A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling

1. A first step in the analysis of complex movement data often involves discretisation of the path into a series of step-lengths and turns, for example in the analysis of specialised random walks, such as Lévy flights. However, the identification of turning points, and therefore step-lengths, in a tortuous path is dependent on ad-hoc parameter choices. Consequently, studies testing for movement patterns in these data, such as Lévy flights, have generated debate. However, studies focusing on one-dimensional (1D) data, as in the vertical displacements of marine pelagic predators, where turning points can be identified unambiguously have provided strong support for Lévy flight movement patterns. 2. Here, we investigate how step-length distributions in 3D movement patterns would be interpreted by tags recording in 1D (i.e. depth) and demonstrate the dimensional symmetry previously shown mathematically for Lévy-flight movements. We test the veracity of this symmetry by simulating several measurement errors common in empirical datasets and find Lévy patterns and exponents to be robust to low-quality movement data. 3. We then consider exponential and composite Brownian random walks and show that these also project into 1D with sufficient symmetry to be clearly identifiable as such. 4. By extending the symmetry paradigm, we propose a new methodology for step-length identification in 2D or 3D movement data. The methodology is successfully demonstrated in a re-analysis of wandering albatross Global Positioning System (GPS) location data previously analysed using a complex methodology to determine bird-landing locations as turning points in a Lévy walk. For this high-resolution GPS data, we show that there is strong evidence for albatross foraging patterns approximated by truncated Lévy flights spanning over 3·5 orders of magnitude. 5. Our simple methodology and freely available software can be used with any 2D or 3D movement data at any scale or resolution and are robust to common empirical measurement errors. The method should find wide applicability in the field of movement ecology spanning the study of motile cells to humans.

Simulation of mackerel (Scomber scombrus) recruitment with an individual-based model and comparison with field data

An individual-based model (IBM) for the simulation of year-to-year survival during the early life-history stages of the north-east Atlantic stock of mackerel (Scomber scombrus) was developed within the EU funded Shelf-Edge Advection, Mortality and Recruitment (SEAMAR) programme. The IBM included transport, growth and survival and was used to track the passive movement of mackerel eggs, larvae and post-larvae and determine their distribution and abundance after approximately 2 months of drift. One of the main outputs from the IBM, namely distributions and numbers of surviving post-larvae, are compared with field data as recruit (age-0/age-1 juveniles) distribution and abundance for the years 1998, 1999 and 2000. The juvenile distributions show more inter-annual and spatial variability than the modelled distributions of survivors; this may be due to the restriction of using the same initial egg distribution for all 3 yr of simulation. The IBM simulations indicate two main recruitment areas for the north-east Atlantic stock of mackerel, these being Porcupine Bank and the south-eastern Bay of Biscay. These areas correspond to areas of high juvenile catches, although the juveniles generally have a more widespread distribution than the model simulations. The best agreement between modelled data and field data for distribution (juveniles and model survivors) is for the year 1998. The juvenile catches in different representative nursery areas are totalled to give a field abundance index (FAI). This index is compared with a model survivor index (MSI) which is calculated from the total of survivors for the whole spawning season. The MSI compares favourably with the FAI for 1998 and 1999 but not for 2000; in this year, juvenile catches dropped sharply compared with the previous years but there was no equivalent drop in modelled survivors.

Composite front maps for improved visibility of dynamic sea-surface features on cloudy SeaWiFS and AVHRR data

Novel techniques have been developed for increasing the value of cloud-affected sequences of Advanced Very High Resolution Radiometer (AVHRR) sea-surface temperature (SST) data and Sea-viewing Wide Field-of-view Sensor (SeaWiFS) ocean colour data for visualising dynamic physical and biological oceanic processes such as fronts, eddies and blooms. The proposed composite front map approach is to combine the location, strength and persistence of all fronts observed over several days into a single map, which allows intuitive interpretation of mesoscale structures. This method achieves a synoptic view without blurring dynamic features, an inherent problem with conventional time-averaging compositing methods. Objective validation confirms a significant improvement in feature visibility on composite maps compared to individual front maps. A further novel aspect is the automated detection of ocean colour fronts, correctly locating 96% of chlorophyll fronts in a test data set. A sizeable data set of 13,000 AVHRR and 1200 SeaWiFS scenes automatically processed using this technique is applied to the study of dynamic processes off the Iberian Peninsula such as mesoscale eddy generation, and many additional applications are identified. Front map animations provide a unique insight into the evolution of upwelling and eddies.

Environmental context explains Lévy and Brownian movement patterns of marine predators

An optimal search theory, the so-called Levy-flight foraging hypothesis(1), predicts that predators should adopt search strategies known as Levy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey(2-4). Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Levy behaviour has recently been questioned(5,6). Consequently, whether foragers exhibit Levy flights in the wild remains unclear. Crucially, moreover, it has not been tested whether observed movement patterns across natural landscapes having different expected resource distributions conform to the theory's central predictions. Here we use maximum-likelihood methods to test for Levy patterns in relation to environmental gradients in the largest animal movement data set assembled for this purpose. Strong support was found for Levy search patterns across 14 species of open-ocean predatory fish (sharks, tuna, billfish and ocean sunfish), with some individuals switching between Levy and Brownian movement as they traversed different habitat types. We tested the spatial occurrence of these two principal patterns and found Levy behaviour to be associated with less productive waters (sparser prey) and Brownian movements to be associated with productive shelf or convergence-front habitats (abundant prey). These results are consistent with the Levy-flight foraging hypothesis(1,7), supporting the contention(8,9) that organism search strategies naturally evolved in such a way that they exploit optimal Levy patterns.

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.