Proceedings of the Third International Conference on Invasive ...

Chapter 2: Spartina Distribution and Spread<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Third</strong> <strong>International</strong> <strong>Conference</strong> on Invasive Spartinarates and, using <strong>the</strong>se parameters, we built a spatially explicitsimulation model <strong>of</strong> <strong>the</strong> spread <strong>of</strong> Spartina. Full details <strong>of</strong> <strong>the</strong>model and its parameterization are given in Taylor et al. 2004.The model represents one square kilometer <strong>of</strong> mudflat,arranged as a square lattice <strong>of</strong> 1000 by 1000 cells; each cell isone square meter and can ei<strong>the</strong>r be occupied by Spartina orvacant. The simulated invasion starts from a single occupiedcell in <strong>the</strong> center <strong>of</strong> <strong>the</strong> lattice, representing a single 1-m 2clone, and is run for 100 years. In each year <strong>the</strong> plants growvegetatively into empty neighboring sites and produce arandom number <strong>of</strong> seeds (distributed according to a Poissondistribution), <strong>the</strong> seeds disperse exponentially away from <strong>the</strong>parents and have a small probability <strong>of</strong> becoming establishedclones. When two clones become adjacent to one ano<strong>the</strong>r, thatpatch <strong>of</strong> Spartina is classified as a meadow. We have twolevels <strong>of</strong> seed production; cells that are classified as clonesproduce a small number <strong>of</strong> seeds; cells that are classified asmeadows produce a larger number. We created a variant <strong>of</strong> <strong>the</strong>model in which we removed <strong>the</strong> Allee effect by setting <strong>the</strong>seed production <strong>of</strong> clones to <strong>the</strong> same as <strong>the</strong> seed production <strong>of</strong>meadows.We found that <strong>the</strong> Allee effect dramatically slows <strong>the</strong>invasion. From 380 runs <strong>of</strong> <strong>the</strong> model, with parameters variedover <strong>the</strong>ir estimated ranges, we calculated an average increasein area occupied <strong>of</strong> about 20% per year with <strong>the</strong> Allee effect;<strong>the</strong> area occupied by Spartina doubles approximately every 5years. Removing <strong>the</strong> Allee effect and repeating those runs gavean average <strong>of</strong> 30% increase per year, a doubling time <strong>of</strong> lessthan 4 years (Taylor et al. 2004) (Fig. 1). This result isconsistent with <strong>the</strong>oretical investigations <strong>of</strong> <strong>the</strong> consequences<strong>of</strong> an Allee effect in invasions (Lewis and Kareiva 1993, Wangand Kot 2001, Wang et al. 2002).ANALYTICAL MODEL OF SPARTINA SPREADWe <strong>the</strong>n created a non-spatial analytical model <strong>of</strong> thissame process (Taylor et al. 2004). We kept some <strong>of</strong> <strong>the</strong>structure <strong>of</strong> <strong>the</strong> simulation model by using as <strong>the</strong> mainvariables <strong>the</strong> area occupied by seedlings (S), <strong>the</strong> area occupiedby clones (C) and <strong>the</strong> area occupied by meadows (M). O<strong>the</strong>rvariables are <strong>the</strong> number <strong>of</strong> individual clones (N C ) and <strong>the</strong>number <strong>of</strong> meadows (N M ).The main equations <strong>of</strong> this model are:S t+1 = f C C t + f M M t (1)C t+1 = S t + (1-)g c C t (2)M t+1 = g c C t + g M M t (3)Equation 1 says that seedlings are created from <strong>the</strong> seedsproduced by clones and seeds produced by meadows. Thefecundity <strong>of</strong> <strong>the</strong> clones (f C ) is much smaller than <strong>the</strong> fecundity<strong>of</strong> <strong>the</strong> meadows (f M ) when <strong>the</strong>re is an Allee effect. We remove<strong>the</strong> Allee effect in <strong>the</strong> same way as in <strong>the</strong> simulation model, bysetting f C equal to fM. Equation 2 says that <strong>the</strong> area occupiedFig. 1: Mean area occupied by Spartina as predicted by 380 runs <strong>of</strong> <strong>the</strong> simulationmodel with and without <strong>the</strong> Allee effect. The upper line (squares)shows <strong>the</strong> predicted area occupied when <strong>the</strong>re is no Allee effect and <strong>the</strong>lower line (circles) shows <strong>the</strong> predicted area occupied with <strong>the</strong> Allee effect.A modified form <strong>of</strong> this figure was originally published in Taylor et al. 2004,Ecology 85(12).by clones increases by seedlings becoming clones and also byvegetative spread <strong>of</strong> existing clones (at growth rate g C ) anddecreases by a proportion <strong>of</strong> <strong>the</strong> area occupied by clones ()coalescing into o<strong>the</strong>r patches <strong>of</strong> Spartina and becomingmeadow. Equation 3 describes <strong>the</strong> dynamics <strong>of</strong> area occupiedby meadow which increases by <strong>the</strong> clones coalescing intomeadow at rate and also by vegetative growth <strong>of</strong> existingmeadow (growth rate g M ). These equations are only a partialdescription <strong>of</strong> <strong>the</strong> model. The full model includes equations for<strong>the</strong> dynamics <strong>of</strong> <strong>the</strong> number <strong>of</strong> clones (N C ) and <strong>the</strong> number <strong>of</strong>meadows (N M ) and also describes how <strong>the</strong> parameters (,f C ,f M ,g C , and g M ) change with <strong>the</strong> area occupied by clones andmeadows and number <strong>of</strong> clones and meadows. A fulldescription <strong>of</strong> this model is provided in (Taylor et al. 2004).Several comparisons <strong>of</strong> <strong>the</strong> analytical model with <strong>the</strong>simulation model give us confidence that <strong>the</strong> two modelspredict <strong>the</strong> same dynamics. We use <strong>the</strong> analytical model to findoptimal density-based eradication strategies. Full details <strong>of</strong> thiswork are given in Taylor and Hastings 2004, and we give abrief summary here.MANAGEMENT STRATEGIESEfforts to control or eradicate Spartina in Willapa Baybegan in <strong>the</strong> early 1990s and it soon became obvious thateradicating this plant this was not going to be easy or cheap.Spartina can be removed mechanically by mowing or diggingand it can be killed with herbicide but all <strong>of</strong> <strong>the</strong> methodsrequire specialized equipment and repeated treatments (Patten,this issue). Large scale efforts to control this invasion began in2003 and current plans predict that <strong>the</strong> invasion will beeradicated within ten years if <strong>the</strong> current level <strong>of</strong> control ismaintained (Murphy 2003).- 122 -