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

Incorporating multidimensional behavior into a risk management tool for a critically endangered and migratory species

Conservation of migratory species exhibiting wide-ranging and multidimensional behaviors is challenged by management efforts that only utilize horizontal movements or produce static spatial-temporal products. For the deep-diving, critically endangered eastern Pacific leatherback turtle, tools that predict where turtles have high risks of fisheries interactions are urgently needed to prevent further population decline. We incorporated horizontal-vertical movement model results with spatial-temporal kernel density estimates and threat data (gear-specific fishing) to develop monthly maps of spatial risk. Specifically, we applied multistate hidden Markov models to a biotelemetry data set (n = 28 leatherback tracks, 2004-2007). Tracks with dive information were used to characterize turtle behavior as belonging to 1 of 3 states (transiting, residential with mixed diving, and residential with deep diving). Recent fishing effort data from Global Fishing Watch were integrated with predicted behaviors and monthly space-use estimates to create maps of relative risk of turtle-fisheries interactions. Drifting (pelagic) longline fishing gear had the highest average monthly fishing effort in the study region, and risk indices showed this gear to also have the greatest potential for high-risk interactions with turtles in a residential, deep-diving behavioral state. Monthly relative risk surfaces for all gears and behaviors were added to South Pacific TurtleWatch (SPTW) (https://www.upwell.org/sptw), a dynamic management tool for this leatherback population. These modifications will refine SPTW's capability to provide important predictions of potential high-risk bycatch areas for turtles undertaking specific behaviors. Our results demonstrate how multidimensional movement data, spatial-temporal density estimates, and threat data can be used to create a unique conservation tool. These methods serve as a framework for incorporating behavior into similar tools for other aquatic, aerial, and terrestrial taxa with multidimensional movement behaviors.

Combining multiple data sources with different biases in state-space models for population dynamics

The resolution at which animal populations can be modeled can be increased when multiple datasets corresponding to different life stages are available, allowing, for example, seasonal instead of annual descriptions of dynamics. However, the abundance estimates used for model fitting can have multiple sources of error, both random and systematic, namely bias. We focus here on the consequences of, and how to address, differing and unknown observation biases when fitting models.State-space models (SSMs) separate process variation and observation error, thus providing a framework to account for different and unknown estimate biases across multiple datasets. Here we study the effects on the inference of including or excluding bias parameters for a sequential life stage population dynamics SSM using a combination of theory, simulation experiments, and an empirical example.When the data, that is, abundance estimates, are unbiased, including bias parameters leads to increased imprecision compared to a model that correctly excludes bias parameters. But when observations are biased and no bias parameters are estimated, recruitment and survival processes are inaccurately estimated and estimates of process variance become biased high. These problems are substantially reduced by including bias parameters and fixing one of them at even an incorrect value. The primary inferential challenge is that models with bias parameters can show properties of being parameter redundant even when they are not in theory.Combining multiple datasets into a single analysis by using bias parameters to rescale data can offer significant improvements to inference and model diagnostics. Because their estimability in practice is dataset specific and will likely require more precise estimates than might be expected from ecological datasets, we outline some strategies for characterizing process uncertainty when it is confounded by bias parameters.

Assessing Ecosystem State Space Models: Identifiability and Estimation

Hierarchical probability models are being used more often than non-hierarchical deterministic process models in environmental prediction and forecasting, and Bayesian approaches to fitting such models are becoming increasingly popular. In particular, models describing ecosystem dynamics with multiple states that are autoregressive at each step in time can be treated as statistical state space models (SSMs). In this paper, we examine this subset of ecosystem models, embed a process-based ecosystem model into an SSM, and give closed form Gibbs sampling updates for latent states and process precision parameters when process and observation errors are normally distributed. Here, we use simulated data from an example model (DALECev) and study the effects changing the temporal resolution of observations on the states (observation data gaps), the temporal resolution of the state process (model time step), and the level of aggregation of observations on fluxes (measurements of transfer rates on the state process). We show that parameter estimates become unreliable as temporal gaps between observed state data increase. To improve parameter estimates, we introduce a method of tuning the time resolution of the latent states while still using higher-frequency driver information and show that this helps to improve estimates. Further, we show that data cloning is a suitable method for assessing parameter identifiability in this class of models. Overall, our study helps inform the application of state space models to ecological forecasting applications where (1) data are not available for all states and transfers at the operational time step for the ecosystem model and (2) process uncertainty estimation is desired.

Integrated Population Models: Achieving Their Potential

Precise and accurate estimates of abundance and demographic rates are primary quantities of interest within wildlife conservation and management. Such quantities provide insight into population trends over time and the associated underlying ecological drivers of the systems. This information is fundamental in managing ecosystems, assessing species conservation status and developing and implementing effective conservation policy. Observational monitoring data are typically collected on wildlife populations using an array of different survey protocols, dependent on the primary questions of interest. For each of these survey designs, a range of advanced statistical techniques have been developed which are typically well understood. However, often multiple types of data may exist for the same population under study. Analyzing each data set separately implicitly discards the common information contained in the other data sets. An alternative approach that aims to optimize the shared information contained within multiple data sets is to use a “model-based data integration” approach, or more commonly referred to as an “integrated model.” This integrated modeling approach simultaneously analyzes all the available data within a single, and robust, statistical framework. This paper provides a statistical overview of ecological integrated models, with a focus on integrated population models (IPMs) which include abundance and demographic rates as quantities of interest. Four main challenges within this area are discussed, namely model specification, computational aspects, model assessment and forecasting. This should encourage researchers to explore further and develop new practical tools to ensure that full utility can be made of IPMs for future studies.

Individual and joint estimation of humpback whale migratory patterns and their environmental drivers in the Southwest Atlantic Ocean

Humpback whales (Megaptera novaeangliae) perform seasonal migrations from high latitude feeding grounds to low latitude breeding and calving grounds. Feeding grounds at polar regions are currently experiencing major ecosystem modifications, therefore, quantitatively assessing species responses to habitat characteristics is crucial for understanding how whales might respond to such modifications. We analyzed satellite telemetry data from 22 individual humpback whales in the Southwest Atlantic Ocean (SWA). Tagging effort was divided in two periods, 2003-2012 and 2016-2019. Correlations between whale's movement parameters and environmental variables were used as proxy for inferring behavioral responses to environmental variation. Two versions of a covariate-driven continuous-time correlated random-walk state-space model, were fitted to the data: i) Population-level models (P-models), which assess correlation parameters pooling data across all individuals or groups, and ii) individual-level models (I-models), fitted independently for each tagged whale. Area of Restricted Search behavior (slower and less directionally persistent movement, ARS) was concentrated at cold waters south of the Polar Front (~ 50°S). The best model showed that ARS was expected to occur in coastal areas and over ridges and seamounts. Ice coverage during August of each year was a consistent predictor of ARS across models. Wind stress curl and sea surface temperature anomalies were also correlated with movement parameters but elicited larger inter-individual variation. I-models were consistent with P-models' predictions for the case of females accompanied by calves (mothers), while males and those of undetermined sex (males +) presented more variability as a group. Spatial predictions of humpback whale behavioral responses showed that feeding grounds for this population are concentrated in the complex system of islands, ridges, and rises of the Scotia Sea and the northern Weddell Ridge. More southernly incursions were observed in recent years, suggesting a potential response to increased temperature and large ice coverage reduction observed in the late 2010s. Although, small sample size and differences in tracking duration precluded appropriately testing predictions for such a distributional shift, our modelling framework showed the efficiency of borrowing statistical strength during data pooling, while pinpointing where more complexity should be added in the future as additional data become available.

Bayesian inference of kinetic schemes for ion channels by Kalman filtering

Inferring adequate kinetic schemes for ion channel gating from ensemble currents is a daunting task due to limited information in the data. We address this problem by using a parallelized Bayesian filter to specify hidden Markov models for current and fluorescence data. We demonstrate the flexibility of this algorithm by including different noise distributions. Our generalized Kalman filter outperforms both a classical Kalman filter and a rate equation approach when applied to patch-clamp data exhibiting realistic open-channel noise. The derived generalization also enables inclusion of orthogonal fluorescence data, making unidentifiable parameters identifiable and increasing the accuracy of the parameter estimates by an order of magnitude. By using Bayesian highest credibility volumes, we found that our approach, in contrast to the rate equation approach, yields a realistic uncertainty quantification. Furthermore, the Bayesian filter delivers negligibly biased estimates for a wider range of data quality. For some data sets, it identifies more parameters than the rate equation approach. These results also demonstrate the power of assessing the validity of algorithms by Bayesian credibility volumes in general. Finally, we show that our Bayesian filter is more robust against errors induced by either analog filtering before analog-to-digital conversion or by limited time resolution of fluorescence data than a rate equation approach.

Direct Discriminative Decoder Models for Analysis of High-Dimensional Dynamical Neural Data

With the accelerated development of neural recording technology over the past few decades, research in integrative neuroscience has become increasingly reliant on data analysis methods that are scalable to high-dimensional recordings and computationally tractable. Latent process models have shown promising results in estimating the dynamics of cognitive processes using individual models for each neuron's receptive field. However, scaling these models to work on high-dimensional neural recordings remains challenging. Not only is it impractical to build receptive field models for individual neurons of a large neural population, but most neural data analyses based on individual receptive field models discard the local history of neural activity, which has been shown to be critical in the accurate inference of the underlying cognitive processes. Here, we propose a novel, scalable latent process model that can directly estimate cognitive process dynamics without requiring precise receptive field models of individual neurons or brain nodes. We call this the direct discriminative decoder (DDD) model. The DDD model consists of (1) a discriminative process that characterizes the conditional distribution of the signal to be estimated, or state, as a function of both the current neural activity and its local history, and (2) a state transition model that characterizes the evolution of the state over a longer time period. While this modeling framework inherits advantages of existing latent process modeling methods, its computational cost is tractable. More important, the solution can incorporate any information from the history of neural activity at any timescale in computing the estimate of the state process. There are many choices in building the discriminative process, including deep neural networks or gaussian processes, which adds to the flexibility of the framework. We argue that these attributes of the proposed methodology, along with its applicability to different modalities of neural data, make it a powerful tool for high-dimensional neural data analysis. We also introduce an extension of these methods, called the discriminative-generative decoder (DGD). The DGD includes both discriminative and generative processes in characterizing observed data. As a result, we can combine physiological correlates like behavior with neural data to better estimate underlying cognitive processes. We illustrate the methods, including steps for inference and model identification, and demonstrate applications to multiple data analysis problems with high-dimensional neural recordings. The modeling results demonstrate the computational and modeling advantages of the DDD and DGD methods.

Vulture distribution and people perception of vultures in Pokhara Valley, Nepal

Due to an abundance and diversity of vultures, Nepal is one of the most important countries for vulture conservation. Within Nepal, the Pokhara Valley is especially significant. We examine the distribution of vultures within the Pokhara Valley by conducting counts at 11 potential feeding or roosting sites using point count method. We further surveyed people of the valley regarding their perception of vulture ecology and conservation, knowledge of diclofenac use within the valley, and burial of livestock carcasses. We detected eight species of vultures, four of which are currently threatened with extinction. White-rumped vulture Gyps bengalensis, Egyptian vulture Nephron percnopterus, and Himalayan vulture G. himalayensis were the most abundant. Almost all respondents (98%) had sighted the vultures in the wild. Formally educated respondents reported seeing vultures' slightly more than nonformally educated respondents. Fifty-eight percent respondents suspected habitat loss was the major threat for the vulture population decline in Pokhara Valley, and 97% respondents were not aware of any diclofenac use. The knowledge of vultures in people with different age groups suggests a more awareness programs are needed for local people, especially those who carry out animal husbandry and provide livestock to the vulture restaurant.

History Marginalization Improves Forecasting in Variational Recurrent Neural Networks

Deep probabilistic time series forecasting models have become an integral part of machine learning. While several powerful generative models have been proposed, we provide evidence that their associated inference models are oftentimes too limited and cause the generative model to predict mode-averaged dynamics. Mode-averaging is problematic since many real-world sequences are highly multi-modal, and their averaged dynamics are unphysical (e.g., predicted taxi trajectories might run through buildings on the street map). To better capture multi-modality, we develop variational dynamic mixtures (VDM): a new variational family to infer sequential latent variables. The VDM approximate posterior at each time step is a mixture density network, whose parameters come from propagating multiple samples through a recurrent architecture. This results in an expressive multi-modal posterior approximation. In an empirical study, we show that VDM outperforms competing approaches on highly multi-modal datasets from different domains.

Probabilistic early warning signals

Ecological communities and other complex systems can undergo abrupt and long-lasting reorganization, a regime shift, when deterministic or stochastic factors bring them to the vicinity of a tipping point between alternative states. Such changes can be large and often arise unexpectedly. However, theoretical and experimental analyses have shown that changes in correlation structure, variance, and other standard indicators of biomass, abundance, or other descriptive variables are often observed prior to a state shift, providing early warnings of an anticipated transition. Natural systems manifest unknown mixtures of ecological and environmental processes, hampered by noise and limited observations. As data quality often cannot be improved, it is important to choose the best modeling tools available for the analysis.We investigate three autoregressive models and analyze their theoretical differences and practical performance. We formulate a novel probabilistic method for early warning signal detection and demonstrate performance improvements compared to nonprobabilistic alternatives based on simulation and publicly available experimental time series.The probabilistic formulation provides a novel approach to early warning signal detection and analysis, with enhanced robustness and treatment of uncertainties. In real experimental time series, the new probabilistic method produces results that are consistent with previously reported findings.Robustness to uncertainties is instrumental in the common scenario where mechanistic understanding of the complex system dynamics is not available. The probabilistic approach provides a new family of robust methods for early warning signal detection that can be naturally extended to incorporate variable modeling assumptions and prior knowledge.

Learning and Animal Movement

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.

Fitting stochastic predator-prey models using both population density and kill rate data

Most mechanistic predator-prey modelling has involved either parameterization from process rate data or inverse modelling. Here, we take a median road: we aim at identifying the potential benefits of combining datasets, when both population growth and predation processes are viewed as stochastic. We fit a discrete-time, stochastic predator-prey model of the Leslie type to simulated time series of densities and kill rate data. Our model has both environmental stochasticity in the growth rates and interaction stochasticity, i.e., a stochastic functional response. We examine what the kill rate data brings to the quality of the estimates, and whether estimation is possible (for various time series lengths) solely with time series of population counts or biomass data. Both Bayesian and frequentist estimation are performed, providing multiple ways to check model identifiability. The Fisher Information Matrix suggests that models with and without kill rate data are all identifiable, although correlations remain between parameters that belong to the same functional form. However, our results show that if the attractor is a fixed point in the absence of stochasticity, identifying parameters in practice requires kill rate data as a complement to the time series of population densities, due to the relatively flat likelihood. Only noisy limit cycle attractors can be identified directly from population count data (as in inverse modelling), although even in this case, adding kill rate data - including in small amounts - can make the estimates much more precise. Overall, we show that under process stochasticity in interaction rates, interaction data might be essential to obtain identifiable dynamical models for multiple species. These results may extend to other biotic interactions than predation, for which similar models combining interaction rates and population counts could be developed.

Detrimental impacts of climate change may be exacerbated by density-dependent population regulation in blue mussels

The climate on our planet is changing and the range distributions of organisms are shifting in response. In aquatic environments, species might not be able to redistribute poleward or into deeper water when temperatures rise because of barriers, reduced light availability, altered water chemistry or any combination of these. How species respond to climate change may depend on physiological adaptability, but also on the population dynamics of the species. Density dependence is a ubiquitous force that governs population dynamics and regulates population growth, yet its connections to the impacts of climate change remain little known, especially in marine studies. Reductions in density below an environmental carrying capacity may cause compensatory increases in demographic parameters and population growth rate, hence masking the impacts of climate change on populations. On the other hand, climate-driven deterioration of conditions may reduce environmental carrying capacities, making compensation less likely and populations more susceptible to the effects of stochastic processes. Here we investigate the effects of climate change on Baltic blue mussels using a 17-year dataset on population density. Using a Bayesian modelling framework, we investigate the impacts of climate change, assess the magnitude and effects of density dependence, and project the likelihood of population decline by the year 2030. Our findings show negative impacts of warmer and less saline waters, both outcomes of climate change. We also show that density dependence increases the likelihood of population decline by subjecting the population to the detrimental effects of stochastic processes (i.e. low densities where random bad years can cause local extinction, negating the possibility for random good years to offset bad years). We highlight the importance of understanding, and accounting for both density dependence and climate variation when predicting the impact of climate change on keystone species, such as the Baltic blue mussel.

The conservation status and population decline of the African penguin deconstructed in space and time

Understanding changes in abundance is crucial for conservation, but population growth rates often vary over space and time. We use 40 years of count data (1979-2019) and Bayesian state-space models to assess the African penguin Spheniscus demersus population under IUCN Red List Criterion A. We deconstruct the overall decline in time and space to identify where urgent conservation action is needed. The global African penguin population met the threshold for Endangered with a high probability (97%), having declined by almost 65% since 1989. An historical low of ~17,700 pairs bred in 2019. Annual changes were faster in the South African population (-4.2%, highest posterior density interval, HPDI: -7.8 to -0.6%) than the Namibian one (-0.3%, HPDI: -3.3 to +2.6%), and since 1999 were almost -10% at South African colonies north of Cape Town. Over the 40-year period, the Eastern Cape colonies went from holding ~25% of the total penguin population to ~40% as numbers decreased more rapidly elsewhere. These changes coincided with an altered abundance and availability of the main prey of African penguins. Our results underline the dynamic nature of population declines in space as well as time and highlight which penguin colonies require urgent conservation attention.

Improving inference for nonlinear state-space models of animal population dynamics given biased sequential life stage data

State‐space models (SSMs) are a popular tool for modeling animal abundances. Inference difficulties for simple linear SSMs are well known, particularly in relation to simultaneous estimation of process and observation variances. Several remedies to overcome estimation problems have been studied for relatively simple SSMs, but whether these challenges and proposed remedies apply for nonlinear stage‐structured SSMs, an important class of ecological models, is less well understood. Here we identify improvements for inference about nonlinear stage‐structured SSMs fit with biased sequential life stage data. Theoretical analyses indicate parameter identifiability requires covariates in the state processes. Simulation studies show that plugging in externally estimated observation variances, as opposed to jointly estimating them with other parameters, reduces bias and standard error of estimates. In contrast to previous results for simple linear SSMs, strong confounding between jointly estimated process and observation variance parameters was not found in the models explored here. However, when observation variance was also estimated in the motivating case study, the resulting process variance estimates were implausibly low (near‐zero). As SSMs are used in increasingly complex ways, understanding when inference can be expected to be successful, and what aids it, becomes more important. Our study illustrates (a) the need for relevant process covariates and (b) the benefits of using externally estimated observation variances for inference about nonlinear stage‐structured SSMs.

Population dynamics of foxes during restricted-area culling in Britain: Advancing understanding through state-space modelling of culling records

Lethal control is widely employed to suppress the numbers of target wildlife species within restricted management areas. The success of such measures is expected to vary with local circumstances affecting rates of removal and replacement. There is a need both to evaluate success in individual cases and to understand variability and its causes. In Britain, red fox (Vulpes vulpes) populations are culled within the confines of shooting estates to benefit game and wildlife prey species. We developed a Bayesian state-space model for within-year fox population dynamics within such restricted areas and fitted it to data on culling effort and success obtained from gamekeepers on 22 shooting estates of 2 to 36 km². We used informative priors for key population processes—immigration, cub recruitment and non-culling mortality–that could not be quantified in the field. Using simulated datasets we showed that the model reliably estimated fox density and demographic parameters, and we showed that conclusions drawn from real data were robust to alternative model assumptions. All estates achieved suppression of the fox population, with pre-breeding fox density on average 47% (range 20%–90%) of estimated carrying capacity. As expected, the number of foxes killed was a poor indicator of effectiveness. Estimated rates of immigration were variable among estates, but in most cases indicated rapid replacement of culled foxes so that intensive culling efforts were required to maintain low fox densities. Due to this short-term impact, control effort focussed on the spring and summer period may be essential to achieve management goals for prey species. During the critical March-July breeding period, mean fox densities on all estates were suppressed below carrying capacity, and some maintained consistently low fox densities throughout this period. A similar model will be useful in other situations to quantify the effectiveness of lethal control on restricted areas.

Scale-insensitive estimation of speed and distance traveled from animal tracking data

BACKGROUND

Speed and distance traveled provide quantifiable links between behavior and energetics, and are among the metrics most routinely estimated from animal tracking data. Researchers typically sum over the straight-line displacements (SLDs) between sampled locations to quantify distance traveled, while speed is estimated by dividing these displacements by time. Problematically, this approach is highly sensitive to the measurement scale, with biases subject to the sampling frequency, the tortuosity of the animal's movement, and the amount of measurement error. Compounding the issue of scale-sensitivity, SLD estimates do not come equipped with confidence intervals to quantify their uncertainty.

METHODS

To overcome the limitations of SLD estimation, we outline a continuous-time speed and distance (CTSD) estimation method. An inherent property of working in continuous-time is the ability to separate the underlying continuous-time movement process from the discrete-time sampling process, making these models less sensitive to the sampling schedule when estimating parameters. The first step of CTSD is to estimate the device's error parameters to calibrate the measurement error. Once the errors have been calibrated, model selection techniques are employed to identify the best fit continuous-time movement model for the data. A simulation-based approach is then employed to sample from the distribution of trajectories conditional on the data, from which the mean speed estimate and its confidence intervals can be extracted.

RESULTS

Using simulated data, we demonstrate how CTSD provides accurate, scale-insensitive estimates with reliable confidence intervals. When applied to empirical GPS data, we found that SLD estimates varied substantially with sampling frequency, whereas CTSD provided relatively consistent estimates, with often dramatic improvements over SLD.

CONCLUSIONS

The methods described in this study allow for the computationally efficient, scale-insensitive estimation of speed and distance traveled, without biases due to the sampling frequency, the tortuosity of the animal's movement, or the amount of measurement error. In addition to being robust to the sampling schedule, the point estimates come equipped with confidence intervals, permitting formal statistical inference. All the methods developed in this study are now freely available in the ctmmR package or the ctmmweb point-and-click web based graphical user interface.

Critical Transitions in Intensive Care Units: A Sepsis Case Study

The progression of complex human diseases is associated with critical transitions across dynamical regimes. These transitions often spawn early-warning signals and provide insights into the underlying disease-driving mechanisms. In this paper, we propose a computational method based on surprise loss (SL) to discover data-driven indicators of such transitions in a multivariate time series dataset of septic shock and non-sepsis patient cohorts (MIMIC-III database). The core idea of SL is to train a mathematical model on time series in an unsupervised fashion and to quantify the deterioration of the model’s forecast (out-of-sample) performance relative to its past (in-sample) performance. Considering the highest value of the moving average of SL as a critical transition, our retrospective analysis revealed that critical transitions occurred at a median of over 35 hours before the onset of septic shock, which suggests the applicability of our method as an early-warning indicator. Furthermore, we show that clinical variables at critical-transition regions are significantly different between septic shock and non-sepsis cohorts. Therefore, our paper contributes a critical-transition-based data-sampling strategy that can be utilized for further analysis, such as patient classification. Moreover, our method outperformed other indicators of critical transition in complex systems, such as temporal autocorrelation and variance.

Improving risk assessments in conservation ecology

Conservation efforts and management decisions on the living environment of our planet often rely on the results from statistical models. Yet, these models are imperfect and quantification of risk associated with the estimate of management-relevant quantities becomes crucial in providing robust advice. Here we demonstrate that estimates of risk themselves could be substantially biased but by combining data fitting with an extensive simulation-estimation procedure, one can back-calculate the correct values. We apply the method to 627 time series of population abundance across four taxa using the Gompertz state-space model as an example. We find that the risk of large bias in population status estimate increases with the species' growth rate, population variability, weaker density dependence, and shorter time series, across taxa. We urge scientists dealing with conservation and management to adopt a similar approach to ensure a more accurate estimate of risk measures and contribute towards a precautionary approach to management.

Generalizing the first-difference correlated random walk for marine animal movement data

Animal telemetry data are often analysed with discrete time movement models. These models are defined with regular time steps. However, telemetry data from marine animals are observed irregularly. To account for irregular data, a time-irregularised first-difference correlated random walk model with drift is introduced. The model generalizes the commonly used first-difference correlated random walk with regular time steps by allowing irregular time steps, including a drift term, and by allowing different autocorrelation in the two coordinates. The model is applied to data from a ringed seal collected through the Argos satellite system, and is compared to related movement models through simulations. Accounting for irregular data in the movement model results in accurate parameter estimates and reconstruction of movement paths. Further, the introduced model can provide more accurate movement paths than the regular time counterpart. Extracting accurate movement paths from uncertain telemetry data is important for evaluating space use patterns for marine animals, which in turn is crucial for management. Further, handling irregular data directly in the movement model allows efficient simultaneous analyses of several animals.

The psychometric properties and temporal dynamics of subjective stress, retrospectively assessed by different informants and questionnaires, and hair cortisol concentrations

To date, there is only scarce evidence for a considerable association of subjective and objective stress measures, which might be attributable to method bias (e.g., confounding) and/or asynchrony of their temporal changes. To validate different subjective stress measures by a physiological measure of long-term stress (hair cortisol concentrations; HCC), 37 heterosexual couples (N = 74) completed a 12-week internet-based assessment protocol comprised of a weekly hassle scale (WHS; once per week), a perceived stress scale (PSS; once per month), and a chronic stress scale (TICS; once after three months). Partners provided vicarious stress ratings. When averaged across time, self-reported WHS significantly predicted HCC (r = 0.27), whereas the PSS and TICS did not (r < 0.22). Dynamic factor analysis (i.e., state-space modelling) confirmed that WHS was the most valid indicator of subjective stress, explaining up to 16% of the variance in HCC (r = 0.37) with a time lag of ~4 weeks. This temporally delayed effect of subjective stress is consistent with the presumed retrospective character of HCC, but also suggests that the majority of variance in hair cortisol is attributable to other causes than subjective stress such as individual disposition to display increased adrenocortical activity.

Estimability of migration survival rates from integrated breeding and winter capture-recapture data

Long-distance migration is a common phenomenon across the animal kingdom but the scale of annual migratory movements has made it difficult for researchers to estimate survival rates during these periods of the annual cycle. Estimating migration survival is particularly challenging for small-bodied species that cannot carry satellite tags, a group that includes the vast majority of migratory species. When capture-recapture data are available for linked breeding and non-breeding populations, estimation of overall migration survival is possible but current methods do not allow separate estimation of spring and autumn survival rates. Recent development of a Bayesian integrated survival model has provided a method to separately estimate the latent spring and autumn survival rates using capture-recapture data, though the accuracy and precision of these estimates has not been formally tested. Here, I used simulated data to explore the estimability of migration survival rates using this model. Under a variety of biologically realistic scenarios, I demonstrate that spring and autumn migration survival can be estimated from the integrated survival model, though estimates are biased toward the overall migration survival probability. The direction and magnitude of this bias are influenced by the relative difference in spring and autumn survival rates as well as the degree of annual variation in these rates. The inclusion of covariates can improve the model's performance, especially when annual variation in migration survival rates is low. Migration survival rates can be estimated from relatively short time series (4-5 years), but bias and precision of estimates are improved when longer time series (10-12 years) are available. The ability to estimate seasonal survival rates of small, migratory organisms opens the door to advancing our understanding of the ecology and conservation of these species. Application of this method will enable researchers to better understand when mortality occurs across the annual cycle and how the migratory periods contribute to population dynamics. Integrating summer and winter capture data requires knowledge of the migratory connectivity of sampled populations and therefore efforts to simultaneously collect both survival and tracking data should be a high priority, especially for species of conservation concern.

A roadmap towards personalized immunology

Big data generation and computational processing will enable medicine to evolve from a "one-size-fits-all" approach to precise patient stratification and treatment. Significant achievements using "Omics" data have been made especially in personalized oncology. However, immune cells relative to tumor cells show a much higher degree of complexity in heterogeneity, dynamics, memory-capability, plasticity and "social" interactions. There is still a long way ahead on translating our capability to identify potentially targetable personalized biomarkers into effective personalized therapy in immune-centralized diseases. Here, we discuss the recent advances and successful applications in "Omics" data utilization and network analysis on patients' samples of clinical trials and studies, as well as the major challenges and strategies towards personalized stratification and treatment for infectious or non-communicable inflammatory diseases such as autoimmune diseases or allergies. We provide a roadmap and highlight experimental, clinical, computational analysis, data management, ethical and regulatory issues to accelerate the implementation of personalized immunology.

Changing measurements or changing movements? Sampling scale and movement model identifiability across generations of biologging technology

Animal movement patterns contribute to our understanding of variation in breeding success and survival of individuals, and the implications for population dynamics. Over time, sensor technology for measuring movement patterns has improved. Although older technologies may be rendered obsolete, the existing data are still valuable, especially if new and old data can be compared to test whether a behavior has changed over time. We used simulated data to assess the ability to quantify and correctly identify patterns of seabird flight lengths under observational regimes used in successive generations of wet/dry logging technology. Care must be taken when comparing data collected at differing timescales, even when using inference procedures that incorporate the observational process, as model selection and parameter estimation may be biased. In practice, comparisons may only be valid when degrading all data to match the lowest resolution in a set. Changes in tracking technology, such as the wet/dry loggers explored here, that lead to aggregation of measurements at different temporal scales make comparisons challenging. We therefore urge ecologists to use synthetic data to assess whether accurate parameter estimation is possible for models comparing disparate data sets before planning experiments and conducting analyses such as responses to environmental changes or the assessment of management actions.

Analysing the natural population growth of a large marine mammal after a depletive harvest

An understanding of the underlying processes and comprehensive history of population growth after a harvest-driven depletion is necessary when assessing the long-term effectiveness of management and conservation strategies. The South American sea lion (SASL), Otaria flavescens, is the most conspicuous marine mammal along the South American coasts, where it has been heavily exploited. As a consequence of this exploitation, many of its populations were decimated during the early 20th century but currently show a clear recovery. The aim of this study was to assess SASL population recovery by applying a Bayesian state-space modelling framework. We were particularly interested in understanding how the population responds at low densities, how human-induced mortality interplays with natural mechanisms, and how density-dependence may regulate population growth. The observed population trajectory of SASL shows a non-linear relationship with density, recovering with a maximum increase rate of 0.055. However, 50 years after hunting cessation, the population still represents only 40% of its pre-exploitation abundance. Considering that the SASL population in this region represents approximately 72% of the species abundance within the Atlantic Ocean, the present analysis provides insights into the potential mechanisms regulating the dynamics of SASL populations across the global distributional range of the species.

A state space approach for piecewise-linear recurrent neural networks for identifying computational dynamics from neural measurements

The computational and cognitive properties of neural systems are often thought to be implemented in terms of their (stochastic) network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a (lower-dimensional) state space representation of the dynamics, but would wish to have access to its statistical properties and their generative equations for in-depth analysis. Recurrent neural networks (RNNs) are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs) within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, and using inference through particle filters for comparison, the approach is applied to multiple single-unit recordings from the rodent anterior cingulate cortex (ACC) obtained during performance of a classical working memory task, delayed alternation. Models estimated from kernel-smoothed spike time data were able to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, however, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast) maximum-likelihood estimation framework for PLRNNs that may enable to recover relevant aspects of the nonlinear dynamics underlying observed neuronal time series, and directly link these to computational properties.