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Determining how to cost‐effectively allocate resources for managing invasive species is a notoriously difficult problem. Invasive species control problems are always spatiotemporal, but much of the current theory about control strategies is either spatial or temporal. This article uses a deterministic spatiotemporal model of invasive species dynamics and identifies the optimal management strategy across a range of situations. The optimal solution points a principle of targeting the source of the population, which in many cases is the region of the landscape where the invader is most abundant. The analysis presented here is the first capable of solving for optimal strategies for invasive species over large and irregular environments. Thus, it is an important step forward for both the understanding of control strategies and the application to management scenarios.

Invading organisms may spread through local movements (giving rise to a diffusion-like process) and by long-distance jumps, which are often human-mediated. The local spread of invading organisms has been fit with varying success to models that couple local population growth with diffusive spread, but to date no quantitative estimates exist for the relative importance of local dispersal relative to human-mediated long-distance jumps. Using a combination of literature review, museum records, and personal surveys, we reconstruct the invasion history of the Argentine ant (Linepithema humile), a wide-spread invasive species, at three spatial scales. Although the inherent dispersal abilities of Argentine ants are limited, in the last century, human-mediated dispersal has resulted in the establishment of this species on six continents and on many oceanic islands. Human-mediated jump dispersal has also been the primary mode of spread at a continental scale within the United States. The spread of the Argentine ant involves two discrete modes. Maximum distances spread by colonies undergoing budding reproduction averaged 150 m/year, whereas annual jump-dispersal distances averaged three orders of magnitude higher. Invasions that involve multiple dispersal processes, such as those documented here, are undoubtedly common. Detailed data on invasion dynamics are necessary to improve the predictive power of future modeling efforts.

The plant trade provides a major mechanism for the long-distance dispersal of land snails, including slugs, which have low natural mobility. Whereas inspections at national borders intercept many in-coming snails, dispersal within countries is much less well regulated and documented. To investigate the role of plant nurseries as a source for the distribution of non-native invertebrates, particularly land snails, we surveyed snails in 28 nurseries in Oklahoma (United States) and compared our survey with similar surveys worldwide. We found 36 taxa, including 16 species not native to the region; 11 of these were new state records. Snail species richness increased with increasing outside area of snail-appropriate habitat, but not with enclosed greenhouse area. Species composition was similar among nurseries and Oklahoma nurseries shared several species with nurseries in Hawaii and Europe. Appropriate models for the dispersal of snails via plant nurseries are the transport hub model (snails moving as contaminants on plants coming into and leaving nurseries) and, for snail populations already established in nurseries, the stratified diffusion model (contamination of plants by snails within nurseries, followed by long-distance jumps as plants are sold and transported). Potted plants are portable habitats that protect snails from detection, pesticides and desiccation. Dispersing snails may survive in urban habitats, where mulching and watering may ameliorate hot, dry summers and cold winters.

The theoretical literature on human population dispersal processes at the large time and space scale is reviewed, including references to and discussions of relevant empirical data. The basic Fisher-KPP reaction-diffusion system is summarized for the single population situation, and developments relating to the Allee effect, density-dependent dispersal, time delay, advection, spatial and temporal heterogeneity, and anomalous and stratified diffusion are reviewed. Two- and three-population competitive reaction-diffusion systems of Lotka-Volterra type are also reviewed, as are dynamic approaches to carrying capacity that incorporate predator-prey instabilities, ecosystem engineering, and gene-culture coevolution.

The glassy-winged sharpshooter, Homalodisca vitripennis (Germar) [formerly Homalodisca coagulata (Say)] (Hemiptera: Cicadellidae), has recently emerged as a serious invasive pest. From its natural range in the southeast USA and northeast Mexico, it invaded successively California (late 1980s), French Polynesia (1999), Hawaii (2004), and recently Easter Island (2005) inadvertently through the transportation of infested plants. In French Polynesia, H. vitripennis has reached impressive densities becoming an important pest threatening agriculture, native biodiversity, as well as being a major social nuisance. Since 1999, H. vitripennis spread rapidly from Tahiti to neighboring islands, colonizing most of the archipelagos of French Polynesia. In this paper, we present the results of surveys of H. vitripennis populations from 15 islands of French Polynesia and use these data to investigate the invasion dynamics and colonization processes of this pest in a tropical climate. We found H. vitripennis present in 10 islands with two new records confirmed. Our analyses suggest that: (1) H. vitripennis abundance is strongly associated with urbanization, with highest pest densities found in the most developed coastal areas of infested islands, (2) H. vitripennis may exhibit an Allee effect during the early phase of an invasion, and (3) the invasion dynamics of H. vitripennis conform to a stratified dispersal model marked by rapid long-distance human-mediated movement.

Successful plant invasions require both the founding and local spread of new populations. High plant densities occur only when founding plants are able to disperse their seeds well locally to quickly colonize and fill the new patch. We test this ability in a 7-year field experiment with Carduus acanthoides, an invasive weed in several North American ecosystems. Founder plants were planted in the center of 64 m² plots and we monitored the recruitment, distribution pattern, mortality, and seed production of the seedlings that originated from these founding plants. Competing vegetation was clipped not at all, once, or twice each year to evaluate the importance of interspecific competition. More seedlings recruited in the intermediate once-clipped plots, and these seedlings also survived better. The control plots had fewer microsites for seedling recruitment; clipping a second time in September stimulated grasses to fill up the gaps. The number of C. acanthoides recruits and their median distances from the founder plants were also explained by the initial seed production of the founding plants. Overall, the experiment shows that the success of founder plants can fluctuate strongly, as 55% of the plots were empty by the sixth year. Our study suggests that the local invasion speed following initial establishment depends strongly on both the propagule pressure and availability of suitable microsites for seedling recruitment and growth.

We investigate the speed of invasion waves for a single species generated by stochastic short‐ and/or long‐distance colonizations in a time‐continuous cellular automaton (CA) model on a two‐dimensional homogenous landscape. By simulating the CA models, we demonstrate that stochasticity can dramatically increase the speed of invasion compared to the corresponding deterministic CA model or the corresponding one‐dimensional stochastic CA model. To explain this phenomenon, we first develop a mathematical model for the invasion involving only short‐distance colonization (i.e., colonization only occurs from the eight adjacent cells), and present several approximation methods for solving the model. Our analyses show that the increased wave speed in the stochastic model is due to irregularity in the shape of the wavefront. Further extension of this model to include long‐distance colonization demonstrates that stochasticity influences speeds to even greater extents in this case. Using dimension analysis, we deduced a semi‐empirical formula for the speed as a function of three parameters intrinsic to short‐ and long‐distance colonization, which agrees well with simulation results. Based on these results, we discuss how important stochasticity in colonization and spatial dimensionality are in the acceleration of invasion speed.

Pepper ( Piper nigrum L.) root rot caused by Fusarium solani f. sp. piperis (FSP; teleomorph: Nectria haematococca f. sp. piperis ) includes two symptom types called root rot (RR) type and stem rot (SR) type. In this study, the temporal and spatial associations between perithecial formation of FSP and development of SR were investigated in naturally infested fields to verify the hypothesis that ascospores from the perithecia are the major inoculum source of the SR type on vines in the field. In surveys of all vines in two neighboring pepper fields every month from December 2005 to November 2006, I mapped the locations of all vines with perithecia and all vines the SR type. The frequency of vines with perithecia increased during April and May, the late rainy season. In June, the early dry season, the number of vines with SR type greatly increased. The vertical range of perithecial formation on the vines extended to 200 cm in height, but was restricted to 30 cm in the dry season in both fields. The join-count statistics showed a significant spatial association between vines with perithecia and vines with SR type in one field ( P  = 0.042), while no significant spatial association was recognized in another field. The results suggested that ascospores from perithecia of FSP on pepper vines are likely to be one of the main inoculum sources of the SR type of the disease on adjacent vines, but they may not be the exclusive source.

We followed the invasion dynamics of the Oriental thiarid snail Thiara granifera on the Martinique island, French Antilles. This freshwater species was first discovered in 1991 in the Charpentier River, and its spread has since been analysed based on a yearly survey of the malacological fauna at more than 100 sites covering the whole island and representing 50 river systems and three pools. Four river systems were sampled at many sites. Thirteen river systems were colonized by 1997. Colonization within river systems occurred at a speed greater than 1km per year, probably resulting from both active and passive dispersal. Our results can, on the whole, be explained by a simple diffusion process. However, stratified diffusion has to be invoked in at least one river. Moreover, colonization was faster downstream than upstream, suggesting that current velocity plays a significant role in dispersal. Dispersal also occurred between river systems at a mean distance of almost 10km, though with a large variance, in accordance with the scattered colony model of stratified diffusion. The relative frequencies of T. granifera and Melanoides tuberculata, another recent invader of Martinique, were followed at three sites on the Lézarde River. The first species quickly outnumbered the second, though never wiped it out. The data therefore do not support any exclusion phenomena between these two parthenogenetic invaders. Our analysis does not indicate any obvious influence of the rise of T. granifera on the local freshwater fauna.[PUBLICATION ABSTRACT]

The paper presents a study of the diffusive transport of passive solute plumes in a two-dimensional non-homogeneous depth stratified flow domain. All the properties of the process are expressed by depth dependent deterministic functions. The method of moments, combined with the method of Green functions are chosen to determine the relevant characteristics of the flow (mass, center of mass, variance, etc.) used to describe the behaviour of the transient motion. General relationships for the n-order concentration moments are proved. Further, it is derived that the transient motion defined by time-dependent parameters tends asymptotically at large time to a stable regime whose characteristics are determined. Consequently, under certain hypotheses, an equivalence between the mean original process and a Fickian diffusive transport at large time may be established. The time required by the process to reach its asymptotic behaviour is also calculated.