Daily travel distance (DTD), the distance an animal moves over the course of the day, is an important metric in movement ecology. It provides data with which to test hypotheses related to energetics and behaviour, e.g. impact of group size or food distribution on DTDs. The automated tracking of movements by applying GPS technology has become widely available and easy to implement. However, due to battery duration constraints, it is necessary to select a tracking-time resolution, which inevitably introduces an underestimation of the true underlying path distance. Here we give a quantification of this inherent systematic underestimation of DTDs for a terrestrial primate, the Guinea baboon. We show that sampling protocols with interval lengths from 1 to 120 min underestimate DTDs on average by 7 to 35 %. For longer time intervals (i.e. 60, 90, 120 min), the relative increase of deviation from the “true” trajectory is less pronounced than for shorter intervals. Our study provides first hints on the magnitude of error, which can be applied as a corrective when estimating absolute DTDs in calculations on travelling costs in terrestrial primates.
Spatial information is crucial for many questions in ecological and behavioural research, e.g. species or resource distribution, habitat utilisation and estimates of home ranges or daily travel paths. The application of a satellite-supported global positioning system (GPS) has improved the collection and accuracy of spatial data (Kays et al., 2015), providing ecologists and behavioural biologists with opportunities to determine spatial patterns and test spatially explicit hypotheses. Similarly, the use of GPS has become more prevalent in primate field studies (Osborne and Glew, 2011; Sterling et al., 2013). Beside the determination of geographical positions of ecological objects or structures within a primate's home range – such as sleeping and resting sites, feeding patches or seed-dispersal events – spatial data have been used to estimate home ranges (position, shape and size), habitat utilisation, and daily travel paths and travel distances. In primatology, the application of GPS collars indicated great potential particularly for semi-terrestrial primates in (semi-)open habitats (Markham and Altmann, 2008), but also for arboreal species (Stark et al., 2017).
A selection of GPS fixing intervals applied in primate and non-primate studies.
Either animals can be equipped with a GPS device, and the respective positions
will be collected automatically at pre-programmed intervals, or a researcher
follows an animal and determines the positions using a handheld device (e.g.
see Table 1). The GPS device consumes energy for every location fix, and thus
battery life limits the number of position attempts or fixes a device can do.
Programming fewer GPS fixes results in longer battery life but at the price
of lower data density. It might not be a big problem if one is interested
in the area an animal uses within a year, which one can probably estimate
fairly well with just 2 or 3 fixes day
Uncertainties in animal movement data, owing e.g. to sampling frequency, may strongly influence interpretations of tracking data (Bradshaw et al., 2007; Harris and Blackwell, 2013; Laube and Purves, 2011). As expected, in a number of studies it was shown that, as sampling intervals increase, the uncertainty of the behaviour between fixes increases; e.g. DTDs estimated from low sampling frequencies were significantly shorter than those based on higher sampling frequencies (Laundré et al., 1987; Mills et al., 2006; Reynolds and Laundré, 1990; Rowcliffe et al., 2012; Edelhoff et al., 2016). How, if at all, this effect can be corrected statistically or by modelling is an open question (Blackwell et al., 2016; Fleming et al., 2014a, b, 2016; Shamoun-Baranes et al., 2011). One way to mitigate these effects can be an empirical estimation of the magnitude of error one yields by applying different sampling frequencies.
In a study on range use of Guinea baboons (
Example of a baboon track line (black) over 4 h and estimated travel distances if sampling is done applying different interval lengths (respective red lines).
In our study we therefore aimed to estimate the magnitude of error when
determining DTDs for Guinea baboons (
Temporal distribution of tracking periods. Tracking periods were either 4 or 2 h long. ID: individual baboon males; numbers in first horizontal line indicate hours of the day. T: tracking periods included in analysis; t: tracking periods excluded, because of gaps in the continuous tracking larger than 60 s.
The study was carried out in the Niokolo-Koba National Park at the
research station of the German Primate Center in Simenti
(13
The baboon community in Simenti comprises 350–400 individuals. They live in a multi-level society consisting of one-male units (OMUs), parties and gangs (Patzelt et al., 2014; Goffe et al., 2016). The baboons were habituated to human observers, so that observations and follows could be done from less than 5 m distance.
We selected four males from different parties, and one of us (Langhalima Diedhiou) followed on
foot one individual baboon at a time, keeping a distance of 5 m to the
respective focal animal. The follows were repeated several times for each
male (Table 2). The respective tracks were recorded with a handheld Garmin
GPSMAP 62. Tracing set-up was “auto-normal”. In sum we recorded 56 2 h tracks.
In nine cases we experienced gaps in the continuous recording of the respective
tracks (leg time
Using a GPS device, even a continuous track consists of a number of fixes, optimally with a very short sampling interval or leg time. Leg time is the delta between the time stamps of the two fixes bounding the leg (e.g. 1 s if the sampling frequency is 1 Hz). However, since conditions are not always optimal, the real leg time varies and is most often larger than the targeted 1 s leg time. As a result, when we overlaid the continuous track with a 1 min sampling interval, for instance, the respective 1 min time stamps did not necessarily match with a fix from the GPS device. For instance, the closest time stamps can be at 57 or 62 s instead of 60 s. Therefore we had to interpolate the tracks and re-discretise them.
We artificially re-discretised the original tracks with regular sampling
intervals of 1, 2, 5, 10, 15, 30, 60, 90 and 120 min (shown on the
To get to a relationship between the deviation from the original travel
distance and the re-discretisation sampling interval duration, we fitted a
Bayesian multilevel log-normal regression model using the Stan-based (Stan
Development Team, 2015) R add-on package brms (Bürkner, 2017), with track
index as grouping factor
To be able to further quantify how the deviation from the original travel distance is related to moving velocity and turning-angle states, we fitted a hidden Markov model (Michelot et al., 2016). As an example, we performed this for a re-discretisation duration of 5 min, which enables us to classify the underlying moving states on the basis of this coarsened information. This grid is still short enough – and therefore close enough to our original quasi-continuous sampling – to allow for making statements about the bias within these re-discretised intervals (too-long intervals would lead to mixing of underlying states; too-short intervals do not leave us with enough deviation from the original travel distances). We based this on the three following states: resting (no movement, state 1), slow velocities with uniformly distributed turning angles (state 2) and higher velocities with a higher likelihood for more straight movements (state 3). The parameters underlying these three states were fitted by a maximum-likelihood approach as implemented in the R package “moveHMM” (Michelot et al., 2016). We then compared the deviation from the original travel distance in metres per minute as introduced by re-discretisation of the original tracks on the 5 min grid, conditional on the reconstructed states by using the “Viterbi algorithm” on the basis of the hidden Markov model's results. Section S2 contains details on the states' parameterisations.
All research adhered to the legal requirements of the countries from which
samples were obtained. The study was carried out in compliance with the
principles of the American Society of Primatologists for the ethical
treatment of non-human primates
(
The database comprised 47 2 h tracks with 18 073 fixes, resulting in
18 026 legs. In 80.7 % of cases the GPS device was able to fix a
position in less than 30 s. In only 0.6 % of cases it took between 45
and 60 s. Two-hour tracks lasted on average 2:00:06 h (
The baboons travelled 1921 m within a 2 h track (median; range:
183–3691 m;
Inter- and intra-individual variation in distance travelled within
2 h. Median as thick solid horizontal line; 1st quartile
The deviation from the real distance covered within a 2 h track increased the longer the sampling interval was (Fig. 3). If we applied a 1 min sampling interval, we already underestimated the distance by 6.3 % on average (median). The deviation from the true distance increased to 32.3 % (median) if we used 2 h sampling intervals. Considerable variation in underestimating the distance could be observed, which can reach in the extreme case more than 80 % at 2 h sampling intervals.
Deviation from original travel distance covered within 2 h (box plots illustrate the same descriptive statistics as described in the caption for Fig. 2), as revealed by applying different sampling intervals.
There is strong support that the expected deviation from the true distance follows an exponential function (Fig. 4), indicating that the relative error increase is larger at shorter sampling intervals, as can be seen in Fig. 4 by the estimated expected error levelling off with increasing re-discretisation interval duration.
Expected deviation from the original travel distances (in %) conditional on re-discretisation interval duration (in minutes). The solid green line shows the estimated expectation (the functional form is described by the function as given on the top right of the figure); the green area shows a point-wise 99 % uncertainty interval for this estimated conditional expectation.
Results of the hidden Markov model estimation. Blue lines on the
left and middle plots illustrate the densities for the “resting” state 1,
dark grey lines show densities for state 2 (slow velocities, i.e. small step
lengths per 5 min interval, approximately uniform distributed turning angles)
and red lines illustrate the densities for state 3 (higher velocities and
higher density for straight movements). The dashed histograms show the
overall empirical distributions. The right figure shows the 47 tracks,
coloured according to the states to which the Viterbi algorithm (based on
the hidden Markov model results) categorised them (
The movement behaviour of the baboons – here categorised in three states: resting (no movement, state 1), slow velocities with uniformly distributed turning angles (state 2) and higher velocities with a higher density for more straight movements (state 3) – had a clear impact on the magnitude of error in estimating travel distances (Figs. 5 and 6). The deviation from true distance was of course smallest if the baboons did not move (stage 1) and largest if the baboons moved fast in a more or less straight direction. This appears counterintuitive at first glance but is explained by the much stronger consequences of even small turning angles at intervals with fast movement than at intervals with slow movement.
Results of our analysis of the DTD of Guinea baboons met the general
expectation: the higher the frequency of positions, the more trustworthy the
movement paths (Nathan et al., 2008). The absolute average underestimate of
DTDs was found to be less than 7 % for 1 fix min
Deviation from original travel distance by the artificial 5 min sampling scheme, conditional on the states as estimated by the Viterbi algorithm applied on the hidden Markov model results shown in Fig. 5. Box plots illustrate the same descriptive statistics as described in the caption for Fig. 2, with values of the median conditional deviations given directly in the figure, and also illustrated by crosses.
The magnitude of error, however, is also dependent on the behaviour of the individuals under consideration. In the extreme, if an animal does not move over a long period, the true travelled distance is 0 and the deviation from the true value also becomes 0, irrespective of the length of the sampling interval. Similarly, it is very likely that the error remains small if an animal moves relatively slowly in a straight direction, whereas one can expect a large deviation if the animal moves quickly with a lot of meandering. In our study, we analysed the impact of movement behaviour exemplarily at a 5 min sampling interval. As expected, in state 1 (mainly resting) the deviation was minimal, whereas it increased minimally if the animal moved slowly (state 2) and increased more if it moved quickly (state 3). Since the spatial behaviour of baboons and other animals is often influenced by ecological condition (e.g. temporal and spatial distribution of food), one can expect season might affect step length and path tortuosity (Calenge et al., 2009; Owen-Smith et al., 2010).
Moreover, the time of day might play an additional role in shaping the
characteristics of a travel path. In Chacma baboons (
We were able to determine underestimations of DTDs in a terrestrial primate, the Guinea baboon, when applying different sampling intervals. The values of underestimation can be used as a corrective in estimations of absolute DTDs and travelling costs, which can make comparisons among different primate groups more reliable. Our analysis also showed, at least for terrestrial primates such as baboons, that there is no significant increase of underestimation beyond a sampling interval of 60 min (60, 90, 120 min). As shown in Fig. 4, this mainly results from a weaker increase in underestimation for larger interval durations, and less from an increase in estimation uncertainty. Such a priori knowledge on underestimations of DTDs is important to inform researchers conducting GPS remote telemetry studies. Based on analyses such as ours, researchers can choose the “appropriate” sampling intensity in order to optimise the trade-off between sampling density and battery longevity.
We think that the overall magnitude of error, as found in our baboon study, will provide an estimate transferable also to other terrestrial or semi-terrestrial primate species. However, if the respective species show largely deviating movement behaviour, the magnitude of error will most likely change.
Data are provided as Supplement S3.
DZ and MK designed the study. LD and MK collected the data in the field. HS-R did most of the data analyses. LD, MK, HS-R and DZ wrote the paper.
The authors declare that they have no conflict of interest.
We thank the Diréction des Parcs Nationaux and Ministère de l'Environnement et de la Protéction de la Nature de la République du Sénégal for permission to work in the Niokolo-Koba National Park (Attestation 0383/24/03/2009 and 0373/10/3/2012). In particular we thank the conservator of the Niokolo-Koba National Park for permitting and supporting this project research in the park. We also thank Vanessa Wilson for English language editing and two anonymous reviewers for their valuable comments. Funding was provided by the German Science Council DFG ZI 548/6-1 and the DAAD D/12/41834. Edited by: Eberhard Fuchs Reviewed by: two anonymous referees