A spherical-plot solution to linking acceleration metrics with animal performance, state, behaviour and lifestyle
- Rory P. Wilson1Email author,
- Mark D. Holton2,
- James S. Walker2,
- Emily L. C. Shepard1,
- D. Mike Scantlebury3,
- Vianney L. Wilson1,
- Gwendoline I. Wilson1,
- Brenda Tysse1,
- Mike Gravenor4,
- Javier Ciancio5,
- Melitta A. McNarry6,
- Kelly A. Mackintosh6,
- Lama Qasem7,
- Frank Rosell8,
- Patricia M. Graf8, 9,
- Flavio Quintana5,
- Agustina Gomez-Laich5,
- Juan-Emilio Sala5,
- Christina C. Mulvenna3,
- Nicola J. Marks3 and
- Mark W. Jones2
© The Author(s). 2016
Received: 26 April 2016
Accepted: 16 September 2016
Published: 23 September 2016
We are increasingly using recording devices with multiple sensors operating at high frequencies to produce large volumes of data which are problematic to interpret. A particularly challenging example comes from studies on animals and humans where researchers use animal-attached accelerometers on moving subjects to attempt to quantify behaviour, energy expenditure and condition.
The approach taken effectively concatinated three complex lines of acceleration into one visualization that highlighted patterns that were otherwise not obvious. The summation of data points within sphere facets and presentation into histograms on the sphere surface effectively dealt with data occlusion. Further frequency binning of data within facets and representation of these bins as discs on spines radiating from the sphere allowed patterns in dynamic body accelerations (DBA) associated with different postures to become obvious.
We examine the extent to which novel, gravity-based spherical plots can produce revealing visualizations to incorporate the complexity of such multidimensional acceleration data using a suite of different acceleration-derived metrics with a view to highlighting patterns that are not obvious using current approaches. The basis for the visualisation involved three-dimensional plots of the smoothed acceleration values, which then occupied points on the surface of a sphere. This sphere was divided into facets and point density within each facet expressed as a histogram. Within each facet-dependent histogram, data were also grouped into frequency bins of any desirable parameters, most particularly dynamic body acceleration (DBA), which were then presented as discs on a central spine radiating from the facet. Greater radial distances from the sphere surface indicated greater DBA values while greater disc diameter indicated larger numbers of data points with that particular value.
We indicate how this approach links behaviour and proxies for energetics and can inform our identification and understanding of movement-related processes, highlighting subtle differences in movement and its associated energetics. This approach has ramifications that should expand to areas as disparate as disease identification, lifestyle, sports practice and wild animal ecology.
UCT Science Faculty Animal Ethics 2014/V10/PR (valid until 2017).
KeywordsSpherical plots Tri-axial acceleration G-sphere Visualisation
Quantification of animal movement is a hugely complex topic. In its broadest sense, it operates over wide (3-dimensional) space-scales and highly variable time periods. For example, it encompasses everything from a single limb motion describing a simple arc lasting less than a second, through co-ordination of repetitive limb motion in a whole animal during travel, which may last hours, to the diversity in the complex movement describing the various behaviours exhibited over the lifetime of an animal. Understanding animal movement is important for a suite of reasons but particularly because voluntary animal movement requires energy. Quantification of the allocation of chemical energy for mechanical output and how this relates to movement is relevant in understanding the costs, efficiencies and values of behaviour, lifestyle and exercise physiology. Judicious use of energy is a major element of optimization studies that seek to define best strategies, which have a broad remit ranging from examining most enhanced performance by elite athletes [1, 2] to animals adopting behaviours that maximize survival .
Unsurprisingly, therefore, the energetics of movement is well studied e.g. , but it has been polarised into essentially two main branches defined by differing methodologies - One branch examines power use , which typically requires measurement across extended periods [6–8] but is limited by the difficulties in attributing instantaneous power to performance . The other seeks to quantify behaviour, relying variously on approaches such as high-speed cameras , point light displays  and force platforms  for work on humans and, primarily, on observation-based methodologies for wild animals .
Increasingly though, both the power use and the behaviour of humans  and animals  are being studied using accelerometers in animal/human-attached tags because these sensors quantify change in speed, a fundamental property of motion, precisely . Thus, in the field of energetics, workers have derived indices, such as those based on dynamic body acceleration (DBA) metrics , that correlate tightly with oxygen consumption , while behavioural studies have used various methods such as random forests, vector machines and artificial neural networks on acceleration data to identify behaviours [19, 20]. However, both groups recognise the problem inherent in the complexity of acceleration data. These provide most value when recorded at high rates (typically >20 Hz) across each of the three axes defining orientation in space, producing effectively 6 channels of data, 3 relating to the gravity-based component of the acceleration and 3 relating to the animal-based movement . Indeed, it is perhaps this complexity that still represents an appreciable challenge for the animal (and human) behaviour community in binding energy use and behaviour within one framework (cf. ), even though they are fundamentally interdependent. Indeed, any framework that enhances consideration of animal movement, behaviour and power use simultaneously should facilitate the identification and understanding of processes and patterns across and between them.
One solution to this is to recognise that, because the earth’s gravity is constant, a tri-axial plot of tri-axial, orthogonally placed, acceleration data fundamentally builds a sphere, a ‘g-sphere’ . Acceleration data derived from animal movement change the form of this sphere. We capitalise on this to create a new visualization paradigm for animal/human-attached acceleration data whereby we generate the g-sphere and then place animal movement data on it, including those that seek to exemplify power use, over any temporal scale. The approach marries behaviour to estimated energetics and highlights some patterns that are not intuitively obvious. We show that g-sphere visualizations should have the capacity to highlight changes in movement patterns associated with e.g. human emotional state, injury and best practice in single sports manoeuvres but extend through to highlighting proxies for energy-based behavioural ecology in wild animals over time periods ranging from seconds to years.
The basic g-sphere
Dealing with over-plotting - the Dubai plot
Allocating putative power use to the g-sphere - the g-urchin
Comparing behaviours and putative power uses - the differential g-urchin
Application of g-spheres and their derivatives to raw tri-axial acceleration data adds another powerful tool to visualize and identify behaviour  that requires no knowledge of the animal in question for behaviour-specific patterns to emerge into groups. This approach concatenates 6 complex lines of acceleration data into one plot binding animal attitude and proxy for power use into one visualization that clearly shows modes of behaviour (Fig. 1). The immediate value lies in its potential for use as a template match approach for specific activity pattern identification across data . Thus, behavioural description and identification (Figs. 1, 2 and 3) do not require matched observed behaviours with example data but stem from a visually apparent clustering within the plot. In particular, differences between various g-sphere derivatives, especially Dubai and urchin plots (Fig. 4), can be used to identify specific variation in posture and power-use proxies between behaviours. For example, the Dubai plots in Fig. 4a provide an example of how the posture of a subject changed according to whether they had watched a happy or sad film clip, with the allocation of time to facet position changing. Similarly, the posture and allocation of DBA to different body postures during walking changed after a fall (Fig. 4b). The g-spheres therefore employ fundamentally different principles to other methods in the manner of data visualization and interpretation.
In a first iteration, the most common behaviours are most easily identified because of the way they dominate the basic g-sphere visualization (Fig. 1), which could be argued is the most important feature of understanding time management in animals. However, even behaviour that is only a small fraction of the time budget, but is energetically distinct and therefore likely to be apparent in the DBA distributions on urchin spines, may be identified by moving from the globally normalized g-urchin to one that is normalized to facet (Fig. 2b, c).
Importantly, mono-, bi-, or even tri-modality in the frequency distributions of DBA allocated to particular facets or groups of adjacent facets, point to multiple behaviours occurring at similar animal postural attitudes. This is illustrated, for example, in the cormorant behaviour where the white arrow in Fig. 1c2 shows multi-modality in DBA due to both dive ascent behaviour and flight behaviour being apparent in the same body attitude facet. It is also exemplified in the stationary and swimming behaviours in the seabass, shown in the bimodality of the DBA distributions along urchin spines at the North Pole (cf. Fig. 2c). The time-based adoption of behaviours can also be studied with this, for example, in the badger data presented (Fig. 3). Here, ‘normal’ walking behaviour is only manifest during day 4 post-sedation, when the urchin spines at the North Pole acquire a DBA mode that is greater than 1.0 g (Fig. 3). Such observations can then readily be incorporated into statistical classifiers and classification algorithms.
Generation of frequency distributions of DBA, as a proxy for power, thus enhances the process of separating behaviours. Importantly, it also helps visualize the overall allocation of power proxies, either to specific behaviours over short periods such as seconds or to collections of behaviour over longer periods (cf. Figs. 1, 2 and 3) extending to months or even years. Depending on the timescales, collections of particular behaviours should provide a representation of different lifestyles, as well as their considered associated energetic outlay, allowing powerful comparisons to be made between systems or scenarios. Examples include comparisons between species with contrasting lifestyles (Figs. 2 and 5) or within-species lifestyle comparisons. Indeed, the precise form of ‘lifestyle’ plots (Fig. 5) may help in defining lifestyle taxa by defining animal capacities. The future may also benefit from the use of g-sphere approaches based on multiple accelerometers used on different parts of the body or even having accelerometers on hand-held objects. The expectation is that this will be particularly useful in sport applications (Additional file 1: Figure S7) where effective movement must be stylized for maximum performance because limb-, or sports equipment-mounted sensors will represent local forces and perhaps local power-usage proxies better than trunk-mounted systems which produce a body-integrated signal. Importantly, such power-proxy comparisons, from trunk-or limb-mounted sensors, can help identify efficient solutions to activities where performance, such as running speed over a given distance or animal breeding success over months, should be equatable with the putative energetic cost. This sort of consideration thus has advantages for elite athletes as well as for conservation bodies examining the costs of the lifestyle of their animals. Equally, changes in behaviour that occur with disease or illness, such as constrained activity stemming from rheumatoid arthritis , should be rapidly identifiable using this approach.
We expect g-spheres and their derivatives (e.g. Fig. 5) to form the basis for summary statistics which highlight particular aspects of performance, behaviour and lifestyle, which may function to be powerful descriptors of e.g. animal lifestyle, linked, among other things, to physical limitations based on taxonomic, allometric or environmental (e.g. water versus terrestrial) constraints . In addition, such visualizations may help both children and adults to understand how the physical activity levels in their lifestyles compare to those recommended .
The treatment of tag-derived tri-axial acceleration data by creating a tri-axial plot of the gravity-based acceleration, leads to a spherical surface on which acceleration proxies for power use can be placed. This process has potential for highlighting behaviour-, and even state-, dependent clusters, irrespective of whether the user has a verified library or not and should illustrate how animals may allocate energy to the different behaviours. Subsequent simplification of the spherical plots into percentage of sphere occupied, mean dynamic body acceleration and time allocated per facet allows simple 2-d plots between these parameters to be created (Fig. 5). This approach should provide a powerful summary of putative energy allocation to behaviour and time, documenting intra-specific differences and showing how animals respond to their environment over time. Inter-specific comparisons of these metrics show promise as a powerful behavioural tool with which to compare and quantify animal lifestyles.
The g-sphere visualization technique has been incorporated into publically available smart sensor analysis software, Framework4 [30, 31], available from http://www.framework4.co.uk. Walker et al.  give more details on this.
The basic g-sphere
In brief, the basic g-sphere is derived from tri-axial acceleration data, where the sensors have orthogonal placement, aligning with the major axes of the tagged animal’s body.
Typically, the acceleration data will be recorded at infra-second rates (e.g. 40 Hz) on a deployment spanning anywhere from a few minutes up to a year. One day of data (24 h) recorded at these rates provides over 10 million measurements. For the g-sphere, we build on a method for visualising accelerometer data in Grundy et al. , using spherical coordinate plots to depict the distributions of data. To deal with large datasets, we utilise frequency-based approaches which show an overview of the data. Firstly, a spherical histogram shows the number of data items in each facet of the spherical coordinate system. Secondly, we build on the surface provided by the g-sphere using location-dependent frequency bins (the ‘g-urchin’ plot), for metrics such as DBA  as proxies for power usage. Multiple urchins can be compared difference operations to analyse across instances, behaviours groupings, or data sets.
Static and dynamic acceleration
Measured acceleration is the product of a static component due to gravity, manifest in accelerometers according to their orientation with respect to the Earth, and a dynamic component, due to the movement of the animal. Separating these components from the raw accelerometer measurements allows isolation of postural attitudes and movement.
Dynamic acceleration-based metrics  have been argued as a predictor of power . Two measures, Overall Dynamic Body Acceleration (ODBA) and Vectorial Dynamic Body Acceleration (VeDBA), have been used, and are essentially equivalent in terms of their power to predict VO2 .
The basic g-sphere plots the static accelerometer data in a three dimensional scatter plot with the animal’s heave axis being allocated the y-axis, the surge the x-axis and the sway the z-axis (Fig. 1a). Each vector is considered as an offset from the origin, directly scatter-plotted in three-dimensional space with, for example, the colour of each data point being linked to any associated attribute in the data set (Fig. 1a). This representation shows short-lived behaviours well, providing a compelling visualization of when forces exceed that exerted by gravity (Additional file 1: Figure S1).
This, projects the normalised vector onto the surface of a sphere in 3-d scatter plots which gives an implicit conversion to spherical coordinates (r, θ, φ) , where θ corresponds to the angle of inclination, φ is the angle of rotation on a two-dimensional plane, and the radius is constant (r = 1) throughout. Each vector is plotted as a point in the display and the size and radius of each point can be adjusted by a fixed amount, to link it to an attribute in the data set. Each point can be joined together in chronological order to show the temporal ordering of the vectors as a path in the three-dimensional space (Additional file 1: Figure S2) so that the spherical scatter plot shows an intuitive summary of the geometric distribution of posture and direction. Linking the radius, r of each coordinate to another attribute allows additional dimensions, such as depth, to be encoded which, in this case, provides a compelling illustration of diving patterns along with the associated state (Additional file 1: Figure S2).
Binning in three-dimensions
Large data set plots incur problems with occlusion and overplotting where data values in a point cloud obscure other values. For this, an overview and focus approach  can be employed which gives a contextual overview of the data while leaving potential to interact with further details in the data. Thus, we divide the surface of the sphere into facets (sphere tessellation) and treat the data within each facet to derive summary statistics (binning).
To represent the underlying data on which the chart is based accurately , we employ a frequency-based approach using regular bin sizes to summarise the data although construction a sphere from a series of uniform geometric primitives is a problem from the cartography domain . The traditional method of constructing a sphere via lines of latitude and longitude results in variable sized facets misrepresenting the underlying data . We thus utilise a geodesic sphere, providing a close to uniform and regular sphere tessellation, using subdivision surfaces and spherical projection of an icosahedron platonic solid. The geodesic sphere starts with an icosahedron. Each facet is then repeatedly subdivided a pre-defined number of times with each of the acquired points projected onto a sphere. This results triangular facets, each of which is of a close to regular shape and area. Despite a slight variation in size and shape of each facet, this has a negligible effect in reconstructing the underlying data .
For each facet, the following statistics are computed; (i) the number of data items intersecting each facet, (ii) the mean value of each data channel for the items in each facet and (iii) a frequency distribution of a user-defined data attribute consisting of a user-defined number of bins. The data for attributes (i) and (ii) are normalised so that the whole sphere adds up to 100 %. The distributions for (iii) are normalised locally which allows the creation of a histogram of each facet of the power usage occurring for a particular movement and postural state independent of the frequency of the underlying data in the facet (since the frequency equates to a percentage).
The binned data for each facet can be displayed as a single histogram projecting perpendicularly from its respective facet (Figs. 1b, 2a and 4a; Additional file 1: Figure S3). Each histogram length and colour is nominally proportional to the normalised sample size for the sphere facet (Additional file 1: Figure S4). This gives an overview of the data distribution over the sphere, illustrating the frequency of postures or movements in the data set. The colour may be encoded as any other data attribute, in addition to the normalised frequency, along with the length.
In a final step of this method, the smoothed, tri-axial acceleration axes can be encoded in addition to the frequency of items in each facet. A histogram for each facet of the sphere is computed for the items residing in the facet, which can be combined in a manner that represents the power usage for each state. This ‘g-urchin’ has spines projecting from the sphere with each spine placed at a user-defined distance away from the sphere to avoid occlusion with any of the other layers of the visualization (although a line is drawn to the centre of the facet it represents). The length and width of each spine can be ascribed to any data attribute. It is most effective when the spine characteristics are linked to histogram frequency or the number of items residing in the facet (Figs. 1c, 2b,c and 3). Each spine consists of a number of stacks, the width of which corresponds to the histogram bin width (Additional file 1: Figure S4 overview):
Difference is used to subtract two g-spheres (GA, GB) from each other. The absolute difference between the two spheres, for each facet in the sphere (f), and each corresponding bin (b) in the frequency distribution is computed. The result is a new operation g-sphere which highlights the difference between GA and GB (Fig. 4b).
Summation is used to combine two g-spheres together. The items in each bin are added together. The result is a new operation g-sphere which combines the spheres GA and GB together.
Each frequency distribution is normalised to eradicate any bias towards data sets containing different number of data points. The effect in the frequency distribution is a percentage where each bin contributes towards a subset of the distribution. As such, the entire frequency distribution totals 100 %. When combining the distributions together by addition or subtraction, the result is the difference in percentage between the two histograms. Percentages of distributions are used to protect against bias resulting from the size of the underlying data.
Dynamic body acceleration
Vectorial dynamic body acceleration
The authors are grateful for technical support given by Phil Hopkins as well as to the liberal and enthusiastic work environment that defines the College of Science at Swansea University.
JSW was funded by an EPSRC doctoral training grant. Acceleration data from many different animals were used in the formalization of this work, even if not presented explicitly, so we acknowledge the funding of NERC (NE/I002030/1) to DMS in this regard. This project was made possible by a generous grant by the Royal Society/Wolfson fund to build the Swansea University Visualization Suite. PMG and FR were funded by Telemark University College, Norway.
Availability of data and materials
All data generated and/or analysed during the current study are available from the corresponding author on reasonable request.
RPW provided the initial concept after discussion with MDH, JSW, MWJ and ELCS. MDH and JSW developed the software. VLW, GIW, MAM, KAM and BT provided human-based data including analysis and interpretation, FQ, AG-L, J-ES, DMS, JC, LQ, FR, and PMG gathered animal data and provided analyses and interpretation. MG contributed to general analyses and all authors contributed to the manuscript and to the ideas contained therein. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
Consent for publication
See above. No named person within this study.
Ethics approval and consent to participate
The fish work was performed under permits from the “Secretaría de Pesca del Chubut” while the bird manipulations were carried out in accordance with the legal standards of the Argentine government and fieldwork approved by The Organismo Provincial de Turismo and Dirección de Fauna y Flora Silvestre of Chubut Province, Argentina. Permission was granted from UK Home Office and protocols approved by the Department of Agriculture, Environment & Rural Affairs, Northern Ireland for all mammal work except for beavers, for which the work was approved by the Norwegian Experimental Animal Board and the Norwegian Directorate for Nature Management. The study procedures for humans were approved by the Swansea University ethics committee and complied with the Declaration of Helsinki. All the participants and their parents/guardians were informed in writing about the demands of the study, and subsequently gave their written informed assent and consent, respectively, for participation prior to commencing the study.
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