Proceedings of the Third International Conference on Invasive ...

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Third</strong> <strong>International</strong> <strong>Conference</strong> on Invasive SpartinaChapter 2: Spartina Distribution and SpreadFeedbacks Among Biomass Distribution, Relative Elevationand Sea-Level RiseSubstituting for B in Eq. 1 yields <strong>the</strong> following equationthat describes <strong>the</strong> absolute change in elevation <strong>of</strong> <strong>the</strong> marshsurface as a function <strong>of</strong> depth:dY/dt = [q + k i(a iD + b iD 2 + c i)]D, for D>0 (3)Equation 3 was solved numerically for a hypo<strong>the</strong>ticalmarsh landscape with one or two species differing in <strong>the</strong>irbiomass distributions. The time-zero marsh elevation andrates <strong>of</strong> sea-level rise were set arbitrarily and model simulations<strong>of</strong> 120-yr duration were generated to allow time forconvergence on a dynamic steady state. A rate <strong>of</strong> sea-levelrise <strong>of</strong> ei<strong>the</strong>r 0.2 or 0.8 cm/yr was specified, and a sinusoidalfunction was used to simulate changes in tidal amplitude <strong>of</strong>± 2.5 cm over <strong>the</strong> 18.6-yr lunar nodal cycle, centered abouta mean tidal amplitude <strong>of</strong> 0.6 m. The coefficient values forq and k were set at 0.00018 yr -1 and 1.5 × 10 -5 cm m 2 g -1 yr -1(0.15 cm 3 g -1 yr -1 ). These parameter values were taken froma calibration <strong>of</strong> <strong>the</strong> model to North Inlet data (Morris etal. 2002). In addition, species distributions were varied inorder to explore effects on equilibrium elevation and speciespersistence. Species distributions (Eq. 2) were describedby specifying a maximum biomass and optimum elevation,operationally defined here as <strong>the</strong> elevation that results in <strong>the</strong>greatest biomass density, and species range, defined as <strong>the</strong>upper and lower depth limits.RESULTS AND DISCUSSIONThe Single Species ExampleWhen <strong>the</strong> model was solved for a single species witha distribution between 15 and 30 cm above mean sea level(Fig. 1A), and a rate <strong>of</strong> sea-level rise <strong>of</strong> 0.2 cm/yr, <strong>the</strong> marshsurface elevation equilibrated at about 26 cm above mean sealevel and a depth <strong>of</strong> 34 ± 2.9 cm (mean ± amplitude) belowMHHW (Fig 1B). This elevation is above <strong>the</strong> optimum elevationspecified in Fig. 1A, which is a condition for stability(Morris et al. 2002). The constraint on productivity imposedby high pore-water salinities that develop at super-optimalelevations is an important factor in maintaining relativeelevation, because a rise in relative sea level brings about anincrease in flooding, decreases pore water salinity (Morris1995), and increases biomass density (Morris 2000). Theincrease in biomass density will enhance sediment depositionby increasing sediment trapping efficiency (Gleason etal. 1979, Leonard & Lu<strong>the</strong>r 1995, Yang 1998).MHHW varies over <strong>the</strong> course <strong>of</strong> <strong>the</strong> 18.6-yr lunar nodalcycle by ± 2.5 cm. Consequently, <strong>the</strong> depth <strong>of</strong> marsh surfacebelow MHHW varies at <strong>the</strong> same frequency (Fig. 1B), resultingin a cycle <strong>of</strong> standing biomass with a range <strong>of</strong> 296 g/m 2(Fig. 1C). This is consistent with empirical measurementsfrom North Inlet, SC where we have seen changes in S.alterniflora productivity <strong>of</strong> 248 g m -2 yr -1 over <strong>the</strong> lunar nodalcycle. It should be noted that MHHW varies independently<strong>of</strong> MSL owing to long-period astronomical forcing, e.g. <strong>the</strong>lunar nodal cycle, but MHHW will also vary directly withchanges in MSL. Consequently, MHHW is a better tidaldatum for purposes <strong>of</strong> defining <strong>the</strong> growth ranges <strong>of</strong> intertidalspecies than is MSL.Result <strong>of</strong> Adding a Competitor with Wider Distribution andHigh BiomassWhen a competing species was added to <strong>the</strong> model witha distribution like that <strong>of</strong> species 2 in Fig. 2A, species 1was eliminated within about 10 yr (Fig. 2C). Examples arecommon <strong>of</strong> this type <strong>of</strong> interaction, such as <strong>the</strong> invasion <strong>of</strong>Fig. 1 Model results with a single species (S1), distributed as above (A), and a rate <strong>of</strong> sea-level rise <strong>of</strong> 0.2 cm/yr, as shown in B. Panel C shows <strong>the</strong>predicted biomass trajectory as (B) <strong>the</strong> marsh surface equilibrates at a relative surface elevation <strong>of</strong> about 25 cm above mean sea level (MSL) and a depthbelow MHHW <strong>of</strong> about 35 cm.- 111 -