Self-organized sulfide-driven traveling pulses shape seagrass meadows.

Seagrasses provide multiple ecosystem services and act as intense carbon sinks in coastal regions around the globe but are threatened by multiple anthropogenic pressures, leading to enhanced seagrass mortality that reflects in the spatial self-organization of the meadows. Spontaneous spatial vegetation patterns appear in such different ecosystems as drylands, peatlands, salt marshes, or seagrass meadows, and the mechanisms behind this phenomenon are still an open question in many cases. Here, we report on the formation of vegetation traveling pulses creating complex spatiotemporal patterns and rings in Mediterranean seagrass meadows. We show that these structures emerge due to an excitable behavior resulting from the coupled dynamics of vegetation and porewater hydrogen sulfide, toxic to seagrass, in the sediment. The resulting spatiotemporal patterns resemble those formed in other physical, chemical, and biological excitable media, but on a much larger scale. Based on theory, we derive a model that reproduces the observed seascapes and predicts the annihilation of these circular structures as they collide, a distinctive feature of excitable pulses. We show also that the patterns in field images and the empirically resolved radial profiles of vegetation density and sediment sulfide concentration across the structures are consistent with predictions from the theoretical model, which shows these structures to have diagnostic value, acting as a harbinger of the terminal state of the seagrass meadows prior to their collapse.

Pulsed Interaction Signals as a Route to Biological Pattern Formation.

We identify a mechanism for biological spatial pattern formation arising when the signals that mediate interactions between individuals in a population have pulsed character. Our general population-signal framework shows that while for a slow signal-dynamics limit no pattern formation is observed for any values of the model parameters, for a fast limit, on the contrary, pattern formation can occur. Furthermore, at these limits, our framework reduces, respectively, to reaction-diffusion and spatially nonlocal models, thus bridging these approaches.

Characteristic signatures of Northern Hemisphere blocking events in a Lagrangian flow network representation of the atmospheric circulation.

In the past few decades, boreal summers have been characterized by an increasing number of extreme weather events in the Northern Hemisphere extratropics, including persistent heat waves, droughts and heavy rainfall events with significant social, economic, and environmental impacts. Many of these events have been associated with the presence of anomalous large-scale atmospheric circulation patterns, in particular, persistent blocking situations, i.e., nearly stationary spatial patterns of air pressure. To contribute to a better understanding of the emergence and dynamical properties of such situations, we construct complex networks representing the atmospheric circulation based on Lagrangian trajectory data of passive tracers advected within the atmospheric flow. For these Lagrangian flow networks, we study the spatial patterns of selected node properties prior to, during, and after different atmospheric blocking events in Northern Hemisphere summer. We highlight the specific network characteristics associated with the sequence of strong blocking episodes over Europe during summer 2010 as an illustrative example. Our results demonstrate the ability of the node degree, entropy, and harmonic closeness centrality based on outgoing links to trace important spatiotemporal characteristics of atmospheric blocking events. In particular, all three measures capture the effective separation of the stationary pressure cell forming the blocking high from the normal westerly flow and the deviation of the main atmospheric currents around it. Our results suggest the utility of further exploiting the Lagrangian flow network approach to atmospheric circulation in future targeted diagnostic and prognostic studies.

Accounting for ocean connectivity and hydroclimate in fish recruitment fluctuations within transboundary metapopulations.

Marine resources stewardships are progressively becoming more receptive to an effective incorporation of both ecosystem and environmental complexities into the analytical frameworks of fisheries assessment. Understanding and predicting marine fish production for spatially and demographically complex populations in changing environmental conditions is however still a difficult task. Indeed, fisheries assessment is mostly based on deterministic models that lack realistic parameterizations of the intricate biological and physical processes shaping recruitment, a cornerstone in population dynamics. We use here a large metapopulation of a harvested fish, the European hake (Merluccius merluccius), managed across transnational boundaries in the northwestern Mediterranean, to model fish recruitment dynamics in terms of physics-dependent drivers related to dispersal and survival. The connectivity among nearby subpopulations is evaluated by simulating multi-annual Lagrangian indices of larval retention, imports, and self-recruitment. Along with a proxy of the regional hydroclimate influencing early life stages survival, we then statistically determine the relative contribution of dispersal and hydroclimate for recruitment across contiguous management units. We show that inter-annual variability of recruitment is well reproduced by hydroclimatic influences and synthetic connectivity estimates. Self-recruitment (i.e., the ratio of retained locally produced larvae to the total number of incoming larvae) is the most powerful metric as it integrates the roles of retained local recruits and immigrants from surrounding subpopulations and is able to capture circulation patterns affecting recruitment at the scale of management units. We also reveal that the climatic impact on recruitment is spatially structured at regional scale due to contrasting biophysical processes not related to dispersal. Self-recruitment calculated for each management unit explains between 19% and 32.9% of the variance of recruitment variability, that is much larger than the one explained by spawning stock biomass alone, supporting an increase of consideration of connectivity processes into stocks assessment. By acknowledging the structural and ecological complexity of marine populations, this study provides the scientific basis to link spatial management and temporal assessment within large marine metapopulations. Our results suggest that fisheries management could be improved by combining information of physical oceanography (from observing systems and operational models), opening new opportunities such as the development of short-term projections and dynamic spatial management.

Inhomogeneities and caustics in the sedimentation of noninertial particles in incompressible flows.

In an incompressible flow, fluid density remains invariant along fluid element trajectories. This implies that the spatial distribution of non-interacting noninertial particles in such flows cannot develop density inhomogeneities beyond those that are already introduced in the initial condition. However, in certain practical situations, density is measured or accumulated on (hyper-) surfaces of dimensionality lower than the full dimensionality of the flow in which the particles move. An example is the observation of particle distributions sedimented on the floor of the ocean. In such cases, even if the initial distribution of noninertial particles is uniform but its support is finite, advection in an incompressible flow will give rise to inhomogeneities in the observed density. In this paper, we analytically derive, in the framework of an initially homogeneous particle sheet sedimenting toward a bottom surface, the relationship between the geometry of the flow and the emerging distribution. From a physical point of view, we identify the two processes that generate inhomogeneities to be the stretching within the sheet and the projection of the deformed sheet onto the target surface. We point out that an extreme form of inhomogeneity, caustics, can develop for sheets. We exemplify our geometrical results with simulations of particle advection in a simple kinematic flow, study the dependence on various parameters involved, and illustrate that the basic mechanisms work similarly if the initial (homogeneous) distribution occupies a more general region of finite extension rather than a sheet.

Introduction to Focus Issue: Complex network perspectives on flow systems.

During the last few years, complex network approaches have demonstrated their great potentials as versatile tools for exploring the structural as well as dynamical properties of dynamical systems from a variety of different fields. Among others, recent successful examples include (i) functional (correlation) network approaches to infer hidden statistical interrelationships between macroscopic regions of the human brain or the Earth's climate system, (ii) Lagrangian flow networks allowing to trace dynamically relevant fluid-flow structures in atmosphere, ocean or, more general, the phase space of complex systems, and (iii) time series networks unveiling fundamental organization principles of dynamical systems. In this spirit, complex network approaches have proven useful for data-driven learning of dynamical processes (like those acting within and between sub-components of the Earth's climate system) that are hidden to other analysis techniques. This Focus Issue presents a collection of contributions addressing the description of flows and associated transport processes from the network point of view and its relationship to other approaches which deal with fluid transport and mixing and/or use complex network techniques.

Clustering coefficient and periodic orbits in flow networks.

We show that the clustering coefficient, a standard measure in network theory, when applied to flow networks, i.e., graph representations of fluid flows in which links between nodes represent fluid transport between spatial regions, identifies approximate locations of periodic trajectories in the flow system. This is true for steady flows and for periodic ones in which the time interval τ used to construct the network is the period of the flow or a multiple of it. In other situations, the clustering coefficient still identifies cyclic motion between regions of the fluid. Besides the fluid context, these ideas apply equally well to general dynamical systems. By varying the value of τ used to construct the network, a kind of spectroscopy can be performed so that the observation of high values of mean clustering at a value of τ reveals the presence of periodic orbits of period 3τ, which impact phase space significantly. These results are illustrated with examples of increasing complexity, namely, a steady and a periodically perturbed model two-dimensional fluid flow, the three-dimensional Lorenz system, and the turbulent surface flow obtained from a numerical model of circulation in the Mediterranean sea.

Flow networks: a characterization of geophysical fluid transport.

We represent transport between different regions of a fluid domain by flow networks, constructed from the discrete representation of the Perron-Frobenius or transfer operator associated to the fluid advection dynamics. The procedure is useful to analyze fluid dynamics in geophysical contexts, as illustrated by the construction of a flow network associated to the surface circulation in the Mediterranean sea. We use network-theory tools to analyze the flow network and gain insights into transport processes. In particular, we quantitatively relate dispersion and mixing characteristics, classically quantified by Lyapunov exponents, to the degree of the network nodes. A family of network entropies is defined from the network adjacency matrix and related to the statistics of stretching in the fluid, in particular, to the Lyapunov exponent field. Finally, we use a network community detection algorithm, Infomap, to partition the Mediterranean network into coherent regions, i.e., areas internally well mixed, but with little fluid interchange between them.

Dominant transport pathways in an atmospheric blocking event.

A Lagrangian flow network is constructed for the atmospheric blocking of Eastern Europe and Western Russia in summer 2010. We compute the most probable paths followed by fluid particles, which reveal the Omega-block skeleton of the event. A hierarchy of sets of highly probable paths is introduced to describe transport pathways when the most probable path alone is not representative enough. These sets of paths have the shape of narrow coherent tubes flowing close to the most probable one. Thus, even when the most probable path is not very significant in terms of its probability, it still identifies the geometry of the transport pathways.

Disentangling the Influence of Mutation and Migration in Clonal Seagrasses Using the Genetic Diversity Spectrum for Microsatellites.

The recurrent lack of isolation by distance reported at regional scale in seagrass species was recently suggested to stem from stochastic events of large-scale dispersal. We explored the usefulness of phylogenetic information contained in microsatellite loci to test this hypothesis by using the Genetic Diversity Spectrum (GDS) on databases containing, respectively, 7 and 9 microsatellites genotypes for 1541 sampling units of Posidonia oceanica and 1647 of Cymodocea nodosa The simultaneous increase of microsatellite and geographic distances that emerges reveals a coherent pattern of isolation by distance in contrast to the chaotic pattern previously described using allele frequencies, in particular, for the long-lived P. oceanica These results suggest that the lack of isolation by distance, rather than the resulting from rare events of large-scale dispersal, reflects at least for some species a stronger influence of mutation over migration at the scale of the distribution range. The global distribution of genetic polymorphism may, therefore, result predominantly from ancient events of step-by-step (re)colonization followed by local recruitment and clonal growth, rather than contemporary gene flow. The analysis of GDS appears useful to unravel the evolutionary forces influencing the dynamics and evolution at distinct temporal and spatial scales by accounting for phylogenetic information borne by microsatellites, under an appropriate mutation model. This finding adds nuance to the generalization of the influence of large-scale dispersal on the dynamics of seagrasses.

Clustering determines who survives for competing Brownian and Lévy walkers.

The competition between two ecologically similar species that use the same resources and differ from each other only in the type of spatial motion they undergo is studied. The latter is assumed to be described either by Brownian motion or Lévy flights. Competition is taken into account by assuming that individuals reproduce in a density-dependent fashion. It is observed that no influence of the type of motion occurs when the two species are in a well-mixed unstructured state. However, as soon as the species develop spatial clustering, the one forming more concentrated clusters gets a competitive advantage and eliminates the other. A similar competitive advantage would occur between walkers of the same type but with different diffusivities if this leads also to different clustering. The coexistence of both species is also possible under certain conditions.

Diversity and noise effects in a model of homeostatic regulation of the sleep-wake cycle.

Recent advances in sleep neurobiology have allowed development of physiologically based mathematical models of sleep regulation that account for the neuronal dynamics responsible for the regulation of sleep-wake cycles and allow detailed examination of the underlying mechanisms. Neuronal systems in general, and those involved in sleep regulation in particular, are noisy and heterogeneous by their nature. It has been shown in various systems that certain levels of noise and diversity can significantly improve signal encoding. However, these phenomena, especially the effects of diversity, are rarely considered in the models of sleep regulation. The present paper is focused on a neuron-based physiologically motivated model of sleep-wake cycles that proposes a novel mechanism of the homeostatic regulation of sleep based on the dynamics of a wake-promoting neuropeptide orexin. Here this model is generalized by the introduction of intrinsic diversity and noise in the orexin-producing neurons, in order to study the effect of their presence on the sleep-wake cycle. A simple quantitative measure of the quality of a sleep-wake cycle is introduced and used to systematically study the generalized model for different levels of noise and diversity. The model is shown to exhibit a clear diversity-induced resonance: that is, the best wake-sleep cycle turns out to correspond to an intermediate level of diversity at the synapses of the orexin-producing neurons. On the other hand, only a mild evidence of stochastic resonance is found, when the level of noise is varied. These results show that disorder, especially in the form of quenched diversity, can be a key-element for an efficient or optimal functioning of the homeostatic regulation of the sleep-wake cycle. Furthermore, this study provides an example of a constructive role of diversity in a neuronal system that can be extended beyond the system studied here.

Optimal wave reflection as a mechanism for seagrass self-organization.

Ecosystems threatened by climate change can boost their resilience by developing spatial patterns. Spatially regular patterns in wave-exposed seagrass meadows are attributed to self-organization, yet underlying mechanisms are not well understood. Here, we show that these patterns could emerge from feedbacks between wave reflection and seagrass-induced bedform growth. We derive a theoretical model for surface waves propagating over a growing seagrass bed. Wave-induced bed shear stress shapes bedforms which, in turn, trigger wave reflection. Numerical simulations show seagrass pattern development once wave forcing exceeds a critical amplitude. In line with Mediterranean Sea field observations, these patterns have half the wavelength of the forcing waves. Our results raise the hypothesis that pattern formation optimizes the potential of seagrass meadows to reflect wave energy, and a clear direction for future field campaigns. If wave-reflecting pattern formation increases ecosystem resilience under globally intensifying wave climates, these ecosystems may inspire nature-based coastal protection measures.

Network percolation provides early warnings of abrupt changes in coupled oscillatory systems: An explanatory analysis.

Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In particular, percolation properties of correlation networks have been employed to identify early warning signals of critical transitions. In this work, we further investigate the corresponding potential of percolation measures for the anticipation of different types of sudden shifts in the state of coupled irregularly oscillating systems. As a paradigmatic model system, we study the dynamics of a ring of diffusively coupled noisy FitzHugh-Nagumo oscillators and show that, when the oscillators are nearly completely synchronized, the percolation-based precursors successfully provide very early warnings of the rapid switches between the two states of the system. We clarify the mechanisms behind the percolation transition by separating global trends given by the mean-field behavior from the synchronization of individual stochastic fluctuations. We then apply the same methodology to real-world data of sea surface temperature anomalies during different phases of the El Niño-Southern Oscillation. This leads to a better understanding of the factors that make percolation precursors effective as early warning indicators of incipient El Niño and La Niña events.

Top marine predators track Lagrangian coherent structures.

Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great Frigatebird. Using a newly developed dynamic concept, the finite-size Lyapunov exponent (FSLE), we identified Lagrangian coherent structures (LCSs) present in the surface flow in the channel over a 2-month observation period (August and September 2003). By comparing seabird satellite positions with LCS locations, we demonstrate that frigatebirds track precisely these structures in the Mozambique Channel, providing the first evidence that a top predator is able to track these FSLE ridges to locate food patches. After comparing bird positions during long and short trips and different parts of these trips, we propose several hypotheses to understand how frigatebirds can follow these LCSs. The birds might use visual and/or olfactory cues and/or atmospheric current changes over the structures to move along these biologic corridors. The birds being often associated with tuna schools around foraging areas, a thorough comprehension of their foraging behavior and movement during the breeding season is crucial not only to seabird ecology but also to an appropriate ecosystemic approach to fisheries in the channel.

Structured interactions as a stabilizing mechanism for competitive ecological communities.

How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from theoretical ecology to mathematics and physics. In this context, modeling the stable coexistence of species competing for limited resources is a particularly challenging task. From a mathematical point of view, coexistence in competitive dynamics can be achieved when dominance among species forms intransitive loops. However, these relationships usually lead to species' relative abundances neutrally cycling without converging to a stable equilibrium. Although in recent years several mechanisms have been proposed, models able to explain species coexistence in competitive communities are still limited. Here we identify locality in the interactions as one of the simplest mechanisms leading to stable species coexistence. We consider a simplified ecosystem where individuals of each species lay on a spatial network and interactions are possible only between nodes within a certain distance. Varying such distance allows to interpolate between local and global competition. Our results demonstrate, within the scope of our model, that species coexist reaching a stable equilibrium when two conditions are met: individuals are embedded in space and can only interact with other individuals within a short distance. On the contrary, when one of these ingredients is missing, large oscillations and neutral cycles emerge.

Scaling properties of protein family phylogenies.

BACKGROUND: One of the classical questions in evolutionary biology is how evolutionary processes are coupled at the gene and species level. With this motivation, we compare the topological properties (mainly the depth scaling, as a characterization of balance) of a large set of protein phylogenies with those of a set of species phylogenies. RESULTS: The comparative analysis between protein and species phylogenies shows that both sets of phylogenies share a remarkably similar scaling behavior, suggesting the universality of branching rules and of the evolutionary processes that drive biological diversification from gene to species level. In order to explain such generality, we propose a simple model which allows us to estimate the proportion of evolvability/robustness needed to approximate the scaling behavior observed in the phylogenies, highlighting the relevance of the robustness of a biological system (species or protein) in the scaling properties of the phylogenetic trees. CONCLUSIONS: The invariance of the scaling properties at levels spanning from genes to species suggests that rules that govern the incapability of a biological system to diversify are equally relevant both at the gene and at the species level.

Network analysis identifies weak and strong links in a metapopulation system.

The identification of key populations shaping the structure and connectivity of metapopulation systems is a major challenge in population ecology. The use of molecular markers in the theoretical framework of population genetics has allowed great advances in this field, but the prime question of quantifying the role of each population in the system remains unresolved. Furthermore, the use and interpretation of classical methods are still bounded by the need for a priori information and underlying assumptions that are seldom respected in natural systems. Network theory was applied to map the genetic structure in a metapopulation system by using microsatellite data from populations of a threatened seagrass, Posidonia oceanica, across its whole geographical range. The network approach, free from a priori assumptions and from the usual underlying hypotheses required for the interpretation of classical analyses, allows both the straightforward characterization of hierarchical population structure and the detection of populations acting as hubs critical for relaying gene flow or sustaining the metapopulation system. This development opens perspectives in ecology and evolution in general, particularly in areas such as conservation biology and epidemiology, where targeting specific populations is crucial.

Network and geometric characterization of three-dimensional fluid transport between two layers.

We consider transport in a fluid flow of arbitrary complexity but with a dominant flow direction. One of the situations in which this occurs is when describing by an effective flow the dynamics of sufficiently small particles immersed in a turbulent fluid and vertically sinking because of their weight. We develop a formalism characterizing the dynamics of particles released from one layer of fluid and arriving in a second one after traveling along the dominant direction. The main ingredient in our study is the definition of a two-layer map that describes the Lagrangian transport between both layers. We combine geometric approaches and probabilistic network descriptions to analyze the two-layer map. From the geometric point of view, we express the properties of lines, surfaces, and densities transported by the flow in terms of singular values related to Lyapunov exponents, and define a specific quantifier, the finite depth Lyapunov exponent. Within the network approach, degrees and an entropy are considered to characterize transport. We also provide relationships between both methodologies. The formalism is illustrated with numerical results for a modification of the ABC flow, a model commonly studied to characterize three-dimensional chaotic advection.

Landscape-induced spatial oscillations in population dynamics.

We study the effect that disturbances in the ecological landscape exert on the spatial distribution of a population that evolves according to the nonlocal FKPP equation. Using both numerical and analytical techniques, we characterize, as a function of the interaction kernel, the three types of stationary profiles that can develop near abrupt spatial variations in the environmental conditions vital for population growth: sustained oscillations, decaying oscillations and exponential relaxation towards a flat profile. Through the mapping between the features of the induced wrinkles and the shape of the interaction kernel, we discuss how heterogeneities can reveal information that would be hidden in a flat landscape.