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Data from: A generalized residual technique for analyzing complex movement models using earth mover's distance
Potts, Jonathan R.; Auger-Méthé, Marie; Mokross, Karl; Lewis, Mark A. — 2015-08-18 1. Complex systems of moving and interacting objects are ubiquitous in the natural and social sciences. Predicting their behavior often requires models that mimic these systems with sufficient accuracy, while accounting for their inherent stochasticity. Though tools exist to determine which of a set of candidate models is best relative to the others, there is currently no generic goodness-of-fit framework for testing how close the best model is to the real complex stochastic system. 2. We propose such a framework, using a novel application of the Earth mover's distance, also known as the Wasserstein metric. It is applicable to any stochastic process where the probability of the model's state at time t is a function of the state at previous times. It generalizes the concept of a residual, often used to analyze 1D summary statistics, to situations where the complexity of the underlying model's probability distribution makes standard residual analysis too imprecise for practical use. 3. We give a scheme for testing the hypothesis that a model is an accurate description of a data set. We demonstrate the tractability and usefulness of our approach by application to animal movement models in complex, heterogeneous environments. We detail methods for visualizing results and extracting a variety of information on a given model's quality, such as whether there is any inherent bias in the model, or in which situations it is most accurate. We demonstrate our techniques by application to data on multi-species flocks of insectivore birds in the Amazon rainforest. 4. This work provides a usable toolkit to assess the quality of generic movement models of complex systems, in an absolute rather than a relative sense.
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Data from: A unifying framework for quantifying the nature of animal interactions
Potts, Jonathan R.; Mokross, Karl; Lewis, Mark A. — 2015-04-29 Collective phenomena, whereby agent-agent interactions determine spatial patterns, are ubiquitous in the animal kingdom. On the other hand, movement and space use are also greatly influenced by the interactions between animals and their environment. Despite both types of interaction fundamentally influencing animal behaviour, there has hitherto been no unifying framework for the models proposed in both areas. Here, we construct a general method for inferring population-level spatial patterns from underlying individual movement and interaction processes, a key ingredient in building a statistical mechanics for ecological systems. We show that resource selection functions, as well as several examples of collective motion models, arise as special cases of our framework, thus bringing together resource selection analysis and collective animal behaviour into a single theory. In particular, we focus on combining the various mechanistic models of territorial interactions in the literature with step selection functions, by incorporate interactions into the step selection framework and demonstrating how to derive territorial patterns from the resulting models. We demonstrate the efficacy of our model by application to a population of insectivore birds in the Amazon rainforest.
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Data from: Energy benefits and emergent space use patterns of an empirically parameterized model of memory-based patch selection
Merkle, Jerod A.; Potts, Jonathan R.; Fortin, Daniel — 2016-07-14 Many species frequently return to previously visited foraging sites. This bias towards familiar areas suggests that remembering information from past experience is beneficial. Such a memory-based foraging strategy has also been hypothesized to give rise to restricted space use (i.e. a home range). Nonetheless, the benefits of empirically derived memory-based foraging tactics and the extent to which they give rise to restricted space use patterns are still relatively unknown. Using a combination of stochastic agent-based simulations and deterministic integro-difference equations, we developed an adaptive link (based on energy gains as a foraging currency) between memory-based patch selection and its resulting spatial distribution. We used a memory-based foraging model developed and parameterized with patch selection data of free-ranging bison Bison bison in Prince Albert National Park, Canada. Relative to random use of food patches, simulated foragers using both spatial and attribute memory are more efficient, particularly in landscapes with clumped resources. However, a certain amount of random patch use is necessary to avoid frequent returns to relatively poor-quality patches, or avoid being caught in a relatively poor quality area of the landscape. Notably, in landscapes with clumped resources, simulated foragers that kept a reference point of the quality of recently visited patches, and returned to previously visited patches when local patch quality was poorer than the reference point, experienced higher energy gains compared to random patch use. Furthermore, the model of memory-based foraging resulted in restricted space use in simulated landscapes and replicated the restricted space use observed in free-ranging bison reasonably well. Our work demonstrates the adaptive value of spatial and attribute memory in heterogeneous landscapes, and how home ranges can be a byproduct of non-omniscient foragers using past experience to minimize temporal variation in energy gains.
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Data from: Predicting local and non-local effects of resources on animal space use using a mechanistic step-selection model
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Potts, Jonathan R.; Bastille-Rousseau, Guillaume; Murray, Dennis L.; Schaefer, James A.; Lewis, Mark A. — 2014-11-19 1. Predicting space use patterns of animals from their interactions with the environment is fundamental for understanding the effect of habitat changes on ecosystem functioning. Recent attempts to address this problem have sought to unify resource selection analysis, where animal space use is derived from available habitat quality, and mechanistic movement models, where detailed movement processes of an animal are used to predict its emergent utilisation distribution. Such models bias the animal's movement towards patches that are easily available and resource-rich, and the result is a predicted probability density at a given position being a function of the habitat quality at that position. However, in reality, the probability that an animal will use a patch of the terrain tends to be a function of the resource quality in both that patch and the surrounding habitat. 2. We propose a mechanistic model where this non-local effect of resources naturally emerges from the local movement processes, by taking into account the relative utility of both the habitat where the animal currently resides and that of where it is moving. We give statistical techniques to parametrize the model from location data, and demonstrate application of these techniques to GPS location data of caribou (Rangifer tarandus) in Newfoundland. 3. Steady-state animal probability distributions arising from the model have complex patterns that cannot be expressed simply as a function of the local quality of the habitat. In particular, large areas of good habitat are used more intensively than smaller patches of equal quality habitat, whereas isolated patches are used less frequently. Both of these are real aspects of animal space use missing from previous mechanistic resource-selection models. 4. Whilst we focus on habitats in this paper, our modelling framework can be readily used with any environmental covariates, and therefore represents a unification of mechanistic modelling and step-selection approaches to understanding animal space use.

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(Author: Potts, Jonathan R.)

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