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.

Climate change-related regime shifts have altered spatial synchrony of plankton dynamics in the North Sea

During the 1980s, the North Sea plankton community underwent a well-documented ecosystem regime shift, including both spatial changes (northward species range shifts) and temporal changes (increases in the total abundances of warmer water species). This regime shift has been attributed to climate change. Plankton provide a link between climate and higher trophic-level organisms, which can forage on large spatial and temporal scales. It is therefore important to understand not only whether climate change affects purely spatial or temporal aspects of plankton dynamics, but also whether it affects spatiotemporal aspects such as metapopulation synchrony. If plankton synchrony is altered, higher trophic-level feeding patterns may be modified. A second motivation for investigating changes in synchrony is that the possibility of such alterations has been examined for few organisms, in spite of the fact that synchrony is ubiquitous and of major importance in ecology. This study uses correlation coefficients and spectral analysis to investigate whether synchrony changed between the periods 1959–1980 and 1989–2010. Twenty-three plankton taxa, sea surface temperature (SST), and wind speed were examined. Results revealed that synchrony in SST and plankton was altered. Changes were idiosyncratic, and were not explained by changes in abundance. Changes in the synchrony of Calanus helgolandicus and Para-pseudocalanus spp appeared to be driven by changes in SST synchrony. This study is one of few to document alterations of synchrony and climate-change impacts on synchrony. We discuss why climate-change impacts on synchrony may well be more common and consequential than previously recognized.

Climate change-related regime shifts have altered spatial synchrony of plankton dynamics in the North Sea

During the 1980s, the North Sea plankton community underwent a well-documented ecosystem regime shift, including both spatial changes (northward species range shifts) and temporal changes (increases in the total abundances of warmer water species). This regime shift has been attributed to climate change. Plankton provide a link between climate and higher trophic-level organisms, which can forage on large spatial and temporal scales. It is therefore important to understand not only whether climate change affects purely spatial or temporal aspects of plankton dynamics, but also whether it affects spatiotemporal aspects such as metapopulation synchrony. If plankton synchrony is altered, higher trophic-level feeding patterns may be modified. A second motivation for investigating changes in synchrony is that the possibility of such alterations has been examined for few organisms, in spite of the fact that synchrony is ubiquitous and of major importance in ecology. This study uses correlation coefficients and spectral analysis to investigate whether synchrony changed between the periods 1959–1980 and 1989–2010. Twenty-three plankton taxa, sea surface temperature (SST), and wind speed were examined. Results revealed that synchrony in SST and plankton was altered. Changes were idiosyncratic, and were not explained by changes in abundance. Changes in the synchrony of Calanus helgolandicus and Para-pseudocalanus spp appeared to be driven by changes in SST synchrony. This study is one of few to document alterations of synchrony and climate-change impacts on synchrony. We discuss why climate-change impacts on synchrony may well be more common and consequential than previously recognized.