Vegetation engineers marsh morphology through multiple competing stable states

Abstract

Marshes display impressive biogeomorphic features, such as zonation, a mosaic of extensive vegetation patches of rather uniform composition, exhibiting sharp transitions in the presence of extremely small topographic gradients. Although generally associated with the accretion processes necessary for marshes to keep up with relative sea level rise, competing environmental constraints, and ecologic controls, zonation is still poorly understood in terms of the underlying biogeomorphic mechanisms. Here we find, through observations and modeling interpretation, that zonation is the result of coupled geomorphological–biological dynamics and that it stems from the ability of vegetation to actively engineer the landscape by tuning soil elevation within preferential ranges of optimal adaptation. We find multiple peaks in the frequency distribution of observed topographic elevation and identify them as the signature of biologic controls on geomorphodynamics through competing stable states modulated by the interplay of inorganic and organic deposition. Interestingly, the stable biogeomorphic equilibria correspond to suboptimal rates of biomass production, a result coherent with recent observations. The emerging biogeomorphic structures may display varying degrees of robustness to changes in the rate of sea level rise and sediment availability, with implications for the overall resilience of marsh ecosystems to climatic changes.

Marsh vegetation zonation patterns occur widely in tidal environments worldwide (1) (SI Text). Although we know that vegetation plays an important role in offsetting the local rate of relative sea level rise through organic soil production and inorganic sediment trapping (2–10), zonation patterns traditionally are explained as the result of interspecific competition and of the “passive” adaptation of marsh vegetation to spatially varying soil conditions (11–16). In fact, this interpretational framework, as well as prevailing explanations of ecotones in general (abrupt edges in vegetation distributions, e.g., see ref. 17), view vegetation distributions chiefly as a response to environmental drivers.

On the basis of detailed observations and modeling, we propose here an interpretation, which couples geomorphic dynamics and species competition in a spatially extended setting, previous models being incapable of insight into zonation-generating mechanisms because they either are lumped in space (18) or are not inclusive of interspecific competition (19–23). We find that marsh landscapes are actively engineered by competing vegetation species through a set of vegetation-controlled equilibrium states, of which zonation patterns are the observable biogeomorphic signatures.

Spatial Biogeomorphodynamics with Competition

We describe the time evolution of a marsh transect oriented in a direction perpendicular to the nearest channel feeding the marsh with inorganic sediment. Changes in soil elevation are everywhere dictated by Exner’s equation,

which expresses variations in soil elevation, referenced to mean sea level (MSL), as the net result of (i) the rate of inorganic soil deposition, Q_s, determined by the hydrodynamic circulation/sediment transport processes; (ii) the rate of organic soil production by vegetation, Q_o = γB₀f_i(z), modulated by compaction/decomposition processes (encapsulated by the factor γ) and by a fitness function (0 ≤ f_i(z) ≤ 1), describing how biomass production and competitive abilities of species i vary as a function of elevation z (summarizing local environmental stressors, such as salinity, sediment aeration, etc.) (3, 18, 24, 25); and (iii) the rate of relative sea level rise, R (SI Text).

Field manipulations of marsh species distributions, when interspecific competition is allowed to take place or is artificially suppressed, show the important role of edaphic constraints on biomass production (26). Detailed biomass determinations in transplant experiments with Spartina spp. further indicate that f_i(z) takes on maximum values at elevations that are characteristic for each species and that it decreases as elevation departs from this optimal range (6, 27). This qualitative feature has important geomorphic consequences, and we incorporate it by adopting the following expression for the fitness function: f_i(ζ) = 2 ⋅ [exp(λ(ζ − ζ_i0)) + exp(−λ(ζ − ζ_i0))]⁻¹, where ζ = z/H. f_i(ζ_i0) = 1 defines the elevation of maximum biomass production (and highest competitive abilities), whereas λ controls the rate at which fitness tends to zero away from its maximum: higher values of λ corresponding to more “specialized” vegetation species (we first consider the case of relatively “specialized” species, λ = 5, and later compare with the case of less “specialized” plants, with λ = 2). Hence, all species have an equal maximum fitness and an equal rate of fitness decrease away from their respective optima (Fig. 1B). This is a convenient and flexible way of expressing the general known properties of marsh vegetation species (18, 28), but other expressions displaying similar general behaviors have been used as well, leading to very similar results.

Fig. 1.

Zonation patterns generated by the model. (A) The time evolution of transect topography was started here from a linear initial condition, but several other initial conditions were explored with analogous results. Monospecific vegetation patches, very similar to observed zonation patterns (Inset), and terrace-like topographic structures emerge as a result of multiple stable states defined by ∂z/∂t = 0 and ∂/∂z(∂z/∂t) < 0. (B) Fitness functions of the species populating the marsh, which define the rate of organic soil production as Q_o = γ ⋅ B₀ ⋅ f_i(z), as well as the species competitive abilities (γ incorporates typical vegetation characteristics and the density of the organic soil produced; B₀ is the biomass density of a fully vegetated marsh). (C) The superscripts “(s)” and “(u)” denote stable and unstable equilibria, respectively. If the initial elevation of the site at is comprised between and , the elevation will tend toward . If the initial elevation of the site at is located below , the elevation will tend toward .

We note that Eq. 1 describes elevation changes taking place on biogeomorphic time scales of 1 y or greater, whereas inorganic deposition is governed by hydrodynamic transport regulated by tidal flooding on subhourly time scales. This clear separation of time scales allows us to decouple the numerical integration of Eq. 1, performed with yearly time steps, and the solution of the sediment transport problem from which the inorganic deposition rate is obtained (5, 24). At the scale of the main, half-daily tidal period, suspended sediment transport from the channel to the marsh and the associated deposition of inorganic sediment on the marsh surface are described here through the advection–dispersion equation (e.g., see ref. 20):

where y(x, t) = z_w(t) − z(x, t) is the water depth, z_w(t) is the elevation of the free surface, k_d is the dispersion coefficient [assumed to be a constant value, k_d = 1.5 m²/s (29), characteristic of the small flow velocities typical in marshes], and u(x, t) is the fluid advective velocity. The latter is computed from the water continuity equation (in a quasi-static propagation of tidal levels assumption) by assuming a sinusoidal fluctuation of the tidal level z_w(t) = H ⋅ sin(2πt/T) (with T = 12 h and H = 0.5 m typical of microtidal settings). Sediment erosion is neglected because of the effective wave dissipation by above-ground biomass on the marsh surface (30, 31). Eq. 2 is solved numerically over one tidal cycle, and the resulting settling term, w_s C(x, t), is integrated over time to yield the Q_s(x, t) to be used in Eq. 1 (see SI Text for further details). It is useful to note here that although Exner’s Eq. 1 describes the local balance between the total deposition rate and the rate of relative sea level rise R, it actually embeds nonlocal dynamics due to the dependence of Q_s(x, t) on space and on the topographic configuration of the entire transect, rather than just on the local topography.

Q_o(x, t) also plays a fundamental role in determining accretion rates, as changes in the distribution of topographic elevation along the marsh transect are strongly affected by changes in species distribution as a consequence of interspecific competition. We consider two possible descriptions of the latter, which are based on either (i) selecting, at each site with coordinate x_k, the species i for which f_i(z_k) is maximum (“fittest takes all”), or (ii) randomly selecting species i with a probability (“stochastic competition” mechanism), to account for the fact that the current species may not be displaced instantaneously by the fittest species, that soil properties and sediment fluxes may be stochastically heterogeneous in space and time, and that stochastic dispersal may locally affect species distribution. Although the second criterion is more realistic, the first allows us to analyze an ideal case in which the effect of competition can be isolated from “environmental noise,” thus providing interesting insights into the relative role of these factors in determining observed biogeomorphic patterns. We note that, in both cases, the fitness function not only regulates biomass production but also species competitive abilities, thus incorporating a competitive displacement mechanism.

In summary, the system evolves in time through the following steps: (i) Computation over a tidal cycle of flow velocity, suspended sediment concentration, and inorganic deposition rates for the current topographic profile. The yearly average deposition rate at year t_j is evaluated as (24) [n_T being the number of tidal cycles in 1 year, C(x_k, t) the local instantaneous suspended sediment concentration, and w_s = 0.2 mm/s a typical settling velocity of fine intertidal sediments (32)]. (ii) Computation of Q_o(x_k, t_j) = γ ⋅ B₀ ⋅ f_i(z(x_k, t_j)), where γ ⋅ B₀ = 2.5 mm⋅y⁻¹ (24), i being the species currently occupying coordinate x_k. (iii) Computation of ∂z/∂t = Q_s(x_k, t_j) + Q_o(x_k, t_j) − R and update of the topography at each site as z(x_k, t_j + Δt) = z(x_k, t_j) + ∂z/∂t(x_k, t_j) ⋅ Δt (Δt = 1 y). (iv) Update of the species distribution throughout the transect using either the fittest-takes-all or the stochastic competition mechanism.

Results and Discussion

The fittest-takes-all colonization mechanism produces stable states characterized by sharp transitions between neighboring biogeomorphic terrace-like structures (Fig. 1A). The marsh profile is characterized by gently sloping areas, colonized by a single vegetation species, very much reminiscent of observed marsh zonation structures (13, 15, 16) (SI Text). It is interesting to see that the sharp boundaries displayed by the emerging morphologies essentially are the result of vegetation pinning topography within near-optimal elevation ranges. In fact, the analysis of the governing equations shows that zonation structures emerge from feedbacks involving biomass production, inorganic deposition, and soil accretion, leading to pairs of stable and unstable equilibrium states. This can be seen by considering, as an illustrative example, the lowest site in the middle patch (species i = 2, in green in Fig. 1). The values of inorganic and organic deposition rates at this site determine two solutions to the equilibrium condition ∂z/∂t = 0: a stable equilibrium with elevation, say, (located above the maximum of f₂(z), solid green circle in Fig. 1 B and C), and an unstable equilibrium (located below the maximum of f₂(z), open circle). To determine the stability properties of the equilibrium state in (Fig. 1A), we numerically find the value of ∂z/∂t from Eq. 1 for a set of transect configurations obtained by perturbing the local elevation in within a neighborhood of and (Fig. 1C). This analysis shows that, indeed, is a stable equilibrium: a perturbation that increases the local elevation with respect to generates a decrease in biomass production (Fig. 1B) as well as a decrease in Q_s (due to an increased local velocity, not shown), which makes ∂z/∂t < 0 (Fig. 1C), thus bringing the system back to the original equilibrium. Similarly, a perturbation that decreased the local soil elevation with respect to would induce an increase in the biomass production (Fig. 1B) and in Q_s, and hence would make ∂z/∂t > 0 (Fig. 1C), again bringing the system back to the stable equilibrium. This analysis may be summarized by noting that ∂/∂z(∂z/∂t) < 0 at , which defines the condition for a stable equilibrium. Note that Q_s(x, t) varies in space, such that stable equilibria for sites within the same vegetation patch located closer to the source of inorganic sediment are higher than , generating a mildly sloping geomorphic structure, consistent with observations. The second equilibrium solution, , is an unstable equilibrium (open green circle in Fig. 1C). A positive perturbation with respect to this elevation enhances the organic deposition rate (Fig. 1B) and reduces Q_s(x, t). However, the increase in Q_o(x, t) outweighs the decrease in Q_s, thereby making ∂z/∂t > 0 (Fig. 1C) and driving the elevation of the site away from toward . If, on the contrary, a perturbation acts to decrease the elevation of the site, the organic deposition rate decreases faster than Q_s increases, making ∂z/∂t < 0 (Fig. 1C), thus pushing the local elevation to even lower values, toward the stable equilibrium, , of the vegetation species i = 3 (blue solid circle in Fig. 1C).

We note that in the case of the “green” species (i = 2) (as well as for the lower “blue” species), ∂Q_s/∂z ≪ ∂Q_o/∂z; therefore, the stability of the equilibria is not influenced by variations of Q_s(x, t), because ∂/∂z(∂z/∂t) ≅ ∂Q_o/∂z. This equilibrium state is completely determined by organic soil production, and the stability of these equilibria may be established by studying f_i(z) alone, the condition df_i/dz < 0 denoting a stable equilibrium.

This is not the case for the portion of the marsh nearest the margin (red in Fig. 1A), where the inorganic deposition rate is very sensitive to changes in the topographic elevation because of the large local availability of inorganic sediment. The equilibrium state in the upper marsh zone (red in Fig. 1) is, in fact, stable as ∂/∂z(∂z/∂t) < 0 even though lies on the branch of the fitness function located below the maximum (Fig. 1B). The stability of the equilibrium near the tidal creek thus is jointly controlled by inorganic deposition and organic soil production.

We note that, in all cases, the terrace-like structures lie, for the most part, above the elevation at which maximum biomass production occurs (Fig. 1B), suggesting that zonation patterns may be associated with a higher morphological stability at the expense of a reduced productivity.

Biogeomorphodynamics in the real world are affected by stochastic forcings, stochasticity in competition mechanisms, heterogenous edaphic conditions, etc. The stochastic competition mechanism thus may be considered to generate more realistic dynamics and nondeterministic patterns (Fig. 2A), which, however, are more difficult to interpret. Also, in this case, one still may identify the role of the underlying biogeomorphic feedbacks by studying the probability distribution of elevations. A multimodal elevation distribution (Fig. 2A), by highlighting the presence of engineered preferential elevation ranges, is a clear signature of the governing feedback between biomass production and elevation, even when vegetational and topographic patterns are significantly less visually evident (Fig. 2A, Inset).

Fig. 2.

(A) Stochastic interspecific competition. Species i is selected as the successful competitor with a probability (for each site x_k and each time step), generating relatively noisy patterns. However, the multimodal frequency distribution of topographic elevation, the signature of the underlying biogeomorphic coupling, remains detectable. Each peak (color coded according to the species that is most abundant within each elevation interval) clearly is associated with the unique species that generates it. (B) In the absence of an organic soil contribution to the accretion rate, the resulting smooth topography is determined entirely by inorganic deposition. Vegetation species colonize the transect in banded patterns according to their respective fitnesses. (C) The frequency distribution of topographic elevation shows uncertain symptoms of multiple peaks when less specialized vegetation species (λ = 2) are considered, a sign that a decreased vegetation specialization produces less easily detectable multiple peaks in the topographic elevation frequency distribution.

In fact, when the organic contribution to accretion is turned off (but vegetation species are still allowed to compete and colonize the transect, without having the possibility to affect its morphodynamic evolution, Fig. 2B), we obtain a smooth topographic profile, in which banded vegetation is present, but multiple peaks in the frequency distribution of topographic elevation are absent. Hence, banded vegetation patterns do not automatically imply biogeomorphic feedbacks, but, by themselves, are just the symptom of a passive adaptation of vegetation species to a topographic profile that cannot be affected by vegetation dynamics. If less specialized vegetation is considered (e.g., λ = 2, Fig. 2C), biologic controls on elevation may be too weak to emerge above environmental noise and multiple peaks in the topographic elevation frequency distribution may be difficult to detect. Thus, we must conclude that multiple peaks in the frequency distribution of topographic elevation, which are univocally associated with single vegetation species, are the distinctive signature of a strong feedback between soil accretion processes and specialized vegetation species.

As our analyses show that zonation structures are determined largely by the degree of species adaptation to characteristic ranges of topographic elevation even in the presence of environmental noise, we now seek the signature of this biogeomorphic coupling in real marshes. To this end, we performed detailed marsh topographic surveys in the Venice lagoon, with a total station (i.e., an electronic theodolite) allowing for a final accuracy better than 1 mm in elevation. The analysis of these data shows the presence of multiple peaks in the frequency distributions of observed topographic elevation (Fig. 3; see also SI Text for an analysis of the whole dataset). Each peak in the elevation distribution is associated with a different and characteristic vegetation species. This correspondence between vegetation and topographic frequency distributions is found consistently in all the data examined (see SI Text for more data analyses).

Fig. 3.

(A and B) Observed zonation patterns. An accurate topographic survey (uncertainty smaller than 1 mm) reveals a multimodal frequency distribution of soil elevation, highly suggestive of the major role played by the biomass-elevation feedback in tuning marsh topography. Each bar is color coded according to the vegetation species that is most abundant within the pertinent elevation interval, showing that, indeed, elevation ranges are characteristic of the vegetation species (or of a typical mix of species at high elevations) that maintain them.

Conclusions

Our observations and model results show that ubiquitous zonation patterns are largely the product of landscape construction by marsh vegetation species through the biomass-elevation feedback. We note that this “active” biogeomorphic mechanism is very different in nature from previously studied “passive” biological controls on the physical environment occurring through biostabilization/bioturbation processes (33). The coupled vegetation–topography dynamics partition marsh topographies into an almost discrete set of stable equilibria, and the ecotones characteristic of salt marsh zonation emerge because of a two-way feedback between biomass production and elevation, rather than as a result of sharp gradients in environmental forcings (17).

Because stability in the marsh zone controlled by organic deposition requires df_i/dz < 0, our findings imply that marsh vegetation species tend not to operate at the maximum biomass production rate, gaining, however, added environmental stability in return. In fact, our results show that entire sections of a vegetation patch, particularly where the accretion process is dominated by plant organic soil production (Fig. 1B), are located well above the elevation corresponding to maximum productivity. Interestingly, root growth by common marsh vegetation species recently was observed to be suboptimal at several study sites (34).

Numerical experiments in which the organic soil contribution to accretion is artificially turned off leads to frequency distributions of topographic elevation with a single maximum. Furthermore, when the degree of specialization of vegetation species is reduced, the tendency toward a multimodal distribution of topographic elevation may be overwhelmed by environmental noise, and may not be detectable. We thus conclude that the detection, in the frequency distribution of topographic elevation, of multiple peaks associated with a single characteristic vegetation species is the distinctive sign of the active tuning of topography by specialized plant species. As a consequence, the observed multimodal elevation frequency distributions show that actual biogeomorphic zonation structures are not compatible with the simplistic picture of a passive adaptation by vegetation to a given distribution of topographic elevations.

The spatial dependence of inorganic sediment deposition, jointly induced by sediment transport processes and the evolving topography, defines the spatial extent of the emerging biogeomorphic structures. The resilience of marsh patterns and ecosystem properties (e.g., as represented by the elevation difference between the stable and the unstable equilibria; Fig. 1C) thus depends on the species-specific landscape-building abilities of intertidal vegetation. Changes in the rate of relative sea level rise may result in the selective disappearance of some or all of the stable equilibria associated with marsh morphological/biological patterns, with consequent reductions in the associated biodiversity.