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 SpreadFig. 2: Grey area shows area occupied by Spartina invasion <strong>of</strong> different agesas predicted by <strong>the</strong> analytical model and black area shows minimum areathat needs to be removed each year for eradication to succeed within tenyears.We used <strong>the</strong> model to explore two questions about control.First, how much Spartina has to be removed each year in orderto clear this invasion? Second, is it better to target <strong>the</strong> highdensity meadows that are producing most <strong>of</strong> <strong>the</strong> seed but notspreading vegetatively very quickly; or is it more effective totarget <strong>the</strong> low density clones that produce very little seed(because <strong>of</strong> <strong>the</strong> Allee effect) but spread vegetatively relativelymuch more quickly because <strong>the</strong>y are surrounded by open mud?We assume a fixed annual budget and that <strong>the</strong>re is a fixed costper square meter <strong>of</strong> removing Spartina; this means that a fixedmaximum area can be removed each year. We define a controlstrategy as (1) T t : <strong>the</strong> actual area <strong>of</strong> Spartina removed in eachyear t and (2) X t <strong>the</strong> proportion <strong>of</strong> <strong>the</strong> area removed that ismeadow in each year t. For a control program that lasts tenyears <strong>the</strong>re will be ten values <strong>of</strong> T, one for each year and tenvalues <strong>of</strong> X. We only consider control <strong>of</strong> clones and meadows(not seedlings) so (1 - X t ) is <strong>the</strong> proportion <strong>of</strong> <strong>the</strong> area removedthat is clones. We model control <strong>of</strong> clones by subtracting T t (1 -X t ) from <strong>the</strong> left hand side <strong>of</strong> equation 2 and we model control<strong>of</strong> meadows by subtracting T t X t from <strong>the</strong> left hand side <strong>of</strong>equation 3 (Taylor and Hastings 2004).In order to be considered successful <strong>the</strong> control strategyhas to completely eradicate <strong>the</strong> invasion within ten years. For asuccessful strategy, <strong>the</strong>re are two o<strong>the</strong>r objectives. The first isto minimize <strong>the</strong> total cost which is <strong>the</strong> same as minimizing <strong>the</strong>total area removed over <strong>the</strong> ten years (since we are assuming afixed cost per square meter). The second is to minimize <strong>the</strong>risk that this one site <strong>of</strong> <strong>the</strong> invasion poses to o<strong>the</strong>r sites inWillapa Bay. We assume that <strong>the</strong> risk <strong>of</strong> seeds escaping andcolonizing o<strong>the</strong>r mudflats in <strong>the</strong> bay is linearly proportional to<strong>the</strong> total number <strong>of</strong> seeds produced during <strong>the</strong> ten years <strong>of</strong>control. In order to minimize both cost and risk, we minimized<strong>the</strong> product <strong>of</strong> <strong>the</strong> two quantities. We used a genetic algorithmto find <strong>the</strong> optimal strategy; for details <strong>of</strong> <strong>the</strong> optimization seeTaylor and Hastings (2004). In <strong>the</strong> case when <strong>the</strong> annualA: Low BudgetB: High BudgetFig. 3: A The top left graph shows <strong>the</strong> optimal strategy (“clone first”) for eradication <strong>of</strong> a 40 year old invasion when 3600 m 2 can be removed per year for up to tenyears. White bars show <strong>the</strong> fraction <strong>of</strong> <strong>the</strong> budget applied to removal <strong>of</strong> clones and grey bars show <strong>the</strong> fraction <strong>of</strong> <strong>the</strong> budget applied to removal <strong>of</strong> meadows. Thebottom left graph shows area occupied by clones and meadows as control strategy is implemented. B. The top right graph shows <strong>the</strong> optimal strategy (“meadowfirst”) for eradication <strong>of</strong> a 40 year old invasion when 5000 m 2 can be removed per year for up to ten years. As in A, white bars show removal <strong>of</strong> clones and greybars show removal <strong>of</strong> meadows. The bottom right graph shows area occupied by clones and meadows as this control strategy is implemented. Details <strong>of</strong> <strong>the</strong> optimizationare given in text and in Taylor and Hastings (2004).- 123 -