Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.

Biological controls on resuspension and the relationship between particle size and the Kolmogorov length scale in a shallow coastal sea

Measurements of suspended particle matter (SPM) and turbulence have been obtained over five tidal surveys during spring and summer 2010 at station L4 (5025 degrees N 04.22 degrees W, depth 50 m), in the Western English Channel. The relationship between turbulence intensity and bed stress is explored, with an in-line holographic imaging system evaluating the extent to which material is resuspended. Image analysis allows for the identification of SPM above a size threshold of 200 pm, capturing particle variability across tidal cycles and the two seasons. Dissipation of turbulent kinetic energy, which exceeds 10(-5) W kg(-1), yields maximum values of bed stress of between 0.17 and 0.20 N m(-2), frequently resulting in the resuspension of material from the bed. Resuspension is shown to promote aggregation of SPM into flocs, where the size of such particles is theoretically determined by the Kolmogorov microscale, l(k). During the spring surveys, flocs of a size larger than lk were observed, though this was not repeated during summer. It is proposed that the presence of gelatinous, biological material in spring allows flocculated particles to exceed l(k). This suggests that under specific circumstances, the limiting factor on the growth of flocculated SPM is not only turbulence, as previously thought, but the presence or absence of certain types of biological particle.

Calorific Ash Carbon And Nitrogen-Content In Relation To Length And Dry-Weight Of Parathemisto-Gaudichaudi (Amphipoda Hyperiidea) In The North-East Atlantic Ocean

The calorific, ash, carbon and nitrogen content, length and dry weight were determined for the hyperiid Parathemisto gaudichaudi (Guerin). Regression equations for all these variables were determined so that they can be estimated by calculation from measurements of length of the hyperiid. Mean values for total nitrogen and carbon were 7.79±0.85% and 36.80±4.18% of the dry weight, respectively. The carbon to calorific equivalent for P. gaudichaudi was 10.37 kcal g-1 carbon (9.13 kcal g-1 when corrected for nitrogen). The calorific value for ash-free adult P. gaudichaudi was 5.138 kcal g-1±1.309 (4.510 kcal g-1 when corrected for nitrogen). This large variation in the calorific content (coefficient of variation of 25.84%) can be accounted for largely by variation in the ash content (coefficient of variation of 21.84%). The calorific value determined for P. gaudichaudi is similar to that measured for other carnivorous crustaceans and adds support to the hypothesis that animals with high calorific content have a low fecundity and an energy-rich store which can be used as a buffer during unfavourable periods in their life.

Ranking of length-class seasonal and regional effects on dietary compositions of the co-occurring Pagrus auratus (Sparidae) and Pseudocaranx georgianus (Carangidae)

Using an effective combination of multivariate testing and ordination analyses, this study compares the extents to which the diets of two co-occurring fish species (Pagrus auratus and Pseudocaranx georgianus) are related to body size (length class), season and region and the rank order importance of those effects. Thus, volumetric dietary compositions were determined for these species on the lower west coast of Australia, where both are abundant, and for P. auratus from the mid west coast and P. georgianus from the south coast. The diet of P. auratus on the lower west coast was strongly related to body size and slightly less to season. With increasing body size, its diet shifted from predominantly ophiuroids to larger prey, such as brachyuran crabs, teleosts, echinoids and ultimately asteroids, probably reflecting a shift from foraging over soft sediments to areas over and around reefs. Seasonal changes on the lower west coast were restricted mainly to small P. auratus, while larger fish underwent seasonal changes further north. Analyses using a common size range of medium to larger P. auratus demonstrated that dietary composition differed more between regions than seasons. The relationships between diet and length class of P. georgianus on both the lower west and south coasts were less pronounced than for P. auratus and seasonal changes were restricted to the south coast, where amphipod consumption increased markedly in summer. The diet of P. georgianus was related far more to region than length class and season, with more small teleosts, small crabs, carideans and littorinids and less amphipods, isopods and small bivalves being ingested on the lower west than south coasts. Although crabs and teleosts were important typifying prey of P. auratus and P. georgianus, when co-occurring, the former predator tended to ingest greater volumes of larger and often less mobile prey. This reflects differences in dentition, jaw morphology and feeding behaviour and reduces the potential for competition for food resources. The results imply that P. auratus and P. georgianus are opportunistic feeders and that the effects of length class, season and region on dietary composition and their rank orders can vary markedly between species and for length class and season between regions for the same species.

Variation among northeast Atlantic regions in the responses of zooplankton to climate change: Not all areas follow the same path

Broad scale climate forcing can interact with local environmental processes to affect the observed ecological phenomena. This causes potential problems of over-extrapolation for results from a limited number of sites or the averaging out of region-specific responses if data from too wide an area are combined. In this study, an area similar in extent to the Celtic Biscay Large Marine Ecosystem, but including off-shelf areas, was partitioned using clustering of satellite chlorophyll (chl-a) measurements. The resulting clusters were used to define areas over which to combine copepod data from the Continuous Plankton Recorder. Following filtering due to data limitations, nine regions were defined with sufficient records for analysis. These regions were consistent with known oceanographic structure in the study area. Off-shelf regions showed a progressively later timing in the seasonal peak of chl-a measurements moving northwards. Generalised additive models were used to estimate seasonal and multiannual signals in the adult and juvenile stages of Calanus finmarchicus, C. helgolandicus and the Paracalanus–Pseudocalanus group. Associations between variables (sea surface temperature (SST), phenology and annual abundance) differed among taxonomic groups, but even within taxonomic groups, relationships were not consistent across regions. For example, in the deep waters off Spain and Portugal the annual abundance of Calanus finmarchicus has a weak positive association with SST, in contrast to the pattern in most other regions. The regions defined in this study provide an objective basis for investigations into the long term dynamics of plankton populations and suggest suitable sub regions for deriving pelagic system indicators.

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.