Paul G. Blackwell’s research while affiliated with The University of Sheffield and other places

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Publications (57)


Figure 2: Human-induced changes have static and dynamic components that interact to create human-271
Understanding and predicting animal movements and distributions in the Anthropocene
  • Preprint
  • File available

January 2025

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140 Reads

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Luca Börger
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Joint inference for telemetry and spatial survey data

October 2024

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82 Reads

Data integration, the joint statistical analysis of data from different observation platforms, is pivotal for data‐hungry disciplines such as spatial ecology. Pooled data types obtained from the same underlying process, analyzed jointly, can improve both precision and accuracy in models of species distributions and species–habitat associations. However, the integration of telemetry and spatial survey data has proved elusive because of the fundamentally different analytical approaches required by these two data types. Here, “spatial survey” denotes a survey that records spatial locations and has no temporal structure, for example, line or point transects but not capture–recapture or telemetry. Step selection functions (SSFs—the canonical framework for telemetry) and habitat selection functions (HSFs—the default approach to spatial surveys) differ in not only their specifications but also their results. By imposing the constraint that microscopic mechanisms (animal movement) must correctly scale up to macroscopic emergence (population distributions), a relationship can be written between SSFs and HSFs, leading to a joint likelihood using both datasets. We implement this approach using maximum likelihood, explore its estimation precision by systematic simulation, and seek to derive broad guidelines for effort allocation in the field. We find that complementarities in spatial coverage and resolution between telemetry and survey data often lead to marked inferential improvements in joint analyses over those using either data type alone. The optimal allocation of effort between the two methods (or the choice between them, if only one can be selected) depends on the overall effort expended and the pattern of environmental heterogeneity. Examining inferential performance over a broad range of scenarios for the relative cost between the two methods, we find that integrated analysis usually offers higher precision. Our methodological work shows how to integrate the analysis of telemetry and spatial survey data under a novel joint likelihood function, using traditional computational methods. Our simulation experiments suggest that even when the relative costs of the two methods favor the deployment of one field approach over another, their joint use is broadly preferable. Therefore, joint analysis of the two key methods used in spatial ecology is not only possible but also computationally efficient and statistically more powerful.


Enclosures with placement of cameras used for video recordings of ground-truth behaviour of ten and nine reindeer, respectively, fitted with acceleration sensors in (a) Sirges reindeer herding community and (b) in Ståkke reindeer herding community, both in northern Sweden
Identification of reindeer fine-scale foraging behaviour using tri-axial accelerometer data

September 2022

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168 Reads

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11 Citations

Movement Ecology

Animal behavioural responses to the environment ultimately affect their survival. Monitoring animal fine-scale behaviour may improve understanding of animal functional response to the environment and provide an important indicator of the welfare of both wild and domesticated species. In this study, we illustrate the application of collar-attached acceleration sensors for investigating reindeer fine-scale behaviour. Using data from 19 reindeer, we tested the supervised machine learning algorithms Random forests, Support vector machines, and hidden Markov models to classify reindeer behaviour into seven classes: grazing, browsing low from shrubs or browsing high from trees, inactivity, walking, trotting, and other behaviours. We implemented leave-one-subject-out cross-validation to assess generalizable results on new individuals. Our main results illustrated that hidden Markov models were able to classify collar-attached accelerometer data into all our pre-defined behaviours of reindeer with reasonable accuracy while Random forests and Support vector machines were biased towards dominant classes. Random forests using 5-s windows had the highest overall accuracy (85%), while hidden Markov models were able to best predict individual behaviours and handle rare behaviours such as trotting and browsing high. We conclude that hidden Markov models provide a useful tool to remotely monitor reindeer and potentially other large herbivore species behaviour. These methods will allow us to quantify fine-scale behavioural processes in relation to environmental events.


Figure 4. The rankings of the visualisations based on participant accuracy, confidence/ease, and preferences. An ' overall' ranking is given based on the aggregation of the rankings for each of these categories.
The ten visualisations included in the survey. From left to right and top to bottom: the line1, line2, dot1, dot2, box1, box2, cascade, radar, heat map and infographic plots. Each visualisation was accompanied by a legend with a minimal description of the content of the visualisation alongside definitions of any statistical terminology used.
The regression coefficients (or 'odds ratios') (95% confidence interval) of the MPPOMs that were used to analyse the confidence and ease with which the participants were able to estimate the mean and minimum/maximum projected temperature change. The levels of the predictor variables that were included in the ‘typical’ response are included in the coefficients associated with the intercept (bottom). SA|A refers to the threshold between somewhat agree and agree, N|SA refers to the threshold between neutral and somewhat agree and so on. Please note the differences in the y-axis limits. A blank space indicates the predictor variable was included in the MPPOM as a nominal effect. *p < 0.05, **p < 0.01, ***p < 0.001.
The predictions of the MPPOMs that were used to analyse the confidence with which the participants were able to estimate the mean (left) or minimum/maximum (right) projected temperature change. The predictions are given as probabilities for each level of the Likert scale, ranging from ‘disagree’ in purple to ‘agree’ in yellow. The reference levels associated with the ‘typical’ response are marked with a tilde.
Improving the visual communication of environmental model projections

September 2021

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185 Reads

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7 Citations

Environmental and ecosystem models can help to guide management of changing natural systems by projecting alternative future states under a common set of scenarios. Combining contrasting models into multi-model ensembles (MMEs) can improve the skill and reliability of projections, but associated uncertainty complicates communication of outputs, affecting both the effectiveness of management decisions and, sometimes, public trust in scientific evidence itself. Effective data visualisation can play a key role in accurately communicating such complex outcomes, but we lack an evidence base to enable us to design them to be visually appealing whilst also effectively communicating accurate information. To address this, we conducted a survey to identify the most effective methods for visually communicating the outputs of an ensemble of global climate models. We measured the accuracy, confidence, and ease with which the survey participants were able to interpret 10 visualisations depicting the same set of model outputs in different ways, as well as their preferences. Dot and box plots outperformed all other visualisations, heat maps and radar plots were comparatively ineffective, while our infographic scored highly for visual appeal but lacked information necessary for accurate interpretation. We provide a set of guidelines for visually communicating the outputs of MMEs across a wide range of research areas, aimed at maximising the impact of the visualisations, whilst minimizing the potential for misinterpretations, increasing the societal impact of the models and ensuring they are well-placed to support management in the future.


Bayesian estimation of heterogeneous environments from animal movement data

May 2021

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53 Reads

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3 Citations

Environmetrics

We describe a flexible class of stochastic models that aim to capture key features of realistic patterns of animal movements observed in radio‐tracking and global positioning system telemetry studies. In the model, movements are represented as a diffusion‐based process evolving differently in heterogeneous regions. In this article, we extend the process of inference for heterogeneous movement models to the case in which boundaries of habitat regions are unknown and need to be estimated. Data augmentation is used in reconstructing the partition of the heterogeneous environment. The augmentation helps to diminish the impact of uncertainty about when and where the animal crosses habitat boundaries, and allows the extraction of additional information from the given observations. The approach to inference is Bayesian, using Markov chain Monte Carlo methods, allowing us to estimate both the parameters of the diffusion processes and the unknown boundaries. The suggested methodology is illustrated on simulated data and applied to real movement data from a radio‐tracking experiment on ibex. Some model checking and model choice issues are also discussed.


Quantifying uncertainty and dynamical changes in multi‐species fishing mortality rates, catches and biomass by combining state‐space and size‐based multi‐species models

March 2021

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60 Reads

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18 Citations

Fish and Fisheries

In marine management, fish stocks are often managed on a stock‐by‐stock basis using single‐species models. Many of these models are based upon statistical techniques and are good at assessing the current state and making short‐term predictions; however, as they do not model interactions between stocks, they lack predictive power on longer timescales. Additionally, there are size‐based multi‐species models that represent key biological processes and consider interactions between stocks such as predation and competition for resources. Due to the complexity of these models, they are difficult to fit to data, and so many size‐based multi‐species models depend upon single‐species models where they exist, or ad hoc assumptions when they do not, for parameters such as annual fishing mortality. In this paper, we demonstrate that by taking a state‐space approach, many of the uncertain parameters can be treated dynamically, allowing us to fit, with quantifiable uncertainty, size‐based multi‐species models directly to data. We demonstrate this by fitting uncertain parameters, including annual fishing mortality, of a size‐based multi‐species model of the Celtic Sea, for species with and without single‐species stock assessments. Consequently, errors in the single‐species models no longer propagate through the multi‐species model and underlying assumptions are more transparent. Building size‐based multi‐species models that are internally consistent, with quantifiable uncertainty, will improve their credibility and utility for management. This may lead to their uptake by being either used to corroborate single‐species models; directly in the advice process to make predictions into the future; or used to provide a new way of managing data‐limited stocks.


Modelling group movement with behavior switching in continuous time

December 2020

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56 Reads

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4 Citations

Biometrics

This article presents a new method for modelling collective movement in continuous time with behavioural switching, motivated by simultaneous tracking of wild or semi‐domesticated animals. Each individual in the group is at times attracted to a unobserved leading point. However the behavioural state of each individual can switch between ‘following’ and ‘independent’. The ‘following’ movement is modelled through a linear stochastic differential equation, while the ‘independent’ movement is modelled as Brownian motion. The movement of the leading point is modelled either as an Ornstein Uhlenbeck process or as Brownian motion, which makes the whole system a higher‐dimensional Ornstein Uhlenbeck process, possibly an intrinsic non‐stationary version. An inhomogeneous Kalman filter Markov chain Monte Carlo algorithm is developed to estimate the diffusion and switching parameters and the behaviour states of each individual at a given time point. The method successfully recovers the true behavioural states in simulated datasets, and is also applied to model a group of simultaneously tracked reindeer (Rangifer tarandus).


Modelling and inference for the movement of interacting animals

October 2020

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40 Reads

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15 Citations

Statistical modelling of animal movement data is a rapidly growing area of research. Typically though, these models have been developed for analysing the tracks of individual animals and we lose sight of the impact animals have on each other with regards to their movement behaviours. We aim to develop a model with a flexible social framework that allows us to capture that information. Our approach is based on the concept of social hierarchies, and this is embedded in a multivariate diffusion process which models the movement of a group of animals. The possibility of switching between behavioural states facilitates dynamic social behaviours and we augment the observed data with sampled state switching times in order to model the animals' behaviour naturally in continuous time. In addition, this enables us to carry out exact inference in a Bayesian setting with the benefits of being able to handle regular, irregular and missing data. All movement and behaviour parameters are estimated with Markov chain Monte Carlo methods. We examine the capability of our model with simulated data before fitting it to GPS locations of five wild olive baboons Papio anubis . The results enable us to identify which animals are influencing the movement of others and when, which provides both a dynamic and long‐term static insight into the group's social behaviours. Our model offers a flexible method in continuous time with which to model the network of social interactions within animal movement. Doing so avoids the limitations caused by a discrete‐time approach and it allows us to capture rich information with regards to a group's social structure, leading to constructive applications in conservation and management decisions. However, currently it is a computationally expensive task to fit the model to data, which in turns limits extending the model to more fruitful but complex cases such as heterogeneity in space or individual characteristics. Furthermore, our social hierarchy approach assumes all relevant animals are tracked and that any interactions have some ordering, both of which narrow the scope within which this approach is appropriate.


Figure 1 An illustration of Bayesian splines. Panel (a) shows some potential calibration curves in the Δ 14 C domain drawn from the prior. These are then compared with the observed data in the F 14 C domain as shown in panel (b) to form our Bayesian posterior. The bottom two panels (c) and (d) show posterior realizations of potential curves (shown in Δ 14 C and F 14 C space respectively) obtained via MCMC that provide a satisfactory trade-off between agreement with our prior penalizing over-roughness and the fit to our observed data.
Figure 7 A sample of posterior information generated alongside curve production-Panel (a) illustrates the difference between sample realizations of the curve, shown in color, and the summarized pointwise IntCal20 mean in black; the rug shows the knot locations in this time period, note the even knot spacing from 14.2-15.2 cal kBP to allow equitable placement of the P305u and P317 tree-ring sequences. Panel (b) plots the posterior estimate of the calibrated age of floating tree-ring sequence P305u.
The IntCal20 Approach to Radiocarbon Calibration Curve Construction: A New Methodology Using Bayesian Splines and Errors-in-Variables

August 2020

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658 Reads

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96 Citations

Radiocarbon

To create a reliable radiocarbon calibration curve, one needs not only high-quality data but also a robust statistical methodology. The unique aspects of much of the calibration data provide considerable modeling challenges and require a made-to-measure approach to curve construction that accurately represents and adapts to these individualities, bringing the data together into a single curve. For IntCal20, the statistical methodology has undergone a complete redesign, from the random walk used in IntCal04, IntCal09 and IntCal13, to an approach based upon Bayesian splines with errors-in-variables. The new spline approach is still fitted using Markov Chain Monte Carlo (MCMC) but offers considerable advantages over the previous random walk, including faster and more reliable curve construction together with greatly increased flexibility and detail in modeling choices. This paper describes the new methodology together with the tailored modifications required to integrate the various datasets. For an end-user, the key changes include the recognition and estimation of potential over-dispersion in ¹⁴ C determinations, and its consequences on calibration which we address through the provision of predictive intervals on the curve; improvements to the modeling of rapid ¹⁴ C excursions and reservoir ages/dead carbon fractions; and modifications made to, hopefully, ensure better mixing of the MCMC which consequently increase confidence in the estimated curve.


Quantifying uncertainty and dynamical changes in multi-species fishing mortality rates, catches and biomass by combining state-space and mechanistic multi-species models

August 2020

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52 Reads

In marine management, fish stocks are often managed on a stock-by-stock basis using single-species models. Many of these models are based upon statistical techniques and are good at assessing the current state and making short-term predictions; however, as they do not model interactions between stocks, they lack predictive power on longer timescales. Additionally, there are mechanistic multi-species models that represent key biological processes and consider interactions between stocks such as predation and competition for resources. Due to the complexity of these models, they are difficult to fit to data, and so many mechanistic multi-species models depend upon single-species models where they exist, or ad hoc assumptions when they don't, for parameters such as annual fishing mortality. In this paper we demonstrate that by taking a state-space approach, many of the uncertain parameters can be treated dynamically, allowing us to fit, with quantifiable uncertainty, mechanistic multi-species models directly to data. We demonstrate this by fitting uncertain parameters, including annual fishing mortality, of a size-based multi-species model of the Celtic Sea, for species with and without single-species stock-assessments. Consequently, errors in the single-species models no longer propagate through the multi-species model and underlying assumptions are more transparent. Building mechanistic multi-species models that are internally consistent, with quantifiable uncertainty, will improve their credibility and utility for management. This may lead to their uptake by being either used to corroborate single-species models; directly in the advice process to make predictions into the future; or used to provide a new way of managing data-limited stocks.


Citations (35)


... However, even though machine-learning potentially offers a high level of accuracy in such behavioral detection, and has been recently used in various species and fashions [6,14,29,47,49,53,56,62,64,65,67,71,73,83,92,94], they most often remain constricted to few behaviors with a limited level of detail. The present study focuses on the grey wolf (Canis lupus), a species that has been extensively studied in various aspects of spatial ecology, from broad landscape use [61] to specific hunting strategies [78], often relying on extensive observations [58] or decades of GPS tracking [13,79], and aims at identifying 12 ecologically significant behaviors. ...

Reference:

A supervised model to identify wolf behavior from tri-axial acceleration
Identification of reindeer fine-scale foraging behaviour using tri-axial accelerometer data

Movement Ecology

... Visual environmental communication is a vital means of raising awareness and promoting action on environmental issues, employing various visual tools and techniques to convey complex information to diverse audiences. Bannister et al. (2021) emphasized the significance of incorporating uncertainties (e.g., consumerism, weather forecasting, plant growth process) associated with complex environmental models into visual communication. While data visualization can be a powerful method for improving communication, the authors stressed the need for further research to identify the most effective ways to visually represent uncertainties. ...

Reference:

EE in Indo
Improving the visual communication of environmental model projections

... In many instances these heterogeneities are due to the presence of permeable interfaces, often referred to as semi or partially permeable barriers. They appear at microscopic scales in different porous media such as biological tissue [1-6], but also at larger scales when whole organisms interact with chemical or physical cues [7][8][9]. ...

Bayesian estimation of heterogeneous environments from animal movement data

Environmetrics

... Despite the improvements, especially for total catch and forage fish, a significant uncertainty persisted, namely the parameterization of F MSY which varies with temperature in the FEISTY model, whereas, both in the FEISTY model and in nature, F MSY varies in a more dynamic way due to biotic interactions within and between functional types. This dynamic nature of F MSY poses a challenge in capturing fishing effects in food web models (Spence et al., 2021). We recommend that other MEMs approximate the temperature effect on F MSY ahead of using the F/F MSY estimates. ...

Quantifying uncertainty and dynamical changes in multi‐species fishing mortality rates, catches and biomass by combining state‐space and size‐based multi‐species models
  • Citing Article
  • March 2021

Fish and Fisheries

... Currently available social movement models that account for social interactions between individuals require unique identification of animals and assume a closed, fully observed population throughout the study period (e.g., Langrock et al., 2014;Scharf et al., 2016Scharf et al., , 2018Niu et al., 2020;Scharf and Buderman, 2020;Milner et al., 2021). Movement data of terrestrial and marine animals has been conventionally derived by tracking individuals singularly, often with telemetry tags. ...

Modelling group movement with behavior switching in continuous time
  • Citing Article
  • December 2020

Biometrics

... Details on the protocol used at Beta Analytic can be found in Moreno et al. (2021). The obtained AMS radiocarbon ages were calibrated by Beta Analytic using the high probability density range method (Beta-Cal3.21) and the database Intcal13 (Reimer et al., 2013) (Table 2). ...

IntCal13 and Marine13 Radiocarbon Age Calibration Curves 0–50,000 Years cal BP

Radiocarbon

... SDEs have recently been proposed to model group movement of animals (Niu, Blackwell and Skarin (2016), Milner, Blackwell and Niu (2021)). That approach could be extended to allow for time-varying dynamics, and using the methods presented in this paper, it could be used to estimate behavioural responses for multiple individual animals. ...

Modelling and inference for the movement of interacting animals

... To mitigate the influence of organic contaminants, a standard acid-alkali-acid treatment along with solvent extraction was implemented before dating. The radiocarbon dates obtained in this study were calibrated using CALIB 8.2 and the IntCal20 calibration curve 34,35 . Detailed dating results are shown in Table 2. ...

The IntCal20 Approach to Radiocarbon Calibration Curve Construction: A New Methodology Using Bayesian Splines and Errors-in-Variables

Radiocarbon

... A promising development in this area is the convergence between the frameworks of resource selection and step selection analyses both in discrete time (Michelot, Blackwell, Chamaillé-Jammes, et al., 2019; and in continuous time using a Langevin diffusion (Michelot, Gloaguen, et al., 2019). This work has established the conditions under which SSF and HSF frameworks agree, and has derived methods for HSF-type inference from telemetry (Michelot, Blackwell, Chamaillé-Jammes, et al., 2019;Michelot, Gloaguen, et al., 2019). ...

Inference in MCMC step selection models
  • Citing Article
  • October 2019

Biometrics

... Feingold et al. (2016) found a steep gradient in a study of nocturnal marine stratocumulus clouds in which six parameters were perturbed. Pope et al. (2021) demonstrated that the steep gradient in this data set could be emulated using a non-stationary method, where Voronoi tessellations defined regions of the 6-dimensional parameter space where separate, stationary emulators could be applied, which followed the assumption of smoothness. The discontinuity was primarily caused by perturbations in aerosol concentration, but the high dimensionality of the parameter space made visualizing the discontinuity difficult. ...

Gaussian Process Modeling of Heterogeneity and Discontinuities Using Voronoi Tessellations
  • Citing Article
  • September 2019

Technometrics