Summary1 Spartina alterniflora sets very little viable seed at the leading edges of an invasion in Willapa Bay, Washington, USA, where it was introduced c . 100 years ago. This largely outbreeding, rhizomatous grass recruits into previously unoccupied areas at low density, so young plants initially grow isolated from one another but eventually coalesce to form continuous meadows. 2 Isolated recruits set approximately one-tenth the seed of meadow plants at five sites, spread over the 230 km 2 of Willapa Bay mudflats, and this seed germinated at only one-third the rate observed in meadow plants. 3 The consistent patterns suggested that the low seed set in the isolated plants was largely due to the demographic effects of density. Differences between sites in the incidence and amount of seed set and germination rate indicated, however, that there was some environmental influence. 4 These data imply that plants in newly invaded, low-density areas produce little viable seed until rhizomatous growth brings them into close contact. This Allee effect could substantially reduce the rate of invasion.

Results from both a spatially explicit stochastic simulation model and a spatially implicit deterministic model show that a weak Allee effect can slow the spread of an invasive plant, Spartina alterniflora, in a Pacific Coast estuary. The mean rate of spread with the Allee effect is ϳ19%; removing the Allee effect results in a mean rate of spread of ϳ31%. Sensitivity analysis both with and without the Allee effect reveal that seedling establishment, inflorescence density, and outcrossed seed production are key factors determining invasion rate. When there is an Allee effect, the invasion rate is sensitive to variation in self-pollinated seed production. By structuring the population according to density classes instead of the more usual age or stage classes, the deterministic model demonstrates a novel way of representing density dependence and an Allee effect in population biology. This approach could be applied to model the population dynamics of any species that spreads from multiple foci and in which these foci later coalesce.

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We present a stochastic model of clonal growth in uncrowded environments and use it to study data of 7,536 clones from the invasion of Willapa Bay, Washington by the Atlantic cordgrass Spartina alterniflora. The model incorporates effects on clone growth of covariates, spatial autocorrelation, and temporal trends. The deterministic component of the model assumes that growth rate of a clone's area is proportional to its perimeter, resulting in constant radial growth of the clone. The full stochastic model is built assuming that the fluctuations of radial growth increments (differences of square root-transformed areas) are normally distributed with constant variance. Graphical fit analysis with the density probability plot technique indicates that the stochastic model provides an excellent description of the S. alterniflora invasion. Variation in Spartina growth was significantly but weakly (5%) related to intertidal elevation, substrate type, year of survey, and the twoway interactions between these variables, suggesting that factors intrinsic to Spartina, along with localized high frequency noise, dominate the effects of larger scale abiotic factors on clone growth. Our model of clonal growth is potentially applicable to other systems with approximately circular plants or lichens.