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 SpreadMODELING THE SPREAD OF INVASIVE SPARTINA HYBRIDS IN SAN FRANCISCO BAYR.J. HALL,A.M.HASTINGS AND D.R. AYRESUniversity <strong>of</strong> California, Davis, One Shields Ave., Davis, CA 95616; rjhall@ucdavis.eduThe emergence <strong>of</strong> highly fit hybrids between native and introduced species is an increasinglywidespread problem that can impact entire ecosystems. In San Francisco Bay, a swarm <strong>of</strong> hybridcordgrass (Spartina foliosa x alterniflora) is covering vast areas <strong>of</strong> intertidal mudflat, threatening <strong>the</strong>native S. foliosa with extinction. Here we outline a modeling approach for assessing <strong>the</strong> relativeimportance <strong>of</strong> elevated hybrid fitness traits in explaining <strong>the</strong> rapidity <strong>of</strong> this invasion. Wedemonstrate that elevated growth rate, seedling survival and pollen production <strong>of</strong> hybrids relative to<strong>the</strong> native species interact to predict <strong>the</strong> observed faster-than-exponential spread <strong>of</strong> cordgrassthrough <strong>the</strong> Bay.Keywords: invasion, model, hybridization, SpartinaINTRODUCTIONAn exotic introduced into a new range is <strong>of</strong>tenphenomenally successful; this may be due to exploitation <strong>of</strong>a previously unfilled niche, a release from natural enemies,or increased competitive ability relative to <strong>the</strong> native biota(Williamson 1996). However, in many ecosystems, <strong>the</strong>emergence <strong>of</strong> hybrids between native and exotic species is<strong>the</strong> greatest threat to local biodiversity, particularly if <strong>the</strong>hybrids have superior fecundity or suvivorship comparedwith <strong>the</strong> native (Wolf et al. 2001). An example <strong>of</strong> this is <strong>the</strong>invasion <strong>of</strong> hybrid cordgrass Spartina foliosa x alterniflorain San Francisco Bay. Since <strong>the</strong> introduction <strong>of</strong> S.alterniflora in <strong>the</strong> 1970s, hybrids have emerged whosegrowth rates, fecundity and tolerance to environmentalconditions exceed that <strong>of</strong> both parental lineages (Ayres et al.2003). The hybrids impact on many organisms in <strong>the</strong> Bayby covering open mudflat crucial to feeding shorebirds,and changing <strong>the</strong> tidal pr<strong>of</strong>ile through sedimentaccumulated in <strong>the</strong>ir root mass. Contrary to classicalecological <strong>the</strong>ory, which suggests that a species withunlimited resources can grow at most exponentially (e.g.,Turchin 2003), <strong>the</strong> area covered by hybrid cordgrass in <strong>the</strong>Bay has increased super-exponentially (i.e. <strong>the</strong> growth rateper unit area is increasing through time; Fig. 1). If thisinvasion continues unchecked, it seems likely that <strong>the</strong>native S. foliosa is doomed to extinction throughintrogression (Ayres et al. 2003).In order to design effective control strategies, it is vitalto determine <strong>the</strong> key hybrid traits responsible for drivingthis invasion. Increased vegetative growth rates, elevatedpollen production and seedling survival <strong>of</strong> hybrid Spartinarelative to <strong>the</strong> native have all been proposed as contributingto <strong>the</strong> rate and extent <strong>of</strong> this invasion (Ayres et al. 2004).Ma<strong>the</strong>matical models are a useful tool for investigating <strong>the</strong>relative importance <strong>of</strong> <strong>the</strong>se mechanisms. In this paper weoutline <strong>the</strong> modeling approach used to describe <strong>the</strong>dynamics <strong>of</strong> this hybridization. We use <strong>the</strong> model to testhow increased vegetative growth rate, seedling survival andpollen production <strong>of</strong> hybrids affect <strong>the</strong> rate <strong>of</strong> populationexpansion in areas <strong>of</strong> high and low recruitment. We find thatdepending on <strong>the</strong> level <strong>of</strong> local recruitment, increasedvegetative growth rate or seedling survival <strong>of</strong> hybrids canresult in super-exponential population growth. Elevatedhybrid pollen production alone results in an increase in <strong>the</strong>frequency <strong>of</strong> hybrids in <strong>the</strong> population, but does not predictsuper-exponential growth unless coupled with elevatedhybrid growth rate or seedling survival.MODEL AND METHODSHere we outline <strong>the</strong> key modeling assumptions andsketch <strong>the</strong> derivation <strong>of</strong> <strong>the</strong> model. The derivation <strong>of</strong> <strong>the</strong> fullquantitative genetic, integro-difference equation model isFig. 1: super-exponential (bold line) vs exponential (dashed line) populationgrowth. After a sufficiently long time, <strong>the</strong> area occupied by aninvasive growing super-exponentially differs from an exponentiallygrowing population by orders <strong>of</strong> magnitude.- 117 -