct a stochastic control, altering the process to have a stationary distribution. We enable tractable control design, approximating the process by one with a stationary distribution. Two controlled models are developed, one acting directly on population size and another also modulating the environment. A threshold-based implementation minimizes the frequency of interventions while maximizing safe time. Simulations demonstrate that the control stabilizes fluctuations around the equilibrium.

q-bio.PE↗

arXiv2025

Parameter variability can produce heavy tails in a model for the spatial distribution of settling organisms

We show that a simple mechanistic model of spatial dispersal for settling organisms, subject to parameter variability, can generate heavy-tailed radial probability density functions. The movement of organisms in the model consists of a two-dimensional diffusion that ceases after a random time, where the parameters that characterize each of these stages have been randomized. Our findings show that these minimal assumptions can yield heavy-tailed dispersal patterns, providing a simplified framework that increases the understanding of long-distance dispersal events in movement ecology.

q-bio.PE↗

arXiv2020

Plastic systemic inhibition controls amplitude while allowing phase pattern in a stochastic neural field model

Oscillatory phase pattern formation and amplitude control for a linearized stochastic neuron field model was investigated by simulating coupled stochastic processes defined by stochastic differential equations. It was found, for several choices of parameters, that pattern formation in the phases of these processes occurred if and only if the amplitudes were allowed to grow large. Stimulated by recent work on homeostatic inhibitory plasticity, we introduced static and plastic (adaptive) systemic inhibitory mechanisms to keep the amplitudes stochastically bounded in subsequent simulations. The systems with static systemic inhibition exhibited bounded amplitudes but no sustained phase patterns, whereas the systems with plastic systemic inhibition exhibited both bounded amplitudes and sustained phase patterns. These results demonstrate that plastic inhibitory mechanisms in neural field models can stochastically control amplitudes while allowing patterns of phase synchronization to develop. Similar mechanisms of plastic systemic inhibition could play a role in regulating oscillatory functioning in the brain.

q-bio.NC↗

arXiv2019

Rapidly forming, slowly evolving, spatial patterns from quasi-cycle Mexican Hat coupling

A lattice-indexed family of stochastic processes has quasi-cycle oscillations if its otherwise-damped oscillations are sustained by noise. Such a family performs the reaction part of a discrete stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice. Quasi-cycles are a proposed mechanism for the production of neural oscillations, and Mexican Hat coupling is ubiquitous in the brain. Thus this combination might provide insight into the function of neural oscillations in the brain. Importantly, we study this system only in the transient case, on time intervals before saturation occurs. In one dimension, for weak coupling, we find that the phases of the coupled quasi-cycles synchronize (establish a relatively constant relationship, or phase lock) rapidly at coupling strengths lower than those required to produce spatial patterns of their amplitudes. In two dimensions the amplitude patterns form more quickly, but there remain parameter regimes in which phase synchronization patterns form without being accompanied by clear amplitude patterns. At higher coupling strengths we find patterns both of phase synchronization and of amplitude (resembling Turing patterns) corresponding to the patterns of phase synchronization. Specific properties of these patterns are controlled by the parameters of the reaction and of the Mexican Hat coupling.

q-bio.NC↗

arXiv2019

Noise Sharing and Mexican Hat Coupling in a Stochastic Neural Field

A diffusion-type coupling operator biologically significant in neuroscience is a difference of Gaussian functions (Mexican Hat operator) used as a spatial-convolution kernel. We are interested in pattern formation by \emph{stochastic} neural field equations, a class of space-time stochastic differential-integral equations using the Mexican Hat kernel. We explore, quantitatively, how the parameters that control the shape of the coupling kernel, coupling strength, and aspects of spatially-smoothed space-time noise, influence the pattern in the resulting evolving random field. We confirm that a spatial pattern that is damped in time in a deterministic system may be sustained and amplified by stochasticity. We find that spatially-smoothed noise alone causes pattern formation even without direct spatial coupling. Our analysis of the interaction between coupling and noise sharing allows us to determine parameter combinations that are optimal for the formation of spatial pattern.

q-bio.NC↗

arXiv2017

The roles of direct and environmental transmission in stochastic avian flu epidemic recurrence

We present an analysis of an avian flu model that yields insight into the role of different transmission routes in the recurrence of avian influenza epidemics. Recent modelling work on avian influenza in wild bird populations takes into account demographic stochasticity and highlights the importance of environmental transmission in determining the outbreak periodicity, but only for a weak between-host transmission rate. We determine the relative contribution of environmental and direct transmission routes to the intensity of outbreaks. We use an approximation method to simulate noise sustained oscillations in a stochastic avian flu model with environmental and direct transmission routes. We see that the oscillations are governed by the product of a rotation and a slowly varying standard Ornstein-Uhlenbeck process (i.e., mean-reverting process). The intrinsic frequency of the damped deterministic version of the system predicts the dominant period of outbreaks. We show, using analytic computation of the intrinsic frequency and theoretical power spectral density, that the outbreak periodicity can be explained in terms of either or both types of transmission.The amplitude of outbreaks tends to be high when both types of transmission are strong.

q-bio.PE↗

arXiv2016

Fluctuation theorems and 1/f noise from a simple matrix

Here we present a model for a small system combined with an explicit entropy bath that is comparably small. The dynamics of the model is defined by a simple matrix, M. Each row of M corresponds to a macrostate of the system, e.g. net alignment, while the elements in the row represent microstates. The constant number of elements in each row ensures constant entropy, which allows reversible fluctuations, similar to information theory where a constant number of bits allows reversible computations. Many elements in M come from the microstates of the system, but many others come from the bath. Bypassing the bath states yields fluctuations that exhibit standard white noise; whereas with bath states the power spectral density varies as S(f)~1/f over a wide range of frequencies, f. Thus, the explicit entropy bath is the mechanism of 1/f noise in this model. Both forms of the model match Crooks' fluctuation theorem exactly, indicating that the theorem applies not only to infinite reservoirs, but also to finite-sized baths. The model is used to analyze measurements of 1/f-like noise from a sub-micron tunnel junction.

cond-mat.stat-mech↗

arXiv2015

A Kuramoto coupling of quasi-cycle oscillators

A family of stochastic processes has quasi-cycle oscillations if the oscillations are sustained by noise. For such a family we define a Kuramoto-type coupling of both phase and amplitude processes. We find that synchronization, as measured by the phase-locking index, increases with coupling strength, and appears, for larger network sizes, to have a critical value, at which the network moves relatively abruptly from incoherence to complete synchonization as in Kuramoto couplings of fixed amplitude oscillators. We compare several aspects of the dynamics of unsynchronized and highly synchronized networks. Our motivation comes from synchronization in neural networks.

math.DS↗