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.

Comparisons of zooplankton time series

Evidence for climate-correlated low frequency variability of various components of marine ecosystems has accumulated rapidly over the past 2 decades. There has also been a growing recognition that society needs to learn how the fluctuations of these various components are linked, and to predict the likely amplitude and steepness of future changes. Demographic characteristics of marine zooplankton make them especially suitable for examining variability of marine ecosystems at interannual to decadal time scales. Their life cycle duration is short enough that there is little carryover of population membership from year to year, but long enough that variability can be tracked with monthly-to-seasonal sampling. Because zooplankton are rarely fished, comparative analysis of changes in their abundance can greatly enhance our ability to evaluate the importance of and interaction between physical environment, food web, and fishery harvest as causal mechanisms driving ecosystem level changes. A number of valuable within-region analyses of zooplankton time series have been published in the past decade, covering a variety of modes of variability including changes in total biomass, changes in size structure and species composition, changes in spatial distribution, and changes in seasonal timing. But because most zooplankton time series are relatively short compared to the time scales of interest, the statistical power of local analyses is often low, and between-region and between-variable comparisons are also needed. In this paper, we review the results of recent within- and between-region analyses, and suggest some priorities for future work.

Distribution and abundance of sardine (Sardina pilchardus) eggs in the English Channel from Continuous Plankton Recorder sampling

Continuous Plankton Recorder (CPR) samples from the English Channel and adjacent Celtic shelf, taken over the period 1958-1980, were analysed for sardine (Sardina pilchardus) eggs. Results showed the progression of sardine spawning along the English Channel from west to east from March to August and a return from east to west from September to November. This corresponds with the two seasonal peaks of sardine egg abundance in the western Channel: the main summer peak being in May/June, with a smaller autumn peak in October/November. Long-term changes in sardine egg abundance in CPR samples showed a decline in summer spawning from the late 1960s, but no clear trend in autumn-spawned egg abundance. Similar patterns were observed in the numbers of sardine eggs sampled by conventional plankton net tows at the time-series Station L5 off Plymouth. This supports the use of the longer time-series of sardine egg data at L5 as being representative of a wider area and emphasizes the importance in continuation of the L5 time-series.

Continuous Plankton Records - Persistence In Time-Series And The Population-Dynamics Of Pseudocalanus-Elongatus And Acartia-Clausi

Rates of population increase in early spring and the sizes of overwintering stocks were calculated for the planktonic copepods Pseudocalanus elongatus and Acartia clausi for a set of areas covering the open waters of the north-east Atlantic Ocean and the North Sea for the period 1948 to 1979. For both species, the rates of population increase were higher in the open ocean than in the North Sea and appear to be related to temperature. The overwintering stocks in the North Sea were larger than those in the open ocean and are probably related to phytoplanton concentration. P. elongatus shows higher overwintering stocks and lower rates of population increase than A. clausi, resulting in different levels of persistence in the stocks of the two species. It is suggested that this difference in persistence is responsible for differences between the two species with respect to geographical distribution in summer and different patterns of year-to-year fluctuations in abundance.

Simulating The Impact Of Technological-Change On Dissolved Cadmium Distribution In The Severn Estuary

An estuarine model is described which computes the dispersive and advective properties of the Severn Estuary. It was calibrated and validated using 50 measured salinity distributions and then used to predict the magnitude and sitings of the major inputs of dissolved cadmium levels throughout the estuary. The results provided an impetus for implementing tighter controls on effluents and for improving estimates of cadmium discharges from industrial sources. The model has also been used to investigate the sensitivity of the estuarine system to changes in dispersion; by considering large reductions in the dispersion coefficients it is hoped that the results might be indicative of the environmental consequences following the construction of a tidal power generating scheme.