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.

Comparing copepod time-series in the north of Spain: Spatial autocorrelation of community composition

Four time-series of copepod species biomass in the north of Spain were contrasted to demonstrate spatial autocorrelation of local communities and their responses to short-term local and regional variability in oceanographic conditions. The series represented coastal and oceanic environments along a marked gradient of influence of seasonal upwelling from Galicia to the Mar Cantábrico (S Bay of Biscay), and each one included at least 10 years of continuous data collected at monthly frequency. Community composition (i.e. species number and diversity) was very consistent through the region, but local variations in the presence of new species and the relative proportions of common species allowed for the characterisation of the response to the environment at each site. Small-sized species were more frequent near the coast. A few species, however, captured the main patterns of variability in all series. Calanus helgolandicus and Acartia (mainly Acartia clausi) were generally the main contributors to total biomass, while other species as Paracalanus parvus and Clausocalanus spp. were important only at some locations. Most copepod indices were positively correlated with upwelling, either considering the whole community (biomass, species richness and diversity) or individual species, but only in the coastal series analysed since 1991. Copepods in the nearby ocean, however, showed negative correlations with upwelling in the period 1960–1986. The effects of upwelling may have been modulated by local factors, as showed by the increases in biomass, number of species and diversity in associations with increases in sea surface temperature in Galicia, while in the Mar Cantábrico only the warming-tolerant species increased and those typical of upwelling decreased. Density stratification of the water column was associated with decreases in total copepod biomass in Galicia, while it favoured the increase in species richness in the Mar Cantábrico. Nearly all significant responses of copepods to environmental variability were delayed by up to 5 months, showing the importance of considering time-lags in the analysis of temporal responses of zooplankton.

Spatial variability of marine climate change impacts in the North Atlantic

There is an accumulating body of evidence to suggest that many marine ecosystems in the North Atlantic, both physically and biologically are responding to changes in regional climate caused predominately by the warming of air and sea surface temperatures (SST) and to a varying degree by the modification of oceanic currents, precipitation regimes and wind patterns. The biological manifestations of rising SST and oceanographic changes have variously taken the form of biogeographical, phenological, physiological and community changes. For example, during the last 40 years there has been a northerly movement of warmer water plankton by 10 degree latitude in the north-east Atlantic and a similar retreat of colder water plankton to the north. This geographical movement is much more pronounced than any documented terrestrial study, presumably due to advective processes playing an important role. Other research has shown that the plankton community in the North Sea has responded to changes in SST by adjusting their seasonality (in some cases a shift in seasonal cycles of over six weeks has been detected), but more importantly the response to climate warming varied between different functional groups and trophic levels, leading to mismatch. Therefore, while it has been documented that marine ecosystems in certain regions of the Atlantic have undergone some conspicuous changes over the last few decades it is not known whether this is a pan-oceanic homogenous response. Using these two most prominent responses and/or indicative signals of pelagic ecosystems to hydro-climatic change, changes in species phenology and the biogeographical movement of populations, we attempt to identify vulnerable regional areas in terms of particularly rapid and marked change.

Spatial demography of Calanus finmarchicus in the Irminger Sea

Continuous Plankton Recorder data suggest that the Irminger Sea supports a major proportion of the surface-living population of the copepod Calanus finmarchicus in the northern North Atlantic, but there have been few studies of its population dynamics in the region. In this paper, we document the seasonal changes in the demographic structure of C finmarchicus in the Irminger Sea from a field programme during 2001/2002, and the associations between its developmental stages and various apparent bio-physical zones. Overwintering stages were found widely at depth (>500 m) across the Irminger Sea, and surviving females were widely distributed in the surface waters the following spring. However, recruitment of the subsequent generation was concentrated around the fringes of the Irminger Sea basin, along the edges of the Irminger and East Greenland Currents, and not in the central basin. In late summer animals were found descending back to overwintering depths in the Central Irminger Sea. The key factors dictating this pattern of recruitment appear to be (a) the general circulation regime, (b) predation on eggs in the spring, possibly by the surviving GO stock, and (c) mortality of first feeding naupliar stages in the central basin where food concentrations appear to be low throughout the year. We compared the demographic patterns in 2001/2002 with observations from the only previous major survey in 1963 and with data from the Continuous Plankton Recorder (CPR) surveys. In both previous data sets, the basic structure of GO ascent from the central basin and G1 recruitment around the fringes was a robust feature, suggesting that it is a recurrent phenomenon. The Irminger Sea is a complex mixing zone between polar and Atlantic water masses, and it has also been identified as a site of sporadic deep convection. The physical oceanographic characteristics of the region are therefore potentially sensitive to climate fluctuations. Despite this, the abundance of C finmarchicus in the region, as measured by the CPR surveys, appears not to have responded to climate factors linked to the North Atlantic Oscillation Index, in contrast with the stocks in eastern Atlantic areas. We speculate that this may because biological factors (production and mortality), rather than transport processes are the key factors affecting the population dynamics in the Irminger Sea. (c) 2007 Elsevier Ltd. All rights reserved.

Spatial and temporal variability in Scotian Shelf zooplankton communities

Zooplankton are indicators of the response of marine ecosystems to environmental variability. The relationships between zooplankton communities on the Scotian Shelf and hydrographic and geographic regions of the Scotian Shelf in the 1990s and 2000s were described using complementary data sets, each resolving different space and time scales. The Atlantic Zone Monitoring Program (AZMP) sampled Scotian Shelf zooplankton from the whole water column twice per year at stations along three cross-shelf transects and semi-monthly at a fixed station on the inshore central shelf, while Continuous Plankton Recorder (CPR) samples were collected from near-surface waters approximately monthly on an along-shelf transect. Variability patterns were compared among these three data sets to identify robust spatial and interannual trends. Stations were clustered based on taxonomic composition, and spatial clusters were compared to hydrographic boundaries and bathymetry to determine whether temporal changes in community composition were driven by changes in water mass distributions on the shelf. This project identifies zooplankton community and abundance shifts that may affect fish recruitment in the northwest Atlantic and contributes to development of ecosystem-based fisheries management on the Scotian Shelf.

Environmental context explains Lévy and Brownian movement patterns of marine predators

An optimal search theory, the so-called Levy-flight foraging hypothesis(1), predicts that predators should adopt search strategies known as Levy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey(2-4). Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Levy behaviour has recently been questioned(5,6). Consequently, whether foragers exhibit Levy flights in the wild remains unclear. Crucially, moreover, it has not been tested whether observed movement patterns across natural landscapes having different expected resource distributions conform to the theory's central predictions. Here we use maximum-likelihood methods to test for Levy patterns in relation to environmental gradients in the largest animal movement data set assembled for this purpose. Strong support was found for Levy search patterns across 14 species of open-ocean predatory fish (sharks, tuna, billfish and ocean sunfish), with some individuals switching between Levy and Brownian movement as they traversed different habitat types. We tested the spatial occurrence of these two principal patterns and found Levy behaviour to be associated with less productive waters (sparser prey) and Brownian movements to be associated with productive shelf or convergence-front habitats (abundant prey). These results are consistent with the Levy-flight foraging hypothesis(1,7), supporting the contention(8,9) that organism search strategies naturally evolved in such a way that they exploit optimal Levy patterns.

Historical data reveal power-law dispersal patterns of invasive aquatic species.

Understanding how invasive species spread is of particular concern in the current era of globalisation and rapid environmental change. The occurrence of super-diffusive movements within the context of Lévy flights has been discussed with respect to particle physics, human movements, microzooplankton, disease spread in global epidemiology and animal foraging behaviour. Super-diffusive movements provide a theoretical explanation for the rapid spread of organisms and disease, but their applicability to empirical data on the historic spread of organisms has rarely been tested. This study focuses on the role of long-distance dispersal in the invasion dynamics of aquatic invasive species across three contrasting areas and spatial scales: open ocean (north-east Atlantic), enclosed sea (Mediterranean) and an island environment (Ireland). Study species included five freshwater plant species, Azolla filiculoides, Elodea canadensis, Lagarosiphon major, Elodea nuttallii and Lemna minuta; and ten species of marine algae, Asparagopsis armata, Antithamnionella elegans, Antithamnionella ternifolia, Codium fragile, Colpomenia peregrina, Caulerpa taxifolia, Dasysiphonia sp., Sargassum muticum, Undaria pinnatifida and Womersleyella setacea. A simulation model is constructed to show the validity of using historical data to reconstruct dispersal kernels. Lévy movement patterns similar to those previously observed in humans and wild animals are evident in the re-constructed dispersal pattern of invasive aquatic species. Such patterns may be widespread among invasive species and could be exacerbated by further development of trade networks, human travel and environmental change. These findings have implications for our ability to predict and manage future invasions, and improve our understanding of the potential for spread of organisms including infectious diseases, plant pests and genetically modified organisms.

A tale of two seas: contrasting patterns of population structure in the small-spotted catshark across Europe.

Elasmobranchs represent important components of marine ecosystems, but they can be vulnerable to overexploitation. This has driven investigations into the population genetic structure of large-bodied pelagic sharks, but relatively little is known of population structure in smaller demersal taxa, which are perhaps more representative of the biodiversity of the group. This study explores spatial population genetic structure of the small-spotted catshark (Scyliorhinus canicula), across European seas. The results show significant genetic differences among most of the Mediterranean sample collections, but no significant structure among Atlantic shelf areas. The data suggest the Mediterranean populations are likely to have persisted in a stable and structured environment during Pleistocene sea-level changes. Conversely, the Northeast Atlantic populations would have experienced major changes in habitat availability during glacial cycles, driving patterns of population reduction and expansion. The data also provide evidence of male-biased dispersal and female philopatry over large spatial scales, implying complex sex-determined differences in the behaviour of elasmobranchs. On the basis of this evidence, we suggest that patterns of connectivity are determined by trends of past habitat stability that provides opportunity for local adaptation in species exhibiting philopatric behaviour, implying that resilience of populations to fisheries and other stressors may differ across the range of species.