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.

Macroalgae contribute to the diet of Patella vulgata from contrasting conditions of latitude and wave exposure in the UK

Analysis of gut contents and stable isotope composition of intertidal limpets (Patella vulgata) showed a major contribution of macroalgae to their diet, along with microalgae and invertebrates. Specimens were collected in areas with limited access to attached macroalgae, suggesting a major dietary component of drift algae. Gut contents of 480 animals from 2 moderately wave-exposed and 2 sheltered rocky shores in each of 2 regions (western Scotland, 55-56°N; and southwest England, 50°N), were analysed in 2 years (n = 30 site-1 yr-1). The abundance of microalgae, macroalgae and invertebrates within the guts was quantified using categorical abundance scales. Gut content composition was compared among regions and wave exposure conditions, showing that the diet of P. vulgata changes with both wave exposure and latitude. Microalgae were most abundant in limpet gut contents in animals from southwestern sites, whilst leathery/corticated macroalgae were more prevalent and abundant in limpets from sheltered and northern sites. P. vulgata appears to have a more flexible diet than previously appreciated, and these keystone grazers consume not only microalgae, but also large quantities of macroalgae and small invertebrates. To date, limpet grazing studies have focussed on their role in controlling recruitment of macroalgae by feeding on microscopic propagules and germlings. Consumption of adult algae suggests that P. vulgata may also directly control the biomass of attached macroalgae on the shore, whilst consumption of drift algae indicates that the species may play important roles in coupling subtidal and intertidal production.

Macroalgae contribute to the diet of Patella vulgata from contrasting conditions of latitude and wave exposure in the UK

Analysis of gut contents and stable isotope composition of intertidal limpets (Patella vulgata) showed a major contribution of macroalgae to their diet, along with microalgae and invertebrates. Specimens were collected in areas with limited access to attached macroalgae, suggesting a major dietary component of drift algae. Gut contents of 480 animals from 2 moderately wave-exposed and 2 sheltered rocky shores in each of 2 regions (western Scotland, 55-56°N; and southwest England, 50°N), were analysed in 2 years (n = 30 site-1 yr-1). The abundance of microalgae, macroalgae and invertebrates within the guts was quantified using categorical abundance scales. Gut content composition was compared among regions and wave exposure conditions, showing that the diet of P. vulgata changes with both wave exposure and latitude. Microalgae were most abundant in limpet gut contents in animals from southwestern sites, whilst leathery/corticated macroalgae were more prevalent and abundant in limpets from sheltered and northern sites. P. vulgata appears to have a more flexible diet than previously appreciated, and these keystone grazers consume not only microalgae, but also large quantities of macroalgae and small invertebrates. To date, limpet grazing studies have focussed on their role in controlling recruitment of macroalgae by feeding on microscopic propagules and germlings. Consumption of adult algae suggests that P. vulgata may also directly control the biomass of attached macroalgae on the shore, whilst consumption of drift algae indicates that the species may play important roles in coupling subtidal and intertidal production.