State-space models' dirty little secrets: even simple linear Gaussian models can have estimation problems

State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (\textit{Ursus maritimus}) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results

A generalized residual technique for analysing complex movement models using earth mover's distance

Complex systems of moving and interacting objects are ubiquitous in the natural and social sciences. Predicting their behaviour often requires models that mimic these systems with sufficient accuracy, while accounting for their inherent stochasticity. Although 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. 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 analyse 1D summary statistics, to situations where the complexity of the underlying model's probability distribution makes standard residual analysis too imprecise for practical use. 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 multispecies flocks of insectivore birds in the Amazon rain forest. 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

Learning and animal movement

Authors acknowledge the following grants for supporting this research: NSERC Discovery (ML and MA-M), NSF DMS-1853465 (WF and EG), and Canada Research Chairs Program (ML and MA-M).Integrating diverse concepts from animal behavior, movement ecology, and machine learning, we develop an overview of the ecology of learning and animal movement. Learning-based movement is clearly relevant to ecological problems, but the subject is rooted firmly in psychology, including a distinct terminology. We contrast this psychological origin of learning with the task-oriented perspective on learning that has emerged from the field of machine learning. We review conceptual frameworks that characterize the role of learning in movement, discuss emerging trends, and summarize recent developments in the analysis of movement data. We also discuss the relative advantages of different modeling approaches for exploring the learning-movement interface. We explore in depth how individual and social modalities of learning can matter to the ecology of animal movement, and highlight how diverse kinds of field studies, ranging from translocation efforts to manipulative experiments, can provide critical insight into the learning process in animal movement.Publisher PDFPeer reviewe

Local Passive Acoustic Monitoring of Narwhal Presence in the Canadian Arctic: A Pilot Project

Long-term community-based monitoring of narwhals (Monodon monoceros) is needed because narwhals are important to local Inuit and are facing changes in their environment. We examined the suitability of passive acoustic recording for monitoring narwhals, using data gathered in the Canadian Arctic from an autonomous acoustic recorder (Repulse Bay, 2006) and a hand-held digital recorder (Koluktoo Bay, 2006 – 08). We found a relationship between the number of narwhals observed passing a fixed point and the number of calls heard. In addition, we found that an automated call detector could isolate segments of recording containing narwhal vocalizations over long recording periods containing non-target sound, thus decreasing the time spent on the analysis. Collectively, these results suggest that combining passive acoustic sampling with an automated call detector offers a useful approach for local monitoring of the presence and relative abundance of narwhals.La nécessité d’avoir un programme communautaire de surveillance à long terme des narvals (Monodon monoceros) s’avère évidente étant donné que les narvals revêtent de l’importance aux yeux des Inuits de la région et que leur environ­nement est en pleine évolution. Nous explorons la pertinence d’un programme de surveillance par acoustique passive pour les populations de narvals à partir de données récoltées dans l’Arctique canadien à l’aide d’une enregistreuse autonome (Repulse Bay, 2006) et d’une enregistreuse portable (Koluktoo Bay, 2006 – 2008). Grâce à des enregistrements accompagnés d’obser­vations sur le terrain, nous avons trouvé une corrélation entre le nombre de vocalisations entendues et le nombre de narvals observés. L’utilisation d’un détecteur automatique de vocalisations de narvals a permis d’isoler des segments d’enregis­trements contenant des vocalisations de narvals sur de longues périodes d’enregistrement contenant des sons non-ciblés, et ainsi diminuer le temps d’analyse. Ces résultats suggèrent que la combinaison de surveillance acoustique passive avec l’utili­sation d’un détecteur automatique offre une approche utile pour la surveillance locale de la présence et de l’abondance relative des narvals

Modelling multi-scale state-switching functional data with hidden Markov models

Data sets comprised of sequences of curves sampled at high frequencies in time are increasingly common in practice, but they can exhibit complicated dependence structures that cannot be modelled using common methods of Functional Data Analysis (FDA). We detail a hierarchical approach which treats the curves as observations from a hidden Markov model (HMM). The distribution of each curve is then defined by another fine-scale model which may involve auto-regression and require data transformations using moving-window summary statistics or Fourier analysis. This approach is broadly applicable to sequences of curves exhibiting intricate dependence structures. As a case study, we use this framework to model the fine-scale kinematic movement of a northern resident killer whale (Orcinus orca) off the coast of British Columbia, Canada. Through simulations, we show that our model produces more interpretable state estimation and more accurate parameter estimates compared to existing methods.Comment: 23 pages, 8 figures, 2 tables. Supplementary material appended to submissio

Diving efficiency at depth and pre-breeding foraging effort increase with haemoglobin levels in gentoo penguins

Individual differences in oxygen storage and carrying capacity have been associated with fitness-related traits and, for air-breathing aquatic animals, to diving ability and foraging success. In winter, many seabirds must replenish the energy reserves they have depleted during the breeding period. Thus, winter foraging efficiency can influence their upcoming breeding behaviour. Using gentoo penguins Pygoscelis papua as a study species, we investigated (1) if inter-individual variation in diving efficiency (proportion of time spent at the bottom) is associated with indices of oxygen storage and carrying capacity (haemoglobin, haematocrit, body mass), and (2) if measures of pre-breeding foraging effort (mean trip duration, total time at sea, and vertical distance travelled) are associated with these oxygen indices and breeding status. Haemoglobin was positively correlated with diving efficiency, particularly for deeper dives, and only penguins with high haemoglobin levels frequently dove to depths ≥140 m. Such differences could affect resource access. However, because reaching deep offshore waters likely requires travelling more than foraging nearshore, vertical distance travelled during pre-breeding increased with haemoglobin levels. The relationship with haematocrit was non-linear, suggesting that commonly used analyses may be inappropriate for this index. We found that early-laying penguins spent less time at sea prior to nesting than non-breeding penguins, suggesting that more efficient foragers lay earlier. Given that diving efficiency at depth is linked to aerobic capacity, anthropogenic activities taking place in either nearshore or offshore waters (e.g. shallow-water fisheries, offshore oil rigs) may have differing impacts on individuals. Further understanding these links could help the conservation of diving species

Density‐ and size‐dependent mortality in fish early life stages

The importance of survival and growth variations early in life for population dynamics depends on the degrees of compensatory density dependence and size dependence in survival at later life stages. Quantifying density‐ and size‐dependent mortality at different juvenile stages is therefore important to understand and potentially predict the recruitment to the population. We applied a statistical state‐space modelling approach to analyse time series of abundance and mean body size of larval and juvenile fish. The focus was to identify the importance of abundance and body size for growth and survival through successive larval and juvenile age intervals, and to quantify how the dynamics propagate through the early life to influence recruitment. We thus identified both relevant ages and mechanisms (i.e. density dependence and size dependence in survival and growth) linking recruitment variability to early life dynamics. The analysis was conducted on six economically and ecologically important fish populations from cold temperate and sub‐arctic marine ecosystems. Our results underscore the importance of size for survival early in life. The comparative analysis suggests that size‐dependent mortality and density‐dependent growth frequently occur at a transition from pelagic to demersal habitats, which may be linked to competition for suitable habitat. The generality of this hypothesis warrants testing in future research.publishedVersio

The resilience of animal behaviour to disturbance

The concept of resilience is now widely used to understand the vulnerability of complex systems to disturbances. It is emerging that more diverse systems are more resilient to disturbances. Here we develop a conceptual understanding of the resilience of behavioral systems and assess how this measure is related to the diversity of behavioral sequences modeled using Markov chains. We show that the resilience of behavior is related to its unpredictability, a diversity measure, using simulations and empirical data collected at ten study sites over 30 years. The more predictable behavior is, the less resilient it becomes. Such influences on behavioral resilience cannot be related to the effect size of disturbances in inter-population comparisons. However, we show that such measures are meaningfully related to the influence of disturbances when comparing the same population exposed to different ecological conditions. We show that behavior predictability can be driven by ecological conditions. For example, an increase in food availability can increase the duration of foraging bouts, hence constraining the dynamics of the population’s behavior. Such constraints increase behavioral predictability and in turn weaken its resilience to disturbance. This empirically-driven theoretical study offers a framework to manage exposure of animal populations to disturbance