<str<strong>on</strong>g>Proceedings</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> <str<strong>on</strong>g>Third</str<strong>on</strong>g> <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> <strong>Invasive</strong> SpartinaChapter 2: Spartina Distributi<strong>on</strong> and SpreadCOMPETITION AMONG MARSH MACROPHYTES BY MEANS OF VERTICALGEOMORPHOLOGICAL DISPLACEMENTJ.T. MORRISBelle W. Baruch Institute for Marine & Coastal Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> South Carolina, Columbia, SC 29208This paper describes a <str<strong>on</strong>g>the</str<strong>on</strong>g>ory <str<strong>on</strong>g>of</str<strong>on</strong>g> biogeomorphology that addresses how intertidal macrophytes canmodify landscape elevati<strong>on</strong>. Competitive interacti<strong>on</strong>s am<strong>on</strong>g marsh plant species are mediated by<str<strong>on</strong>g>the</str<strong>on</strong>g> influence <str<strong>on</strong>g>of</str<strong>on</strong>g> vegetati<strong>on</strong> <strong>on</strong> sediment accreti<strong>on</strong> and <str<strong>on</strong>g>the</str<strong>on</strong>g>ir modificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> relative elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><str<strong>on</strong>g>the</str<strong>on</strong>g> marsh surface. A model described here dem<strong>on</strong>strates <str<strong>on</strong>g>the</str<strong>on</strong>g> effects <str<strong>on</strong>g>of</str<strong>on</strong>g> feedback between physicalprocesses like sediment accreti<strong>on</strong> and biological processes such as those that determine speciesz<strong>on</strong>ati<strong>on</strong> patterns. Changes in geomorphology, primary productivity and <str<strong>on</strong>g>the</str<strong>on</strong>g> spatial distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g>plant species are explained by competitive interacti<strong>on</strong>s and by interacti<strong>on</strong>s am<strong>on</strong>g <str<strong>on</strong>g>the</str<strong>on</strong>g> tides, biomassdensity, and sediment accreti<strong>on</strong> that move marsh elevati<strong>on</strong> towards an equilibrium with mean sealevel (MSL). This equilibrium is affected positively (relative elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> marsh surface increases)by <str<strong>on</strong>g>the</str<strong>on</strong>g> biomass density <str<strong>on</strong>g>of</str<strong>on</strong>g> emergent, salt marsh macrophytes and negatively by <str<strong>on</strong>g>the</str<strong>on</strong>g> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> sea-levelrise. It was dem<strong>on</strong>strated that a dominant, invading species is able to modify its envir<strong>on</strong>ment toexclude competitively inferior species. However, <str<strong>on</strong>g>the</str<strong>on</strong>g> outcome depends <strong>on</strong> a number <str<strong>on</strong>g>of</str<strong>on</strong>g> variablesincluding <str<strong>on</strong>g>the</str<strong>on</strong>g> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> sea-level rise and <str<strong>on</strong>g>the</str<strong>on</strong>g> fundamental biomass distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> species across <str<strong>on</strong>g>the</str<strong>on</strong>g>intertidal gradient. The model predicts that a marsh can move toward alternative states, depending<strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> sea-level rise and species biomass distributi<strong>on</strong>s within <str<strong>on</strong>g>the</str<strong>on</strong>g> tidal frame.Keywords: sedimentati<strong>on</strong>, marshes, Spartina, sea level, models, geomorphology, competiti<strong>on</strong>INTRODUCTIONPhysical ecosystem engineering is a process comm<strong>on</strong>to organisms that possess <str<strong>on</strong>g>the</str<strong>on</strong>g> ability to physically modify<str<strong>on</strong>g>the</str<strong>on</strong>g>ir habitats (J<strong>on</strong>es et al. 1997). This trait is comm<strong>on</strong> tointertidal marsh macrophytes that have <str<strong>on</strong>g>the</str<strong>on</strong>g> potential toraise <str<strong>on</strong>g>the</str<strong>on</strong>g> relative elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g>ir habitat and modify <str<strong>on</strong>g>the</str<strong>on</strong>g>geomorphology <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> coastal landscape, potentially to <str<strong>on</strong>g>the</str<strong>on</strong>g>benefit and detriment <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>the</str<strong>on</strong>g>r species (Zedler & Kercher2004). Historically, coastal wetlands have maintained anelevati<strong>on</strong> in equilibrium with mean sea level by <str<strong>on</strong>g>the</str<strong>on</strong>g> accumulati<strong>on</strong><str<strong>on</strong>g>of</str<strong>on</strong>g> mineral sediment or organic matter (Redfield1972; Stevens<strong>on</strong> et al. 1986). Comm<strong>on</strong>ly, stable intertidalsalt marshes occupy a broad, flat expanse <str<strong>on</strong>g>of</str<strong>on</strong>g> landscape <str<strong>on</strong>g>of</str<strong>on</strong>g>tenreferred to as <str<strong>on</strong>g>the</str<strong>on</strong>g> marsh platform at an elevati<strong>on</strong> within<str<strong>on</strong>g>the</str<strong>on</strong>g> intertidal z<strong>on</strong>e that approximates that <str<strong>on</strong>g>of</str<strong>on</strong>g> local meanhigh water (MHW) (Kr<strong>on</strong>e 1985). Marsh species typicallysegregate al<strong>on</strong>g gently sloping gradients across <str<strong>on</strong>g>the</str<strong>on</strong>g> marshplatform (Hacker & Bertness 1999; Silvestri et al. 20005).The elevati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> marsh platform relative to sea leveldetermine inundati<strong>on</strong> frequency, durati<strong>on</strong> and, c<strong>on</strong>sequently,wetland productivity and species distributi<strong>on</strong>s.Recent work in a North Inlet, SC marsh has shown that<str<strong>on</strong>g>the</str<strong>on</strong>g> relative elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> sediment surface is a criticallyimportant variable that ultimately c<strong>on</strong>trols <str<strong>on</strong>g>the</str<strong>on</strong>g> productivity<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> salt marsh plant community (Morris et al. 2002).Productivity has a positive feedback <strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> accreti<strong>on</strong><str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> marsh surface. This feedback is key to predicting <str<strong>on</strong>g>the</str<strong>on</strong>g>resp<strong>on</strong>ses <str<strong>on</strong>g>of</str<strong>on</strong>g> coastal wetlands to rising sea level, includingchanges to <str<strong>on</strong>g>the</str<strong>on</strong>g> geometry <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> land margin and to <str<strong>on</strong>g>the</str<strong>on</strong>g> totalarea <str<strong>on</strong>g>of</str<strong>on</strong>g> wetland habitat. It is also fundamental to understanding<str<strong>on</strong>g>the</str<strong>on</strong>g> spread <str<strong>on</strong>g>of</str<strong>on</strong>g> invasive marsh macrophytes, such asSpartina hybrids in San Francisco Bay, that have <str<strong>on</strong>g>the</str<strong>on</strong>g> abilityto physically alter <str<strong>on</strong>g>the</str<strong>on</strong>g>ir envir<strong>on</strong>ment in a manner that benefits<str<strong>on</strong>g>the</str<strong>on</strong>g> invading species (Cuddingt<strong>on</strong> & Hastings 2004).The objective <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> study reported here is to explore <str<strong>on</strong>g>the</str<strong>on</strong>g>behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> a model that explicitly treats <str<strong>on</strong>g>the</str<strong>on</strong>g> modificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g>habitat elevati<strong>on</strong> by a hypo<str<strong>on</strong>g>the</str<strong>on</strong>g>tical group <str<strong>on</strong>g>of</str<strong>on</strong>g> marsh macrophytescompeting for habitat space within <str<strong>on</strong>g>the</str<strong>on</strong>g> intertidal z<strong>on</strong>e.The model accounts for <str<strong>on</strong>g>the</str<strong>on</strong>g> species-specific effect <str<strong>on</strong>g>of</str<strong>on</strong>g> marshvegetati<strong>on</strong> <strong>on</strong> mineral sediment accreti<strong>on</strong>, and for feedbacksam<strong>on</strong>g sea-level rise, relative elevati<strong>on</strong>, species replacement,and primary producti<strong>on</strong>. From this work it should be possibleto generalize about <str<strong>on</strong>g>the</str<strong>on</strong>g> types <str<strong>on</strong>g>of</str<strong>on</strong>g> adaptati<strong>on</strong>s that enable macrophytespecies to exploit a particular range <str<strong>on</strong>g>of</str<strong>on</strong>g> habitat within<str<strong>on</strong>g>the</str<strong>on</strong>g> intertidal z<strong>on</strong>e and that endow some species with superiorcompetitive abilities. The c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> geomorphologicaldisplacement is described whereby <strong>on</strong>e species displacesano<str<strong>on</strong>g>the</str<strong>on</strong>g>r by modifying <str<strong>on</strong>g>the</str<strong>on</strong>g> relative elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> its habitat.MODEL DESCRIPTIONThe model described here is based <strong>on</strong> fieldwork thatwas carried out in a salt marsh at North Inlet, South Carolina(Morris et al. 2002). The model was initially developedand calibrated for a single species, Spartina alterniflora,which forms a m<strong>on</strong>oculture over <str<strong>on</strong>g>the</str<strong>on</strong>g> majority <str<strong>on</strong>g>of</str<strong>on</strong>g> this marshwithin a narrow range between 0.22 and 0.481 m relative- 109 -
Chapter 2: Spartina Distributi<strong>on</strong> and Spread<str<strong>on</strong>g>Proceedings</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> <str<strong>on</strong>g>Third</str<strong>on</strong>g> <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> <strong>Invasive</strong> Spartinato NAVD88 (Morris et al. 2005). At North Inlet, <str<strong>on</strong>g>the</str<strong>on</strong>g> meanhigh water level was 0.618 m (2001 through May, 2003)with a mean tidal range <str<strong>on</strong>g>of</str<strong>on</strong>g> 1.39 m. Details about <str<strong>on</strong>g>the</str<strong>on</strong>g> NorthInlet marsh can be found in a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> sources (Eiser &Kjerfve 1986; Dame et al. 2000; Morris 2000; Morris et al.2005). Below, <str<strong>on</strong>g>the</str<strong>on</strong>g> model is generalized for two or morespecies and its predicti<strong>on</strong>s for <str<strong>on</strong>g>the</str<strong>on</strong>g> case <str<strong>on</strong>g>of</str<strong>on</strong>g> two hypo<str<strong>on</strong>g>the</str<strong>on</strong>g>ticalspecies are discussed.The Elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> Marsh SurfaceThe elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> marsh platform equilibrates at apositi<strong>on</strong> where erosi<strong>on</strong> and depositi<strong>on</strong> are equal. It is clearthat sediment depositi<strong>on</strong> must approach zero at elevati<strong>on</strong>snear that <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> highest high tide and should increase as<str<strong>on</strong>g>the</str<strong>on</strong>g> c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> suspended sediment and hydroperiodincrease. This logic is based up<strong>on</strong> a c<strong>on</strong>siderati<strong>on</strong><str<strong>on</strong>g>of</str<strong>on</strong>g> abiotic processes al<strong>on</strong>e and predicts that intertidalmarshes approach an equilibrium elevati<strong>on</strong> that approximatesMHW (Kr<strong>on</strong>e 1985). A rise in relative sea levelwill increase flooding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> marsh and inundati<strong>on</strong> time<str<strong>on</strong>g>the</str<strong>on</strong>g>reby increasing <str<strong>on</strong>g>the</str<strong>on</strong>g> opportunity for sediment depositi<strong>on</strong>and re-establishing <str<strong>on</strong>g>the</str<strong>on</strong>g> elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> marsh relativeto <str<strong>on</strong>g>the</str<strong>on</strong>g> new MSL (Pethick 1981, Kr<strong>on</strong>e 1985, French 1993).Sedimentati<strong>on</strong> rate is <str<strong>on</strong>g>the</str<strong>on</strong>g> product <str<strong>on</strong>g>of</str<strong>on</strong>g> settling velocity andtime <str<strong>on</strong>g>of</str<strong>on</strong>g> inundati<strong>on</strong>. Since depth below mean higher highwater (MHHW) and time <str<strong>on</strong>g>of</str<strong>on</strong>g> inundati<strong>on</strong> are roughly proporti<strong>on</strong>al,<str<strong>on</strong>g>the</str<strong>on</strong>g> net rate <str<strong>on</strong>g>of</str<strong>on</strong>g> change in <str<strong>on</strong>g>the</str<strong>on</strong>g> elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g>marsh surface (dY/dt), is proporti<strong>on</strong>al to <str<strong>on</strong>g>the</str<strong>on</strong>g> depth (D) <str<strong>on</strong>g>of</str<strong>on</strong>g><str<strong>on</strong>g>the</str<strong>on</strong>g> marsh surface: dY/dt D. Strictly speaking, sedimentati<strong>on</strong>rate should be proporti<strong>on</strong>al to depth, whereaso<str<strong>on</strong>g>the</str<strong>on</strong>g>r processes that affect elevati<strong>on</strong>, like compacti<strong>on</strong>and decompositi<strong>on</strong>, may or may not be depth-dependent.However, compacti<strong>on</strong> can be taken to be a c<strong>on</strong>stant that isaccounted for in <str<strong>on</strong>g>the</str<strong>on</strong>g> local rate <str<strong>on</strong>g>of</str<strong>on</strong>g> sea-level rise.Feedbacks between <str<strong>on</strong>g>the</str<strong>on</strong>g> marsh vegetati<strong>on</strong> and <str<strong>on</strong>g>the</str<strong>on</strong>g> sedimentsare also important. The rate <str<strong>on</strong>g>of</str<strong>on</strong>g> change <str<strong>on</strong>g>of</str<strong>on</strong>g> elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><str<strong>on</strong>g>the</str<strong>on</strong>g> marsh platform is a positive functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> standingdensity <str<strong>on</strong>g>of</str<strong>on</strong>g> plant biomass (B). For simplicity it is assumed thatthis relati<strong>on</strong>ship is linear: dY/dt q + kB, where parametersq and k are proporti<strong>on</strong>al to <str<strong>on</strong>g>the</str<strong>on</strong>g> settling velocity and <str<strong>on</strong>g>the</str<strong>on</strong>g> efficiency<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> vegetati<strong>on</strong> as a sediment trap, respectively. Theproduct <str<strong>on</strong>g>of</str<strong>on</strong>g> kB represents <str<strong>on</strong>g>the</str<strong>on</strong>g> positive effect that abovegroundbiomass density has <strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g> trapping <str<strong>on</strong>g>of</str<strong>on</strong>g> suspended sediments(e.g. Le<strong>on</strong>ard & Lu<str<strong>on</strong>g>the</str<strong>on</strong>g>r, 1995; Christiansen et al 2000). Thevalues <str<strong>on</strong>g>of</str<strong>on</strong>g> q and k are likely to vary locally and regi<strong>on</strong>allyas a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sediment availability and tidal range (e.g.Stevens<strong>on</strong> et al. 1986). Note that k also may vary by species.This implies that <str<strong>on</strong>g>the</str<strong>on</strong>g> efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> sediment trapping may varyam<strong>on</strong>g species (e.g. Rooth and Stevens<strong>on</strong> 2000). Combining<str<strong>on</strong>g>the</str<strong>on</strong>g>se c<strong>on</strong>cepts, <str<strong>on</strong>g>the</str<strong>on</strong>g> absolute change in elevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> marshsurface, for depths (D) within <str<strong>on</strong>g>the</str<strong>on</strong>g> intertidal z<strong>on</strong>e, can beapproximated by:dY/dt = (q + kB)D, for D>0 (1)The kB term implicitly accounts for <str<strong>on</strong>g>the</str<strong>on</strong>g> c<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g>organic matter accreti<strong>on</strong> when <str<strong>on</strong>g>the</str<strong>on</strong>g> model is calibrated to <str<strong>on</strong>g>the</str<strong>on</strong>g>total accreti<strong>on</strong> rate. It assumes that organic matter accreti<strong>on</strong>is proporti<strong>on</strong>al to <str<strong>on</strong>g>the</str<strong>on</strong>g> standing biomass density <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> vegetati<strong>on</strong>.We have recent unpublished results that show that thisassumpti<strong>on</strong> overly simplistic, but <str<strong>on</strong>g>the</str<strong>on</strong>g> qualitative behavior<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> model with respect to total sediment accreti<strong>on</strong> andsea-level rise is not changed by breaking out organic matteraccreti<strong>on</strong> as a separate term.The Vertical-Distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Standing BiomassBiomass density, B (g/m 2 ), is variable and changes witha number <str<strong>on</strong>g>of</str<strong>on</strong>g> envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s including <str<strong>on</strong>g>the</str<strong>on</strong>g> relativeelevati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> marsh platform. For any intertidal species,<str<strong>on</strong>g>the</str<strong>on</strong>g>re exist upper and lower limits <str<strong>on</strong>g>of</str<strong>on</strong>g> relative elevati<strong>on</strong>. For<str<strong>on</strong>g>the</str<strong>on</strong>g> hybrid in San Francisco Bay as for S. alterniflora <strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g>Atlantic coast, <str<strong>on</strong>g>the</str<strong>on</strong>g> lower limit is probably set by <str<strong>on</strong>g>the</str<strong>on</strong>g> hypoxiaresulting from tidal flooding, while <str<strong>on</strong>g>the</str<strong>on</strong>g> upper elevati<strong>on</strong> isdetermined by salt stress, desiccati<strong>on</strong>, and competitivepressure from o<str<strong>on</strong>g>the</str<strong>on</strong>g>r species. The dominant representativesfrom different plant communities al<strong>on</strong>g a topographicgradient will have different biomass distributi<strong>on</strong>s (a, band c values in Eq. 2) that may or may not overlap, andinterspecific competiti<strong>on</strong> or facilitative interacti<strong>on</strong>s maymodify <str<strong>on</strong>g>the</str<strong>on</strong>g> shapes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> curves where overlap occurs (eg.Bertness 1991; Emery et al. 2001; Bertness & Ewanchuk2002; Pennings et al. 2005). These distributi<strong>on</strong>s can bedescribed by a family <str<strong>on</strong>g>of</str<strong>on</strong>g> curves:B i= a iD + b iD 2 + c i(2)where a, b, and c are coefficients that determine <str<strong>on</strong>g>the</str<strong>on</strong>g> upperand lower depth limits, and magnitude <str<strong>on</strong>g>of</str<strong>on</strong>g> B and where <str<strong>on</strong>g>the</str<strong>on</strong>g>subscript i refers to a specific dominant species or communitytype. Depth, D (cm), is positive for depths lessthan MHHW. These curves can be viewed as dimensi<strong>on</strong>s<str<strong>on</strong>g>of</str<strong>on</strong>g> a species’ fundamental (in <str<strong>on</strong>g>the</str<strong>on</strong>g> absence <str<strong>on</strong>g>of</str<strong>on</strong>g> competitors)or realized (in <str<strong>on</strong>g>the</str<strong>on</strong>g> presence <str<strong>on</strong>g>of</str<strong>on</strong>g> competitors) niche, sensuHutchins<strong>on</strong> (1957). The values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> coefficients a, b, and cwill also differ regi<strong>on</strong>ally as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tide range, salinity,or climate. In examples discussed below, <str<strong>on</strong>g>the</str<strong>on</strong>g> values <str<strong>on</strong>g>of</str<strong>on</strong>g>a, b, and c where chosen to represent hypo<str<strong>on</strong>g>the</str<strong>on</strong>g>tical specieswith biomass distributi<strong>on</strong>s that span different ranges al<strong>on</strong>gan intertidal gradient.MHHW is used as <str<strong>on</strong>g>the</str<strong>on</strong>g> zero datum (D 0) for c<strong>on</strong>veniencesince it is approximates <str<strong>on</strong>g>the</str<strong>on</strong>g> elevati<strong>on</strong> where biomassdensity and sedimentati<strong>on</strong> rate approach zero. However,because MHHW is based up<strong>on</strong> an arithmetic average <str<strong>on</strong>g>of</str<strong>on</strong>g><str<strong>on</strong>g>the</str<strong>on</strong>g> higher high water height <str<strong>on</strong>g>of</str<strong>on</strong>g> each tidal day observedover <str<strong>on</strong>g>the</str<strong>on</strong>g> Nati<strong>on</strong>al Tidal Datum Epoch, D 0may differ fromMHHW regi<strong>on</strong>ally, depending <strong>on</strong> factors such as windtides. The departure <str<strong>on</strong>g>of</str<strong>on</strong>g> D 0from MHHW is probably greatestin microtidal estuaries where wind tides <str<strong>on</strong>g>of</str<strong>on</strong>g>ten dominateastr<strong>on</strong>omical tides. Moreover, MHHW will vary due tolow frequency variability in mean sea level and with <str<strong>on</strong>g>the</str<strong>on</strong>g>18.6-yr lunar nodal cycle (Stumpf and Haines, 1998). Thelunar nodal cycle changes <str<strong>on</strong>g>the</str<strong>on</strong>g> tidal amplitude by about 5 cmand is simulated below by allowing D 0to vary by 5 cm at afrequency <str<strong>on</strong>g>of</str<strong>on</strong>g> 1/18.6 yr.- 110 -