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.

The role of advection in the distribution of plankton populations at a moored 1-D coastal observatory

The degree to which advection modulates the distribution of plankton populations at a 1-D coastal observatory was assessed at station L4 in the western English Channel (50°15′N 4°13′W, depth 50 m), part of the Western Channel Observatory (WCO). Five tidal-cycle surveys were conducted, three in spring and two in summer 2010. Observations of the physical characteristics of L4 were obtained by using a moored acoustic doppler current profiler (ADCP) and a free-falling microstructure sensor (MSS). The moored ADCP highlighted the presence of vertical shear, with typical values of U during spring tides of ∼0.5 m s−1 at the surface and ∼0.2 m s−1 at the bed. The distribution of phyto- and zooplankton populations above a size threshold of 200 μm were examined using an in-line holographic imaging system, the Holocam. Variability in time as well as depth is a common feature throughout each of the surveys, with examples of recorded numbers of phytoplankton that ranged between 1300 L−1 and 2300 L−1 at the same depth but at different points within the tidal cycle. Further, at the same points in the tidal cycle the number of recorded zooplankton was also seen to vary, specifically with the identification of gelatinous planula in spring that increased the observed number to maximums of between 140 L−1 and 220 L−1 in the upper layer, considerably higher that the corresponding WP-2 net counts for a similar period. Specific aspects of the movement and transfer of plankton relating to advection and interaction with the pycnocline are identified, both across tidal cycles and seasons.