Historical data reveal power-law dispersal patterns of invasive aquatic species.

Understanding how invasive species spread is of particular concern in the current era of globalisation and rapid environmental change. The occurrence of super-diffusive movements within the context of Lévy flights has been discussed with respect to particle physics, human movements, microzooplankton, disease spread in global epidemiology and animal foraging behaviour. Super-diffusive movements provide a theoretical explanation for the rapid spread of organisms and disease, but their applicability to empirical data on the historic spread of organisms has rarely been tested. This study focuses on the role of long-distance dispersal in the invasion dynamics of aquatic invasive species across three contrasting areas and spatial scales: open ocean (north-east Atlantic), enclosed sea (Mediterranean) and an island environment (Ireland). Study species included five freshwater plant species, Azolla filiculoides, Elodea canadensis, Lagarosiphon major, Elodea nuttallii and Lemna minuta; and ten species of marine algae, Asparagopsis armata, Antithamnionella elegans, Antithamnionella ternifolia, Codium fragile, Colpomenia peregrina, Caulerpa taxifolia, Dasysiphonia sp., Sargassum muticum, Undaria pinnatifida and Womersleyella setacea. A simulation model is constructed to show the validity of using historical data to reconstruct dispersal kernels. Lévy movement patterns similar to those previously observed in humans and wild animals are evident in the re-constructed dispersal pattern of invasive aquatic species. Such patterns may be widespread among invasive species and could be exacerbated by further development of trade networks, human travel and environmental change. These findings have implications for our ability to predict and manage future invasions, and improve our understanding of the potential for spread of organisms including infectious diseases, plant pests and genetically modified organisms.

Unbiased Linear Property Estimation For Spheres From Sections Exhibiting Overprojection And Truncation

In the biological sciences, stereological techniques are frequently used to infer changes in structural parameters (volume fraction, for example) between samples from different populations or subject to differing treatment regimes. Non-homogeneity of these parameters is virtually guaranteed, both between experimental animals and within the organ under consideration. A two-stage strategy is then desirable, the first stage involving unbiased estimation of the required parameter, separately for each experimental unit, the latter being defined as a subset of the organ for which homogeneity can reasonably be assumed. In the second stage, these point estimates are used as data inputs to a hierarchical analysis of variance, to distinguish treatment effects from variability between animals, for example. Techniques are therefore required for unbiased estimation of parameters from potentially small numbers of sample profiles. This paper derives unbiased estimates of linear properties in one special case—the sampling of spherical particles by transmission microscopy, when the section thickness is not negligible and the resulting circular profiles are subject to lower truncation. The derivation uses the general integral equation formulation of Nicholson (1970); the resulting formulae are simplified, algebraically, and their efficient computation discussed. Bias arising from variability in slice thickness is shown to be negligible in typical cases. The strategy is illustrated for data examining the effects, on the secondary lysosomes in the digestive cells, of exposure of the common mussel to hydrocarbons. Prolonged exposure, at 30 μg 1−1 total oil-derived hydrocarbons, is seen to increase the average volume of a lysosome, and the volume fraction that lysosomes occupy, but to reduce their number.