Self-organized sulfide-driven traveling pulses shape seagrass meadows

Significance

Vegetation forms surprising patterns at the landscape level due to the interaction among plants. While in semiarid regions, biomass–water feedbacks are the main driving, in coastal marine ecosystems, the mechanisms at play are largely an open question. In this work, we report the discovery of traveling pulses of vegetation forming strikingly complex seascapes in Posidonia oceanica meadows and prove on the basis of mathematical modeling, field measurements, and historical aerial images that these spatiotemporal structures arise due to the excitable dynamics mediated by the accumulation of sulfides in the sediment, which are toxic to the plants. A remarkable feature we have observed and reproduced is the collision and subsequent annihilation of two vegetation traveling pulses, a characteristic behavior of excitable media.

Abstract

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.

Spatial patterns of vegetation, observed across such contrasting habitats as semiarid ecosystems (1, 2), peatlands (3), salt marshes (4), and seagrass meadows (5), have important implications for the functionality of ecosystems (6–8). Nevertheless, the dynamics underlying the spatial distribution of vegetation are only partially understood mainly because the mechanisms that drive the spatiotemporal evolution include long-range spatial interactions, often referred to as scale-dependent feedbacks (SDF) (9, 10), which are difficult to resolve. Very large-scale patterns attributable to SDF are also observed in cold-water coral reefs (11).

In general, when reproduction and mortality are in approximate balance, SDF become important enough to drive the evolution of the system and give rise to the formation of regular patterns of vegetation as striking as the Namibian (2, 12) and Australian (1) fairy circles. Patchy vegetation in Sudan, bands in Niger, and labyrinths in northern Negev (13–17) are other examples of pattern formation in arid ecosystems. Vegetation patterns in marine environments have been much less studied, at least from the theoretical point of view (18–20). Some examples have been reported in seagrass meadows, including banded and patchy vegetation associated with sand dune migration (18, 21), leopard skin patterns (22), and striped patterns (23). The largest seagrass pattern, mostly consisting in periodically arranged bare circular holes extending over kilometers, has been reported for Mediterranean Posidonia oceanica meadows around the Balearic Islands (Pollença and Alcudia bays) (5). The mechanisms behind the SDF responsible for self-organization remain speculative and largely unexplored in all these cases.

Beyond periodic patterns, more complex spatiotemporal structures have recently been reported. Grazing, for instance, can induce spiral patterns in high-latitude wetlands (24). Autotoxicity has also been proposed as an interaction mechanism leading to complex traveling spatiotemporal structures in arid ecosystems (25–27), grasslands (28), and salt marshes (4), underlining the relevance of transient patterns to the understanding of ecosystem dynamics. In shallow waters, rings have been observed in the Danish Kattegat for Zostera marina (29) and on the Corsican coast for P. oceanica (30), but no detailed mechanism of the interaction or comparison between data and theoretical modeling was

reported in those works. In the Danish Kattegat, the rings of vegetation were postulated to result from increased shoot mortality in the center due to sulfide intrusion, which is toxic to seagrass (29) and maybe drive spatial organization in seagrass meadows through a strong coupling between the dynamics of the seagrass and this phytotoxin. In fact, satellite images show that the presence of rings, arches, and spirals occupying regions several hundred meters wide is commonplace in seagrass meadows (Fig. 1). These complex spatiotemporal structures are typically associated with a type of dynamical behavior known as excitability and the formation of traveling pulses (31–34), consisting in this context in bands of vegetation a few meters wide moving at a constant velocity of a few centimeters per year maintaining their shape.

Fig. 1.

Examples of traveling pulses forming rings, arches, and spirals in different seagrass meadows. The satellite image in panel (A) shows rings on the coast of Denmark (54° 54’45.9"N 12° 01’30.0"E). Panel (B) shows ring-like and spiral shapes on the Greek coast (40° 08’28.8"N 23° 22’37.2"E). Panel (C) shows rings on the Corsican coast (42° 40’33.9"N 9° 17’13.6"E). Panel (D) shows arches on the Tunisian coast (33° 14’22.1"N 11° 22’55.9"E). Finally, panel (E) shows rings and arches on the Balearic coast (39° 53’49.4"N 3° 04’54.4"E). Satellite images (A–D) are taken from Google maps. Image (E) is a high-resolution drone image. Further images of the study site on the Balearic coast are available in SI Appendix.

Here, we implement the interaction between seagrass growth and porewater sulfide dynamics in a mathematical model and show that it induces an excitable behavior that can explain the observed patterns. The predicted traveling pulses are consistent with empirical-resolved profiles of vegetation density and sediment sulfide concentration, providing evidence of sulfide as a mediator of spatial interactions leading to seagrass self-organization.

Results and Discussion

Hydrogen sulfide is a byproduct of sulfate reduction by bacteria, which is the dominant metabolism in seagrass sediments when high organic inputs drive them to anoxic conditions (35–37). Essentially, the presence of seagrasses increases the accretion of organic matter within the meadow due to accumulation of seagrass biomass production and enhanced sedimentation of allochthonous organic carbon-rich particles (38, 39). High decomposition of organic matter leads to oxygen consumption, with further organic carbon oxidation due to sulfate-reducing bacteria, which reduce sulfates (SO₄²⁻) into hydrogen sulfide (H₂S). Then, the latter can be absorbed by the roots of neighboring plants and be transported all the way to the leaf meristems and leaves. Sulfide intrusion into plant tissue can inhibit seagrass growth and cause shoot and meristem mortality (29, 37, 40). This negative allelopathic relation established between different parts of the meadow can drive complex spatiotemporal dynamics of the vegetation.

To implement this mechanism in a mathematical model, we first describe seagrass clonal-growth colonization using a partial differential equation for the vegetation density, n, Eq. S1 in SI Appendix derived from the Advection-Branching-Death model (5). It explicitly accounts for the velocity of elongation of the rhizomes, the branching rate (ω_b), and the branching angle that, encoded in the terms with spatial derivatives, allows to determine the spatial and temporal scales of the spreading for different seagrass species using experimentally measured parameters (41). The dynamics of porewater sulfide concentration, S, is modeled through a diffusion equation including the rate of production of sulfides, the rate of removal, and the diffusion of sulfide in space, Eq. S3 in SI Appendix. The coupling between these two equations is introduced bidirectionally. On the one hand, sulfides couple to plant density through the mortality term ω_d(n, S), Eq. S2 in SI Appendix, where mortality increases with sulfide concentration (37) with a proportionality constant γ, that measures the sensitivity of the plant to sulfides. On the other hand, the production of sulfide in the sediment is increased proportionally to the density of dead plants. The intrinsic mortality rate (ω_d0) determined by the typical lifespan of a single shoot in the absence of neighboring plants and the sensitivity of the plant to sulfide concentration (γ) are key parameters to understand the resulting dynamics.

In particular, our model predicts an excitable regime (orange region in Fig. 2) for mortality rates above but close to the critical value for homogeneous meadows to form (blue line in Fig. 2) and a moderate sensitivity to sulfides. In such a regime, due to facilitative effects of moderate vegetation densities, vegetation can grow if it exceeds a critical density n_u^*. Vegetation with densities below this threshold will decay exponentially to zero, while densities larger than n_u^* will allow the vegetation to transiently grow, increasing also the sulfide concentration until a certain point in which mortality overshoots leading to vegetation density to decrease again below n_u^* and then to zero. In this excitable regime, the final state is always bare soil independently of the initial density, but if the initial vegetation is dense enough to overcome the threshold (n_u^*), then the system produces a burst of vegetation before ending up in bare soil. The excitable region is relatively small in parameter space but, thanks to the parameter variability in natural systems, meadows at different locations explore different regions of the phase diagram, some falling in the excitable regime as spotted in the aerial and satellite images (Fig. 1). The bistable regime covers a larger area of the parameter space, many of the Posidonia homogeneous meadows are in this regime as they are often in decline, and the mortality rate is higher than the branching rate (42).

Fig. 2.

Phase diagram of P. oceanica using the dimensionless sensitivity of the plant to sulfide concentration $\gamma \frac{c_s}{\sqrt{{\omega }_{b}b}}$ and mortality rate ω_d0/ω_b as control parameters. The white region corresponds to parameter values where bare soil is the only solution. Blue-shaded areas correspond to parameter regions where the homogeneous populated solution is stable. Darker blue indicates bistability between the populated and unpopulated states. The pink region corresponds to the homogeneous populated solution being unstable to oscillations, while the orange region corresponds to the excitable region emerging from two Takens-Bogdanov (TB) codimension-2 points. Dashed lines indicate the onset of the Turing instability for different values of the sulfide diffusion constant D_s corresponding to different interaction distances $\sqrt{D_s/{\delta }_s}=0.5,1,10$ m. Other parameters, as explained in ((5, 41)), are: ω_b = 0.6 y⁻¹, a = 15 cm² y⁻¹, b = 6.67 cm⁴ y⁻¹, d₀ = 31.1 cm² y⁻¹, d₁ = 1.04 × 10² cm⁴ y⁻¹, c_s = 30.6 μM cm², δ_s = 3.6 × 10⁻² y⁻¹, δ_o = 6 × 10⁻² y⁻¹ cm², P_s = 1.13 μM y⁻¹. For more details on the parameters, SI Appendix.

Excitability has important implications for the spatiotemporal dynamics of vegetation, leading to the formation of traveling pulses and rings (31, 32). In this regime, a dense-enough spot of vegetation that experiences an excitable excursion of growth and decay in its center may excite the growth of vegetation at the edges, where the sulfide concentration is low, in such a way that, while vegetation dies at the center due to the accumulation of sulfide, it grows outward generating a traveling pulse that propagates at constant velocity and maintaining shape. If the initial condition was more or less round, the traveling pulse forms a ring, which in some cases may break down into spirals. As a result of this dynamics, a patch of homogeneous vegetation, which experiences an environmental perturbation such that mortality changes to a value inside the excitable regime, will form a vegetation ring that expands radially in a pulse leaving bare soil with a high concentration of sulfide behind. After some time, sulfide will decay in the center of the ring, as the supply of labile organic matter will become rate-limiting, allowing the growth of new vegetation, which can be from the same clone expanding from other parts within the ring or from new recruits. The model allows to attribute the appearance of these spatial structures to a rate of sulfide removal smaller than the branching rate of the plant, a condition that can be approximately calculated for the existence of the excitable region, SI Appendix, Eq. S8. This suggests that vegetation rings may be likely to appear in shallow waters with carbonate sediments where clonal growth through branching is faster than in deeper regions and sulfide removal is low relative to production.

The behavior of excitable pulses forming rings is shown in Fig. 3, where we compare numerical simulations of our model with aerial photographs of the coast of the Balearic Islands (Pollena bay, Mallorca) dating back as far as 1973 and empirical data retrieved from in situ sampling of the vegetation and sediment sulfides in this area. The observed historical evolution of the vegetation (Fig. 3K–N) is compatible with the excitable behavior predicted by our model. In 1973, dense patches of Posidonia were observed, which were subsequently emptied in their core, leading to two expanding vegetation rings, which collided between 2002 and 2010. The collision of two excitable pulses leads to their annihilation, as the high sulfide concentration behind each pulse does not allow the other to continue to advance, leading to their loss and merging of the two rings as in the 2021 image (Fig. 3N). Other collisions are expected to happen in the following years (Fig. 1E).

Fig. 3.

Excitable rings of P. oceanica. Panels (A–E) and (F–J) show numerical simulations starting from an initial condition resembling the initial distribution of vegetation from the orthophoto in panel (K) showing the time evolution of the vegetation and the annihilation of two pulses after colliding. The simulations are performed under spatially homogeneous mortality (A–E) and the heterogeneous (F–J) mortality shown in panel (O). Panels (K–N) show ortophotos of different years in which the evolution of the vegetation can be appreciated as well as the annihilation predicted for colliding excitable pulses. Panel (P) shows the comparison between experimental data and the theoretical radial profile of a ring. In this plot, the pulse is traveling to the right. Vegetation density is represented in green and porewater sulfide in orange. The experimental data taken along different transects from six rings are represented using dots, and the smoothed data from local weighted scatterplot smoothing (LOWESS) using dashed lines. All transects have been aligned with the inner edge of the vegetation ring, and the origin of the r coordinate is set at the first measured position inside the ring. The theoretical vegetation and sulfide radial profiles of a ring obtained from our model are shown with solid lines. Numerical simulations are performed for the same set of parameters used in Fig. 2 with ω_d0 = 3.88 × 10⁻¹ y⁻¹, γ = 7.19 × 10⁻³ μ M⁻¹ y⁻¹ ($\frac{{\omega }_{d0}}{{\omega }_b}=6.46\times {10}^{-1}$, $\gamma \frac{c_s}{\sqrt{{\omega }_{b}b}}=1.1\times {10}^{-1}$ in Fig. 2), and D_s = 3.6 cm² y⁻¹. Movies of the time evolution are available in SI Appendix.

Numerical simulations of the model reproduce remarkably close the observed dynamics of the seagrass meadow. With homogeneous parameters (Fig. 3A–E), the P. oceanica rings expand seamlessly at constant velocity and without changing shape until they collide. Spatial variability (Fig. 3F–J) introduces deformities in the rings, even breaking them at some points, as observed in the real images. In this case, plants can regrow in the regions of lower mortality, creating new vegetation patches inside and outside the rings. In these simulations, we take the sensitivity of the plants to the sulfide concentration to be γ = 7.19 × 10⁻³ μM⁻¹ y⁻¹, equivalent to a mortality rate of 0.719% per year for each μM of sulfide in the sediment porewaters, compatible with values previously obtained in the literature (37), and ω_d0 = 3.88 × 10⁻¹ y⁻¹ inside the excitable region (Fig. 2). The diffusion length D_s = 3.6 cm² y⁻¹ and the decay rate δ_s = 3.6  × 10⁻²y⁻¹ of sulfides have been adjusted to fit the observations, while the rest of the parameters take values derived from the literature (SI Appendix). The speed of the pulses predicted by the model (2.9 cm y⁻¹), which is mainly determined by the elongation rate of the rhizome, is consistent with the velocity of progression of these rings measured from historical images.

Transects of shoot density and sediment sulfide concentration measured across six rings of P. oceanica found in Pollena Bay (Fig. 1E) also show an excellent agreement between the profile of vegetation density predicted by the model (dark green line in Fig. 3P) and the empirical data (green dashed line in Fig. 3P), exhibiting the same asymmetry with a more abrupt transition outward the ring as compared to the inner part, which is consistent with a type I traveling pulse (34).

The measured sediment sulfide concentration shows the presence of this phytotoxin along all the radial profile, with higher concentration behind the traveling pulses and largely agreeing with the simulated radial profile of sulfide concentration (Fig. 3P). Most observed sediment sulfide concentrations at the time measurements were conducted (summer 2021) exceed the threshold (10 μM) to enhance high shoot mortality in P. oceanica (37). Furthermore, the natural abundance of δ³⁴S in P. oceanica leaves was below 20.5‰ (δ³⁴S_in = 17.36 ± 0.52 ‰, δ³⁴S_out = 15.99 ± 0.55‰) revealing that the plants suffered sulfide intrusion that would have damaged rhizome–leaf meristems (40) during leaf life span (303 d, ref. (43)), confirming the interaction of the seagrass dynamics and the sulfide in the sediment. The very high concentrations of sulfide observed in bare sediment (Fig. 3P) and the detection of sulfide intrusion in leaves at the seagrass margins indicate that this interaction at these locations may be sometimes masked by an external supply of organic matter fueling the production of sediment sulfide. Indeed, inputs of seston to sediment carbon pools have increased in this bay during the past century (44). Moreover, while shoot density dynamics are rather stable over time due to the slow turnover of the shoot population (< 0.1 y⁻¹) (45), sediment sulfide turnover in P. oceanica sediments is very fast (> 1 d⁻¹) (46), implying that sulfide concentrations are expected to fluctuate and be highly variable over time (Fig. 3P).

We cannot discard additional mechanisms contributing to the coupled dynamics of vegetation and sulfides not included in the model. Besides root oxygen release into the sediments through diffusion from the water column

and, at daylight, also from photosynthesis (47), that can oxidize sulfide neutralizing its toxicity, seagrasses can also transfer oxygen through the rhizome from the older

shoots to the rhizome apices (47) located mainly at the leading part of the vegetation front. This could provide some additional resistance to apical meristems against

sulfides, allowing the vegetation to overcome temporally high concentrations.

These results provide evidence of sulfides as a source of nonlinear dynamics and spatial interactions leading to the formation of expanding rings. Our simple model predicts also other self-organized regimes such as periodic patterns or spatiotemporal disorders. Considering the case in which the diffusion of sulfides is larger, in particular, when the resultant interaction length $\sqrt{\frac{D_s}{{\delta }_s}}$ is in the scale of meters, the Turing instability characteristic of SDF begins to predominate in parameter space (Fig. 2). By increasing sulfide diffusion, the pattern-forming instability overlaps with the excitable region, which precludes the formation of rings since periodic patterns form on a faster time scale. However, the presence of this instability and the formation of regular patterns may be consistent with previously reported vegetation patterns (5) and provide a possible explanation for the interaction mechanism, which still remains an open question in that regime. The spatial scales of pattern formation and traveling pulses are clearly different, with organic matter export, which represents, on average, 24.3% of seagrass net primary production (48) likely to play a more relevant role in the former as compared to sulfide diffusion through the sediment for the later.

Conclusions

The theoretical results and empirical validation provided here deliver a detailed description of the formation of vegetation rings of P. oceanica as a consequence the nonlinear dynamics and spatial coupling induced by the interaction between plant growth and sulfide dynamics, characterizing the radial profile of the density of shoots and sulfide concentration, and the speed of propagation. The verified prediction of the annihilation of the fringes after a collision identifies these structures as excitable pulses. Moreover, the presence of similar structures has been shown for different seagrass species, such as Z. marina in the Danish Kattegat (29), for which the model based on clonal growth can be applied using appropriate parameters. The simplicity of the model allows also to encompass different processes in the diffusion, making it useful to describe different phenomenologies of the spatial distribution of vegetation driven by sulfide dynamics.

From the point of view of the conservation of the ecosystem, traveling pulses and rings can be interpreted as an indication of resilience (49), as homogeneous meadows would have collapsed for lower values of mortality, at the homoclinic bifurcation signaling the left limit of the excitable region in Fig. 2, while traveling structures can survive for larger mortalities in the excitable region. Thus, in addition to explaining complex pattern formation and dynamics, our results identify ring structures as terminal states in seagrass meadows, that precede their collapse if seagrass mortality is increased further (Fig. 2) driven by a temperature increase or excess sulfide production resulting from organic inputs. Novel remote sensing tools have the capacity, combined with artificial intelligence, to automatically detect and track ring structures, thereby alerting the presence of seagrass meadows at risk of collapse.

Supplementary Material

Appendix 01 (PDF)

Movie S1.

Time evolution of excitable rings under spatially homogeneous mortality: Movie of the simulation shown in Figs. 3 (a-e) for homogeneous mortality conditions starting from initial conditions resembling aerial pictures of the vegetation from 1973. A collision of two rings is observed during the evolution.

Movie S2.

Time evolution of excitable rings under spatially heterogeneous mortality conditions: Movie of the simulations shown in Figs. 3 (f-j) for spatially heterogeneous mortality conditions starting from vegetation initial conditions resembling aerial pictures from 1973.

Movie S3.

Animation of aerial images of the study site in Pollença bay from 1973 to 2018 showing the actual evolution of the spatial distribution of vegetation patterns.

Movie S4.

Animation showing a zoom of the collision of two excitable rings from historic aerial images from 1973 to 2018.

Data, Materials, and Software Availability

All study data are included in the article and/or SI Appendix. Raw data of Fig. 3 is available upon request.