Pulsed interactions unify reaction-diffusion and spatial nonlocal models for biological pattern formation

Abstract

The emergence of a spatially-organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how self-organization is triggered, namely, reaction-diffusion and spatially nonlocal models. Nevertheless, these models implicitly assume smooth propagation scenarios, neglecting that individuals many times interact by exchanging short and abrupt pulses of the mediating substance. A recently proposed framework advances in the direction of properly accounting for these short-scale fluctuations by applying a coarse-graining procedure on the pulse dynamics. In this paper, we generalize the coarse-graining procedure and apply the extended formalism to new scenarios in which mediators influence individuals' reproductive success or their motility. We show that, in the slow- and fast-mediator limits, pulsed interactions recover, respectively, the reaction-diffusion and nonlocal models, providing a mechanistic connection between them. Furthermore, at each limit, the spatial stability condition is qualitatively different, leading to a timescale-induced transition where spatial patterns emerge as mediator dynamics becomes sufficiently fast.

References in corpus (16)

• Novel type of phase transition in a system of self-driven particles
• Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
• Superfluid transport of information in turning flocks of starlings
• Arrested phase separation in reproducing bacteria: a generic route to pattern formation?
• Non-local Interaction Effects on Pattern Formation in Population Dynamics
• Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates
• Species clustering in competitive Lotka-Volterra models
• Optimizing the search for resources by sharing information: Mongolian gazelles as a case study
• Strong-coupling dynamics of a multi-cellular chemotactic system
• Vegetation pattern formation in semiarid systems without facilitative mechanisms
• Fluctuations impact on a pattern-forming model of population dynamics with non-local interactions
• Integrating theory and experiments to link local mechanisms and ecosystem-level consequences of vegetation patterns in drylands
• Motility of \textit{Escherichia coli} in a quasi-two-dimensional porous medium
• Critical patch size reduction by heterogeneous diffusion
• Spatial eco-evolutionary feedbacks mediate coexistence in prey-predator systems
• Pulsed interaction signals as a route to biological pattern formation