Vegetation engineers marsh morphology throughmultiple competing stable statesMarco Marania,b,1, Cristina Da Liob, and Andrea D’Alpaosc

aDivision of Earth and Ocean Sciences, Nicholas School of the Environment and Department of Civil and Environmental Engineering, Pratt School ofEngineering, Duke University, Durham, NC 27708; and Departments of bCivil, Environmental, and Architectural Engineering and cGeosciences, University ofPadova, I-35131 Padova, Italy

Edited by Ignacio Rodriguez-Iturbe, Princeton University, Princeton, NJ, and approved January 2, 2013 (received for review October 21, 2012)

Marshes display impressive biogeomorphic features, such aszonation, a mosaic of extensive vegetation patches of ratheruniform composition, exhibiting sharp transitions in the pres-ence of extremely small topographic gradients. Although gen-erally associated with the accretion processes necessary formarshes to keep up with relative sea level rise, competingenvironmental constraints, and ecologic controls, zonation is stillpoorly understood in terms of the underlying biogeomorphicmechanisms. Here we find, through observations and modelinginterpretation, that zonation is the result of coupled geomor-phological–biological dynamics and that it stems from the abilityof vegetation to actively engineer the landscape by tuning soilelevation within preferential ranges of optimal adaptation. Wefind multiple peaks in the frequency distribution of observedtopographic elevation and identify them as the signature ofbiologic controls on geomorphodynamics through competingstable states modulated by the interplay of inorganic and organicdeposition. Interestingly, the stable biogeomorphic equilibriacorrespond to suboptimal rates of biomass production, a resultcoherent with recent observations. The emerging biogeomor-phic structures may display varying degrees of robustness tochanges in the rate of sea level rise and sediment availability,with implications for the overall resilience of marsh ecosystemsto climatic changes.

biogeomorphology | ecohydrology | ecotone

Marsh vegetation zonation patterns occur widely in tidalenvironments worldwide (1) (SI Text). Although we know

that vegetation plays an important role in offsetting the local rateof relative sea level rise through organic soil production andinorganic sediment trapping (2–10), zonation patterns tradi-tionally are explained as the result of interspecific competitionand of the “passive” adaptation of marsh vegetation to spatiallyvarying soil conditions (11–16). In fact, this interpretationalframework, as well as prevailing explanations of ecotones ingeneral (abrupt edges in vegetation distributions, e.g., see ref.17), view vegetation distributions chiefly as a response to envi-ronmental drivers.On the basis of detailed observations and modeling, we

propose here an interpretation, which couples geomorphic dy-namics and species competition in a spatially extended setting,previous models being incapable of insight into zonation-gener-ating mechanisms because they either are lumped in space (18) orare not inclusive of interspecific competition (19–23). We find thatmarsh landscapes are actively engineered by competing vegetationspecies through a set of vegetation-controlled equilibrium states,of which zonation patterns are the observable biogeomorphicsignatures.

Spatial Biogeomorphodynamics with CompetitionWe describe the time evolution of a marsh transect oriented ina direction perpendicular to the nearest channel feeding themarsh with inorganic sediment. Changes in soil elevation areeverywhere dictated by Exner’s equation,

∂z∂tðx; tÞ=Qsðx; tÞ+Qoðx; tÞ−R; [1]

which expresses variations in soil elevation, referenced to meansea level (MSL), as the net result of (i) the rate of inorganic soildeposition, Qs, determined by the hydrodynamic circulation/sediment transport processes; (ii) the rate of organic soil pro-duction by vegetation, Qo = γB0fi(z), modulated by compaction/decomposition processes (encapsulated by the factor γ) and bya fitness function (0 ≤ fi(z) ≤ 1), describing how biomass pro-duction and competitive abilities of species i vary as a function ofelevation z (summarizing local environmental stressors, such assalinity, sediment aeration, etc.) (3, 18, 24, 25); and (iii) the rateof relative sea level rise, R (SI Text).Field manipulations of marsh species distributions, when in-

terspecific competition is allowed to take place or is artificiallysuppressed, show the important role of edaphic constraints onbiomass production (26). Detailed biomass determinations intransplant experiments with Spartina spp. further indicate thatfi(z) takes on maximum values at elevations that are character-istic for each species and that it decreases as elevation departsfrom this optimal range (6, 27). This qualitative feature hasimportant geomorphic consequences, and we incorporate it byadopting the following expression for the fitness function: fi(ζ) =2 · [exp(λ(ζ − ζi0)) + exp(−λ(ζ − ζi0))]

−1, where ζ = z/H. fi(ζi0) = 1defines the elevation of maximum biomass production (andhighest competitive abilities), whereas λ controls the rate atwhich fitness tends to zero away from its maximum: higher valuesof λ corresponding to more “specialized” vegetation species (wefirst consider the case of relatively “specialized” species, λ = 5,and later compare with the case of less “specialized” plants, withλ = 2). Hence, all species have an equal maximum fitness and anequal rate of fitness decrease away from their respective optima(Fig. 1B). This is a convenient and flexible way of expressing thegeneral known properties of marsh vegetation species (18, 28),but other expressions displaying similar general behaviors havebeen used as well, leading to very similar results.We note that Eq. 1 describes elevation changes taking place on

biogeomorphic time scales of 1 y or greater, whereas inorganicdeposition is governed by hydrodynamic transport regulated bytidal flooding on subhourly time scales. This clear separation oftime scales allows us to decouple the numerical integration ofEq. 1, performed with yearly time steps, and the solution of thesediment transport problem from which the inorganic depositionrate is obtained (5, 24). At the scale of the main, half-daily tidalperiod, suspended sediment transport from the channel to the

Author contributions: M.M. designed research; M.M. and A.D. lead model development;C.D.L. coded the model and ran the simulations; C.D.L. and A.D. collected the data; M.M.,C.D.L., and A.D. analyzed data; and M.M. and A.D. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. E-mail: marco.marani@duke.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1218327110/-/DCSupplemental.

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marsh and the associated deposition of inorganic sediment onthe marsh surface are described here through the advection–dispersion equation (e.g., see ref. 20):

∂yC∂t

+∂∂x

�uCy− kdy

∂C∂x

�= −wsC; [2]

where y(x, t) = zw(t) − z(x, t) is the water depth, zw(t) is the el-evation of the free surface, kd is the dispersion coefficient [as-sumed to be a constant value, kd = 1.5 m2/s (29), characteristic ofthe small flow velocities typical in marshes], and u(x, t) is thefluid advective velocity. The latter is computed from the watercontinuity equation (in a quasi-static propagation of tidal levelsassumption) by assuming a sinusoidal fluctuation of the tidallevel zw(t) = H · sin(2πt/T) (with T = 12 h and H = 0.5 m typicalof microtidal settings). Sediment erosion is neglected because ofthe effective wave dissipation by above-ground biomass on themarsh surface (30, 31). Eq. 2 is solved numerically over one tidalcycle, and the resulting settling term, ws C(x, t), is integrated overtime to yield the Qs(x, t) to be used in Eq. 1 (see SI Text forfurther details). It is useful to note here that although Exner’sEq. 1 describes the local balance between the total depositionrate and the rate of relative sea level rise R, it actually embedsnonlocal dynamics due to the dependence of Qs(x, t) on spaceand on the topographic configuration of the entire transect,rather than just on the local topography.Qo(x, t) also plays a fundamental role in determining accretion

rates, as changes in the distribution of topographic elevationalong the marsh transect are strongly affected by changes inspecies distribution as a consequence of interspecific com-petition. We consider two possible descriptions of the latter,which are based on either (i) selecting, at each site with co-ordinate xk, the species i for which fi(zk) is maximum (“fittesttakes all”), or (ii) randomly selecting species i with a probabilitypði; xkÞ= fiðzkÞ=

PjfjðzkÞ (“stochastic competition” mechanism),

to account for the fact that the current species may not be dis-placed instantaneously by the fittest species, that soil propertiesand sediment fluxes may be stochastically heterogeneous inspace and time, and that stochastic dispersal may locally affectspecies distribution. Although the second criterion is more re-alistic, the first allows us to analyze an ideal case in which theeffect of competition can be isolated from “environmental

noise,” thus providing interesting insights into the relative role ofthese factors in determining observed biogeomorphic patterns.We note that, in both cases, the fitness function not only regu-lates 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, sus-pended sediment concentration, and inorganic deposition ratesfor the current topographic profile. The yearly average depositionrate at year tj is evaluated as Qsðxk; tjÞ= nT=T ·

RTws ·Cðxk; tÞdt

(24) [nT being the number of tidal cycles in 1 year, C(xk, t) thelocal instantaneous suspended sediment concentration, and ws =0.2 mm/s a typical settling velocity of fine intertidal sediments(32)]. (ii) Computation of Qo(xk, tj) = γ · B0 · fi(z(xk, tj)), where γ ·B0 = 2.5 mm·y−1 (24), i being the species currently occupyingcoordinate xk. (iii) Computation of ∂z/∂t = Qs(xk, tj) + Qo(xk, tj) −R and update of the topography at each site as z(xk, tj + Δt) = z(xk,tj) + ∂z/∂t(xk, tj) · Δt (Δt = 1 y). (iv) Update of the species dis-tribution throughout the transect using either the fittest-takes-allor the stochastic competition mechanism.

Results and DiscussionThe fittest-takes-all colonization mechanism produces stablestates characterized by sharp transitions between neighboringbiogeomorphic terrace-like structures (Fig. 1A). The marshprofile is characterized by gently sloping areas, colonized bya single vegetation species, very much reminiscent of observedmarsh zonation structures (13, 15, 16) (SI Text). It is interestingto see that the sharp boundaries displayed by the emergingmorphologies essentially are the result of vegetation pinningtopography within near-optimal elevation ranges. In fact, theanalysis of the governing equations shows that zonation struc-tures emerge from feedbacks involving biomass production, in-organic deposition, and soil accretion, leading to pairs of stableand 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 andorganic deposition rates at this site determine two solutions tothe equilibrium condition ∂z/∂t = 0: a stable equilibrium withelevation, say, zðsÞ2 (located above the maximum of f2(z), solidgreen circle in Fig. 1 B and C), and an unstable equilibrium zðuÞ2(located below the maximum of f2(z), open circle). To determine

A B C

Fig. 1. Zonation patterns generated by the model. (A) The time evolution of transect topography was started here from a linear initial condition, but severalother initial conditions were explored with analogous results. Monospecific vegetation patches, very similar to observed zonation patterns (Inset), andterrace-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 speciespopulating the marsh, which define the rate of organic soil production as Qo = γ · B0 · fi(z), as well as the species competitive abilities (γ incorporates typicalvegetation 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 x̂2 is comprised between zðuÞ2 and zðsÞ2 , the elevation will tendtoward zðsÞ2 . If the initial elevation of the site at x̂2 is located below zðuÞ2 , the elevation will tend toward zðsÞ3 .

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the stability properties of the equilibrium state in x̂2 (Fig. 1A), wenumerically find the value of ∂z/∂t from Eq. 1 for a set of transectconfigurations obtained by perturbing the local elevation in x̂2within a neighborhood of zðuÞ2 and zðsÞ2 (Fig. 1C). This analysisshows that, indeed, zðsÞ2 is a stable equilibrium: a perturbationthat increases the local elevation with respect to zðsÞ2 generatesa decrease in biomass production (Fig. 1B) as well as a decreasein Qs (due to an increased local velocity, not shown), whichmakes ∂z/∂t < 0 (Fig. 1C), thus bringing the system back to theoriginal equilibrium. Similarly, a perturbation that decreased thelocal soil elevation with respect to zðsÞ2 would induce an increasein the biomass production (Fig. 1B) and in Qs, and hence wouldmake ∂z/∂t > 0 (Fig. 1C), again bringing the system back to thestable equilibrium. This analysis may be summarized by notingthat ∂/∂z(∂z/∂t) < 0 at zðsÞ2 , which defines the condition for a stableequilibrium. Note that Qs(x, t) varies in space, such that stableequilibria for sites within the same vegetation patch locatedcloser to the source of inorganic sediment are higher than zðsÞ2 ,generating a mildly sloping geomorphic structure, consistent withobservations. The second equilibrium solution, zðuÞ2 , is an un-stable equilibrium (open green circle in Fig. 1C). A positiveperturbation with respect to this elevation enhances the organicdeposition rate (Fig. 1B) and reduces Qs(x, t). However, the in-crease in Qo(x, t) outweighs the decrease in Qs, thereby making∂z/∂t > 0 (Fig. 1C) and driving the elevation of the site away fromzðuÞ2 toward zðsÞ2 . If, on the contrary, a perturbation acts to de-crease the elevation of the site, the organic deposition ratedecreases faster than Qs increases, making ∂z/∂t < 0 (Fig. 1C),thus pushing the local elevation to even lower values, toward thestable equilibrium, zðsÞ3 , of the vegetation species i = 3 (blue solidcircle in Fig. 1C).We note that in the case of the “green” species (i = 2) (as well

as for the lower “blue” species), ∂Qs/∂z � ∂Qo/∂z; therefore, thestability of the equilibria is not influenced by variations of Qs(x,t), because ∂/∂z(∂z/∂t) ≅ ∂Qo/∂z. This equilibrium state is com-pletely determined by organic soil production, and the stability ofthese equilibria may be established by studying fi(z) alone, thecondition dfi/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 isvery sensitive to changes in the topographic elevation because ofthe large local availability of inorganic sediment. The equilib-rium state in the upper marsh zone (red in Fig. 1) is, in fact,stable as ∂/∂z(∂z/∂t) < 0 even though zðsÞ1 lies on the branch of thefitness function located below the maximum (Fig. 1B). The sta-bility of the equilibrium near the tidal creek thus is jointly con-trolled 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 pro-duction occurs (Fig. 1B), suggesting that zonation patterns maybe associated with a higher morphological stability at the expenseof a reduced productivity.Biogeomorphodynamics in the real world are affected by

stochastic forcings, stochasticity in competition mechanisms,heterogenous edaphic conditions, etc. The stochastic competitionmechanism thus may be considered to generate more realisticdynamics and nondeterministic patterns (Fig. 2A), which, how-ever, are more difficult to interpret. Also, in this case, one stillmay identify the role of the underlying biogeomorphic feedbacksby studying the probability distribution of elevations. A multimodalelevation distribution (Fig. 2A), by highlighting the presence ofengineered preferential elevation ranges, is a clear signature ofthe governing feedback between biomass production and elevation,even when vegetational and topographic patterns are significantlyless visually evident (Fig. 2A, Inset).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 itsmorphodynamic evolution, Fig. 2B), we obtain a smooth topo-graphic profile, in which banded vegetation is present, but

A

B

C

Fig. 2. (A) Stochastic interspecific competition. Species i is selected as thesuccessful competitor with a probability pði; xkÞ= fiðzkÞ=

Pj fjðzkÞ (for each

site xk and each time step), generating relatively noisy patterns. However,the multimodal frequency distribution of topographic elevation, the signa-ture of the underlying biogeomorphic coupling, remains detectable. Eachpeak (color coded according to the species that is most abundant withineach elevation interval) clearly is associated with the unique species thatgenerates it. (B) In the absence of an organic soil contribution to the ac-cretion rate, the resulting smooth topography is determined entirely by in-organic deposition. Vegetation species colonize the transect in bandedpatterns according to their respective fitnesses. (C) The frequency distribu-tion of topographic elevation shows uncertain symptoms of multiple peakswhen less specialized vegetation species (λ = 2) are considered, a sign thata decreased vegetation specialization produces less easily detectable multi-ple peaks in the topographic elevation frequency distribution.

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multiple peaks in the frequency distribution of topographic ele-vation are absent. Hence, banded vegetation patterns do notautomatically imply biogeomorphic feedbacks, but, by them-selves, are just the symptom of a passive adaptation of vegetationspecies to a topographic profile that cannot be affected by veg-etation dynamics. If less specialized vegetation is considered (e.g.,λ = 2, Fig. 2C), biologic controls on elevation may be too weak toemerge above environmental noise and multiple peaks in thetopographic elevation frequency distribution may be difficult todetect. Thus, we must conclude that multiple peaks in the fre-quency distribution of topographic elevation, which are univo-cally associated with single vegetation species, are the distinctivesignature of a strong feedback between soil accretion processesand specialized vegetation species.As our analyses show that zonation structures are de-

termined largely by the degree of species adaptation to char-acteristic ranges of topographic elevation even in the presence

of environmental noise, we now seek the signature of this bio-geomorphic coupling in real marshes. To this end, we performeddetailed marsh topographic surveys in the Venice lagoon, witha total station (i.e., an electronic theodolite) allowing for a finalaccuracy better than 1 mm in elevation. The analysis of thesedata shows the presence of multiple peaks in the frequencydistributions of observed topographic elevation (Fig. 3; seealso SI Text for an analysis of the whole dataset). Each peak inthe elevation distribution is associated with a different andcharacteristic vegetation species. This correspondence be-tween vegetation and topographic frequency distributions isfound consistently in all the data examined (see SI Text formore data analyses).

ConclusionsOur observations and model results show that ubiquitous zonationpatterns are largely the product of landscape construction by marshvegetation species through the biomass-elevation feedback. Wenote that this “active” biogeomorphic mechanism is very differentin nature from previously studied “passive” biological controls onthe physical environment occurring through biostabilization/bio-turbation processes (33). The coupled vegetation–topography dy-namics partition marsh topographies into an almost discrete set ofstable equilibria, and the ecotones characteristic of salt marsh zo-nation emerge because of a two-way feedback between biomassproduction and elevation, rather than as a result of sharp gradientsin environmental forcings (17).Because stability in the marsh zone controlled by organic

deposition requires dfi/dz < 0, our findings imply that marshvegetation species tend not to operate at the maximum biomassproduction rate, gaining, however, added environmental stabil-ity in return. In fact, our results show that entire sections ofa vegetation patch, particularly where the accretion process isdominated by plant organic soil production (Fig. 1B), are lo-cated well above the elevation corresponding to maximumproductivity. Interestingly, root growth by common marsh veg-etation species recently was observed to be suboptimal at severalstudy sites (34).Numerical experiments in which the organic soil contribution

to accretion is artificially turned off leads to frequency dis-tributions of topographic elevation with a single maximum.Furthermore, when the degree of specialization of vegetationspecies is reduced, the tendency toward a multimodal distribu-tion of topographic elevation may be overwhelmed by environ-mental noise, and may not be detectable. We thus conclude thatthe detection, in the frequency distribution of topographic ele-vation, of multiple peaks associated with a single characteristicvegetation species is the distinctive sign of the active tuning oftopography by specialized plant species. As a consequence, theobserved multimodal elevation frequency distributions show thatactual biogeomorphic zonation structures are not compatiblewith the simplistic picture of a passive adaptation by vegetationto a given distribution of topographic elevations.The spatial dependence of inorganic sediment deposition,

jointly induced by sediment transport processes and the evolvingtopography, defines the spatial extent of the emerging bio-geomorphic structures. The resilience of marsh patterns andecosystem properties (e.g., as represented by the elevation dif-ference between the stable and the unstable equilibria; Fig. 1C)thus depends on the species-specific landscape-building abilities ofintertidal vegetation. Changes in the rate of relative sea level risemay result in the selective disappearance of some or all of thestable equilibria associated with marsh morphological/biologicalpatterns, with consequent reductions in the associated biodiversity.

ACKNOWLEDGMENTS. We thank Massimiliano Ignaccolo for discussions onthe mathematical representation of vegetation fitness functions as well astwo anonymous reviewers whose contributions significantly improved the

A

B

Fig. 3. (A and B) Observed zonation patterns. An accurate topographicsurvey (uncertainty smaller than 1 mm) reveals a multimodal frequencydistribution of soil elevation, highly suggestive of the major role played bythe biomass-elevation feedback in tuning marsh topography. Each bar iscolor coded according to the vegetation species that is most abundantwithin the pertinent elevation interval, showing that, indeed, elevationranges are characteristic of the vegetation species (or of a typical mix ofspecies at high elevations) that maintain them.

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manuscript. We acknowledge support by Duke University, the PhD School ofCivil and Environmental Engineering Sciences at the University of Padova,

and the Italian National Project “Eco-Morfodinamica di Ambienti a Marea eCambiamenti Climatici.”

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