arXiv subjects

Luis F. Gordillo

Publications and source records attributed to Luis F. Gordillo.

6 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

The Curse of Black Sigatoka: A Backward Bifurcation Perspective

Black Sigatoka disease (BSD), also known as black leaf streak disease, is an airborne fungal infection caused by \textit{Pseudocercospora fijiensis} that severely impacts global banana and plantain production. Its persistence and resistance to eradication make it one of the most challenging plant diseases to manage. In this paper, we propose a deterministic pathogen-host model to describe BSD dynamics. Due to dual transmission pathways (ascospores and conidia) and mate limitation in sexual reproduction, the model exhibits a backward bifurcation: a stable endemic equilibrium coexists with the disease-free equilibrium for certain parameter values in which the basic reproduction number, $\mathcal{R}_0$, is less than 1. This phenomenon explains why control strategies that solely reduce $\mathcal{R}_0$ below one may fail. For the backward bifurcation regime, we perform sensitivity analysis of the endemic equilibrium using normalized forward sensitivity indices, Latin Hypercube Sampling, and Partial Rank Correlation Coefficients. Results indicate that effective control must extend beyond $\mathcal{R}_0$ reduction and prioritize (1) limiting production of new susceptible leaves during high-risk periods and (2) developing and deploying disease-resistant plant varieties. To incorporate transmission variability, we also formulate a stochastic version of the model using the Stochastic Simulation Algorithm (SSA). Extensive numerical simulations compare stochastic realizations with deterministic predictions and quantify variability in disease dynamics. To identify the principal drivers of persistence and variability, we analyze the endemic equilibrium using Sobol's variance-based sensitivity method, which highlights the role of nonlinear parameter interactions in shaping variability.

q-bio.PE↗

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↗

arXiv2021

Stability of steady state solutions in a predator-prey model with density-dependent diffusion

In this note we present a study of the solutions associated to a particular spatial extension of the Rosenzweig-MacArthur model for predator and prey. The analysis presented here shows that positive steady state solutions emerge via a transcritical bifurcation mechanism, in accordance with the insight obtained from previous numerical and analytical results. In the model under discussion, prey is assumed to move avoiding crowds via a density-dependent diffusion and also incorporates the existence of a refuge zone, where predators cannot consume prey. Saturation in prey consumption is also included through a Holling type II functional response.

math.DS↗