Abstract
Understanding the drivers of animal movement is significant for ecology and biology. Yet researchers have so far been unable to fully understand these drivers, largely due to low data resolution. In this study, we analyse a highfrequency movement dataset for a group of grazing cattle and investigate their spatiotemporal patterns using a simple twostate ‘stopandmove’ mobility model. We find that the dispersal kernel in the moving state is best described by a mixture exponential distribution, indicating the hierarchical nature of the movement. On the other hand, the waiting time appears to be scaleinvariant below a certain cutoff and is best described by a truncated powerlaw distribution, suggesting that the nonmoving state is governed by timevarying dynamics. We explore possible explanations for the observed phenomena, covering factors that can play a role in the generation of mobility patterns, such as the context of grazing environment, the intrinsic decisionmaking mechanism or the energy status of different activities. In particular, we propose a new hypothesis that the underlying movement pattern can be attributed to the most probable observable energy status under the maximum entropy configuration. These results are not only valuable for modelling cattle movement but also provide new insights for understanding the underlying biological basis of grazing behaviour.
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Introduction
Animal movement is a highly complex process driven by various random and deterministic mechanisms involving a large number of causing factors^{1,2}. It has been proposed that spatiotemporal patterns in movement may arise from moving strategies that evolve to optimise foraging efficiency^{3,4}, decisionmaking processes in response to external stimuli^{5}, environmental conditions or landscape features^{6,7,8}, collective dynamics and social interactions^{9,10}, memory and homereturn behaviour^{11,12}, just to name a few. Fully unravelling the complexity of animal movement as well as sorting out the intricate relations between the observed spatiotemporal pattern and various underlying causing factors remains a difficult scientific challenge.
For over a century, our attempts to understand animal movement have been limited to a qualitative level due to the lack of highquality data that can provide finegrained spatiotemporal description of movement^{2}. Recently, new tracking technologies such as the Global Positioning System (GPS) have been deployed in animal tracking to obtain continuous timeresolved moving trajectories with high spatiotemporal resolution. The emerging highquality movement data enables the application of quantitative analysis and mathematical characterization on mobility patterns at different spatiotemporal scales, which provides new insights into possible factors that drive movement decisions.
One common approach to analyze animal movement is to represent the timeresolved trajectory as discrete moving steps under the framework of random walk^{13,14,15}. In this context, the dispersal kernel p(r) in space, which characterizes the general distribution of step length r in the trajectory, is considered to be a significant footprint of movement^{16,17}. The detailed functional form of p(r) is indicative of a specific type of random walk and the underlying dynamics of movement. For example, an exponential kernel function with r_{c} being the characteristic length scale is the signature of the classic Brownian walk that obeys the centrallimit theorem and exhibits a normaldiffusive pattern. A scaling dispersal kernel characterized by a powerlaw function p(r) ~ r^{−γ} with γ being the scaling exponent is the signature of the Lévy walk which exhibits high heterogeneity and superdiffusive pattern. Much effort has been devoted to study the dispersal kernel p(r) for different animal species using real movement data, from small insects like honey bees^{18}, marine life like jelly fish and whales^{19}, birds like albatross^{20,21}, to mammals like monkeys^{22} and human^{17,23}. For example, a controversial topic that attracts tremendous attention is whether the observed movement follows a Brownianlike motion or a Lévy walk. Although many studies have shown strong evidence for the existence of Lévy walks in animals, it has been argued that this evidence may come from statistical artifacts or inappropriate manipulation of data^{24,25,26}, suggesting the necessity of using highresolution data and robust statistical methods to validate the characterization of movement patterns.
Despite its importance in characterizing movement, the dispersal kernel p(r) only provides partial information on the spatial pattern and does not fully capture all important aspects in animal movement such as the temporal spectrum that depicts the switch between different activity modes over time. Recently it has been found that scaling phenomena in movement can also arise in the waiting time distribution p(τ_{w}) that characterizes the time span of nonmoving period, or the interevent time distribution p(τ_{e}) that characterizes the time between two successive moving activities^{11,17,27}. These findings suggest there is a need for more detailed investigation on the spatiotemporal pattern in movement beyond the dispersal kernel.
Here we use a dataset of highfrequency GPS samples to study the movement of grazing cattle. In contrast to most previous studies on animal movement that only focus on the dispersal kernel or statistics for one specific activity mode such as the waiting time, the highresolution trajectories in our dataset allows us to do activity classification on the trajectory and gain more comprehensive insight into the spatiotemporal pattern in each activity mode. In particular, we use a twostate ‘stopandmove’ model to describe the mobility pattern, dividing the trajectory into alternate moving and nonmoving states (see Material and Methods). The nonmoving state indicates that the animal remains within a radius Δr in space for at least Δt in time, where Δr represents the spatial resolution limit in the observation and Δt is a tuning threshold parameter to specify the minimum time span. The nonmoving segment in the trajectory can be viewed as a single point in space, which we call waiting location, with a length τ_{w} ≥ Δt in time, which we call waiting time correspondingly. On the other hand, the moving state indicates that the animal is in a transition from one waiting location to another, which can be described as a trip (l, τ_{m}) in the trajectory with l being the distance between the two waiting locations and τ_{m} being the time elapse of the trip. The representation of mobility pattern in this approach is shown in the schematic diagram of Fig. 1.
Under this representation, we observe a very interesting spatiotemporal pattern in which the two activity states are of unique statistical characterization. In particular, we find that the dispersal kernel or trip length distribution p(l) is best described by a hybrid exponential distribution, which indicates that the trajectory has a twolevel hierarchical structure in space and each level appears to follow a Brownian walk. This is in contrast to the widelyobserved Lévy walk patterns in other species. Despite the absence of scaling law in the spatial dispersal, we find that the waiting distribution p(τ_{w}) in the time domain is best described by a truncated powerlaw. Possible underlying mechanisms and ecological implications accounting for this phenomena are discussed (see Discussions).
Understanding grazing/foraging animal movements is not only a critical issue in biological science but also of fundamental importance to many practical issues such as farm and livestock management^{28}, the maintenance of biodiversity in ecosystems^{29} and developing better tracking^{30} and virtual fencing technologies^{31}. Our results provide new quantitative insights into grazing cattle movement that are largely lacking in most previous work. Our statistical characterization of the multimodal mobility pattern is useful for understanding the biological basis of the complex grazing behaviors as well as the underlying driving factors behind these behaviors. The simple twostate model along with the statistics extracted for each activity state can be also used as a building block to develop more realistic mobility simulation platform that can benefit disease spread modelling^{17} as well as the design of virtual fencing systems^{31}.
Results
Dispersal kernel in moving state
We first turn attention to the spatial dispersal kernel or the trip length distribution p(l) over the whole population. Obtaining the functional form of p(l) directly from empirical data requires a binning process, which has been known to have statistical distortion for data with a broad distribution^{26}. To avoid the disadvantage of binning, we use the complementary cumulative distribution for statistical analysis. We process the data using three different parameter sets with Δr = 5 m corresponding to the resolution limit of positioning device and Δt = 1, 2 and 5 mins respectively^{32}. To describe the dispersal kernel P(l) shown in Fig. 2a–c, we consider four commonlyused candidate models^{8}: (1) powerlaw; (2) truncated powerlaw with exponential cutoff; (3) exponential; (4) mixture exponential. Using the maximumlikelihood estimation (MLE) to fit the candidate models and the Akaikeinformationcriterion (AIC) for model selection^{24} (see Supporting Information), we find that the best model to describe P(l) is the mixture exponential
where l_{1} and l_{2} are the characteristic lengths in each mixture component, q is a parameter specifying the mixture proportion and l_{min} = Δr = 5 m is the lower bound in observation. Another significant statistical feature of the moving state is the trip time distribution p(τ_{m}), which is also best described by the mixture exponential model, as shown in Fig. 2d–f. This is consistent with our expectation that the trip time τ_{m} is strongly correlated with the trip length l.
The mixture exponential here indicates that the spatial pattern of grazing cattle is governed by two different Brownianlike dynamics with different characteristic scales, suggesting a hierarchical structure of the movement. If we consider that the landscape is formed by a number of patchy areas, the first exponential distribution will represent the shortrange movement that occurs within a patch and the second exponential distribution with a larger characteristic length will represent interpatch movements. To better reveal this hierarchy structure in mobility pattern, we perform clustering on the waiting locations using a densitybased clustering algorithm DBSCAN which is efficient in discovering significant clusters with irregular shape from noisy data points, as shown in Fig. 3. After grouping the waiting locations into clusters, the trips in the mobility pattern fall into two categories, intracluster trip and intercluster trip. We find that the trip length distribution for each of these two types of trips can be well described by a single exponential distribution, as shown in Fig. 4. It is worth noting that the mixture exponential still renders the highest AIC weight among the four candidate models for the intracluster trip length distribution, while the single exponential has the highest AIC weight without the mixture exponential. However the difference between the two components in the mixture model is comparably small (l_{1} = 11.20, l_{2} = 22.05, q = 0.44, Δt = 2 mins), suggesting that the two components are not strongly distinguishable and a single exponential is a reasonable alternative model in this scenario. We also observe that some longdistance intercluster trips are of high similarity, indicating that transitions from one cluster to another are not completely random and spontaneous, but could be driven by a deterministic process such as memory or herding.
Waiting time distribution
To characterise the waiting time distribution, we compare three different models, namely exponential, powerlaw and truncated powerlaw with exponential cutoff (see Supporting Information). We observe that the waitingtime distribution p(τ_{w}) is best described by a truncated powerlaw distribution
with γ being the scaling exponent and being the structural cutoff. As shown in Fig. 5, varying the threshold parameter Δt in data processing does not affect the emergence of scaling phenomena. The scaling law in the waiting time distribution is indicative of the heterogeneous grazing dynamics of cattle, which could be related to the landscape heterogeneity, the complex decisionmaking dynamics or the energy management of movement (See Discussion). We also find that the waiting time distributions in the main clusters discovered by the DBSCAN algorithm are all well described by a truncated powerlaw, suggesting the scaling behaviour in waiting time distribution is invariant at the clusterlevel.
Without taking into account correlation between activities, the temporal spectrum of mobility pattern can be approximated as a twostate renewal process where the time span of the alternate moving and nonmoving activities are randomly drawn from the distribution functions p(τ_{m}) and p(τ_{w}) respectively. To test the validity of this approximation, we measure the pairwise Pearson correlation coefficient between the time span of consecutive activity segments in the following four situations: (1) the nonmoving segment and the next moving segment (r = −0.0344, p = 0.0363); (2) the moving segment and the next nonmoving segment (r = −0.0616, p = 0.000174); (3) two consecutive nonmoving segment (r = 0.0787, p = 1.58 × 10^{−6}); (4) two consecutive moving segment (r = 0.0719, p = 1.24 × 10^{−6}). We find that none of these shows significant correlation. The result suggests that shortrange correlation does not exist in the temporal spectrum, i.e. the time span of the previous activity has little influence on the time span of the next activity and the temporal dynamics can be approximately described by a twostate renewal process without considering longrange correlation.
Individual mobility pattern
The populationbased statistics presented above are not necessarily representative of the individual patterns. It has been suggested that the characteristics of population statistics may differ from their individual counterpart after being aggregated over population. For example, the observed Lévy walk pattern in population may arise from individual heterogeneity^{33}. To test whether the individual pattern is consistent with the populationbased statistics, we use the same model selection procedure to fit the individual statistics (Δr = 5 m, Δt = 2 mins). We find that the trip length and trip time distribution for each individual is best described by the hybrid exponential, with only one exception in the trip length distribution. On the other hand, the waiting distribution for each individual is best described by powerlaw or truncated powerlaw (see Supporting Information). This suggests that the composite Brownian walk in space as well as the scaling law in waiting time distribution are not a statistical artefact due to the mixture of different individual patterns, but they appear to be universal for all individuals. Although all individual spatiotemporal patterns are best described by the same distribution functions, the fitted parameters vary from individual to individual. For example, the exponents of the truncated powerlaw for waiting distribution estimated by the maximumlikelihood method range from γ = 1.6 to γ = 2.5. This indicates that the internal properties encapsulated by the scaling exponent γ are different among individual cows, although their activities appear to be governed by the same dynamics.
Discussion
In this study we have found that under a twostate ‘stopandmove’ representation the spatiotemporal pattern of grazing cattle exhibits a hierarchical structure in space and an asymmetric temporal spectrum, which can be described by a composite Brownian walk interspersed with powerlaw distributed nonmoving periods. This finding is in contrast to the patterns observed in human^{27} and Tcell^{34} mobility where the moving and nonmoving states are both characterised by a scaling law. Since detailed statistical characterisation on freerange animal movement based on highfrequency GPS trajectories is still largely missing, this finding can provide new perspectives to our understanding for grazing animals movement and useful leads to the underlying ecological basis of grazing behaviour.
A simple deterministic scenario that can give rise to the observed scaling law in waiting time distribution is that the environment is structured according to the same heterogenous statistics. We can consider that different location in the landscape is of different quality or resource abundance, which can be described a quality function . If the cattle simply spend their time for feeding on one location proportional to the quality at that location, i.e. a ‘greedy’ strategy, would be the observed waiting distribution.
Stochastic processes and spontaneous behaviour can also account for the observed spatiotemporal pattern. Recently, a plausible decisionbased queueing process in which the animal executes activities from a stochastic priority list has been used to interpret the scaling law observed in the waiting time of marine predators^{19}. This model was originally proposed to explain the powerlaw distributed interevent time observed in the communication pattern in human dynamics^{23}. Specifically, the model assumes that the animal performs the two activities waiting and moving with probability x_{1} and x_{2} = 1 − x_{1} at a regular basis, where x_{1} and x_{2} are the priority of the activity drawn from a random distribution p(x). If the animal moves, it changes its context and therefore its likelihood to move or stay also changes. As a result, the priority will be redrawn from the random distribution, representing the change of state due to the movement. This model can generate the powerlaw distribution in waiting time as well as the exponential distribution in stepsize. By introducing a deterministic component to the decision probability, the model can be also tuned to generate different scaling exponent γ accounting for the various scaling phenomena in different species. The model is recast in a dynamic preypredator environment where the moving probability x_{1} can be interpreted as the likelihood of finding a prey in the vicinity.
We can also consider the movement as a twostate point process, in which the probabilities that the animal switches its state are q_{A} (from moving to nonmoving) and q_{B} (from nonmoving to moving)^{35,36}. It is well known that the state duration is exponential distributed when the switching probability is constant and independent of time^{36}. Recently, it has been suggested that the powerlaw distributed duration can be attributed to the reinforcement dynamics, such that the switching probability is proportional to the time that animal has spend in its current state, i.e. the longer the animal stays in its current state the less likely it will change it ref. 35,37 and 38.
Another explanation is to associate the movement pattern with the energy state of the animal using a maximum entropy approach. In this context, each moving and nonmoving activity is associated with a certain amount of energy loss E_{l} or energy gain E_{g}. According to the maximum entropy principle, the distribution of E_{l} and E_{g} over all activity segments should follow a Boltzmann distribution (See Material and methods). The validation of the maximum entropy approach is mainly subject to two conditions: (1) each individual activity is independent and has no influence on others; and (2) the energy intake and expenditure is maintained by two different mechanisms and can be treated as two isolated systems. The first condition is ed by our test on the correlation between consecutive activities, while the second is intuitively understandable. Following this formulation, it is straightforward to derive that when E_{g} ∝ log τ_{w} and E_{l} ∝ τ_{m} the observed scaling law in waiting time as well as the exponential distribution in trip time can be reproduced. That is to say, the energy intake increases logarithmically as grazing time increases, while the energy expenditure due to moving increases linearly with the moving time or distance. It is interesting to note that the logarithmic energy intake function has been suggested for grazing animals before^{39} and the linear energy expenditure or cost function has been widely observed in many singlemode movements of human transportation activities^{40,41}. It is well known that energy status can affect animal movement, but a quantitative understanding of their relation is still unclear. Our proposed maximum entropy approach can potentially fill this gap by establishing a connection between the energy function and the observed mobility pattern, suggesting that the detailed energy intake or expenditure as a function of time in different activities can be inferred from statistical features of the macroscopic mobility patterns such as waiting time or steplength distributions. The conjectured relation can be tested in future experiments by measuring detailed energy intake or consumption using laboratory techniques.
So far our study has been focused on using a simple twostate movement model to reveal the statistical characterization of the spatiotemporal pattern of grazing cattle in a short observation window and a small confined area. In future, it is interesting to extend this approach to build more realistic mobility model to capture more complex dynamics in movement, such as longterm memory effect and returning behavior that can be extracted from data with a larger observation window in time and space^{11,42}. For example, one can build a twolevel mobility model to capture the hierarchy nature of the mobility pattern, with one level describing the bimodal ‘stopandmove’ continuously random walk within a specific grazing area and another level describing transitions and recurrent movements between the grazing areas. Our results also opens new avenues for studying the relation between the observed bimodal mobility pattern and other dynamical processes such as epidemic spreading and diffusion^{17,43,44}.
Material and Methods
Dataset description
The dataset consists of continuous 0.5Hz GPS samples for 34 individuals covering an observation period of over 50 hours. We select the data of 31 individuals in which there is no discontinuity in GPS samples and we choose a continuous 30hour observation window during which the animals were grazing in a confined 600 m × 400 m rectangular area. The trajectory for each individual cow can be denoted by a sequence L = {p_{i}}, where p_{i} = (x_{i}, y_{i}, t_{i}) represents a GPS sample with (x_{i}, y_{i}) being the position coordinates and t_{i} being the timestamp. We use moving average filtering to reduce the noise and smooth the trajectory with a 10 sec moving window, such that p_{i} = 〈p_{i−2}, p_{i−1}, p_{i}, p_{i+1}, p_{i+2}〉.
Classification of mobility pattern
We define the nonmoving segment of a trajectory as a set of consecutive points L_{w} = {p_{k}, p_{k+1}, …, p_{k+m−1}}, which satisfies the following three conditions: (1) the distance d_{k,j} from the starting point p_{k} to any other point p_{j} of the segment must be smaller than a certain threshold Δd, i.e. max_{k<j<k+m}d_{k,j} ≤ Δr; (2) the distance from the starting point p_{k} to the point following the ending point of the segment p_{k+m} must be larger than Δr, i.e. d_{k,k+m} > Δr; (3) the time span of the segment must be longer than a certain threshold Δt, i.e. t_{k+m} − t_{k} > Δt. In this definition, the first two constraints are made to identify consecutive points that are likely to represent an identical position within in a certain proximity. The third constraint imposes a minimum time span of the nonmoving segment that can be tuned to exclude some veryshort random activities such as a pause when encountering an obstacle, as well as making the extracted nonmoving segments more representative of meaningful activities such as grazing or resting. After extracting the nonmoving segments, we simply define the points between two nonmoving segments as the moving segments. The approach here is in analogy to the definition of staying points for continuous GPS samples in most spatiotemporal analysis of human mobility^{27,45}. The value of Δt is suggested to be 2–3 mins^{32}.
Maximum entropy principle
The maximum entropy principle originates from statistical mechanics, which assumes that the configuration of microscopic states of a complex system (e.g. the energy of each particle) leading to the macroscopic observation is the one that maximise the entropy of the system. Suppose the system consists of N noninteracting particles and has a total energy U, such that and where n_{i} denotes the number of particles at a specific energy state E_{i}. Then the ensemble that represents all possible configurations of the system is called the canonical ensemble and the probability p(E) that a particle has a specific energy state E is denoted by . Here we assume that the alternate moving and nonmoving activities in the mobility pattern operate in two independent systems, while the individual activities are regarded as ‘particles’ and the associated energy state of the activity is the incurred energy gain (or loss) due to the activity. To obtain the distribution of the time span τ in each activity, we use the transformation where E(τ) is the energy function that describes the energy gain as a function of the time span during the activity. The detailed form of the distribution function p(τ) is then subject to the energy function E(τ). For example, a logarithmic function E(τ) ∝ log τ will lead to a powerlaw distribution p(τ) ∝ τ^{β}, while a linear function will simply maintain a exponential form p(τ) ∝ e^{−kτ}.
Additional Information
How to cite this article: Zhao, K. and Jurdak, R. Understanding the spatiotemporal pattern of grazing cattle movement. Sci. Rep. 6, 31967; doi: 10.1038/srep31967 (2016).
References
Nathan, R. et al. A movement ecology paradigm for unifying organismal movement research. Proc Natl Acad Sci USA 105, 19052–19059 (2008).
Kays, R., Crofoot, M. C., Jetz, W. & Wikelski, M. Terrestrial animal tracking as an eye on life and planet. Science 348, aaa2478 (2015).
Viswanathan, G. M. et al. Optimizing the success of random searches. Nature 401, 911–914 (1999).
Zhao, K. et al. Optimal Lévyflight foraging in a finite landscape. J. R. Soc. Interface. 12, 20141158 (2015).
Wearmouth, V. J. et al. Scaling laws of ambush predator ‘waiting’ behaviour are tuned to a common ecology. Proc. R. Soc. B: Biological Sciences 281, 20132997 (2014).
Bronikowski, A. M. & Altmann, J. Foraging in a variable environment: weather patterns and the behavioral ecology of baboons. Behavioral Ecology and Sociobiology 39, 11–25 (1996).
Humphries, N. E. et al. Environmental context explains Lévy and Brownian movement patterns of marine predators. Nature 465, 1066–1069 (2010).
De Jager, M., Weissing, F. J., Herman, P. M., Nolet, B. A. & Van de Koppel, J. Lévy walks evolve through interaction between movement and environmental complexity. Science 332, 1551–1553 (2011).
Pelletier, F. & FestaBianchet, M. Effects of body mass, age, dominance and parasite load on foraging time of bighorn rams, Ovis canadensis. Behavioral Ecology and Sociobiology Behavioral Ecology and Sociobiology 56, 546–551 (2004).
StrandburgPeshkin, A., Farine, D. R., Couzin, I. D. & Crofoot, M. C. Shared decisionmaking drives collective movement in wild baboons. Science 348, 1358–1361 (2015).
Song, C., Koren, T., Wang, P. & Barabási, A. L. Modelling the scaling properties of human mobility. Nature Physics 6(10), 818–823 (2010).
Zhao, Y. M., Zeng, A., Yan, X. Y., Wang, W. X. & Lai, Y. C. Unified underpinning of human mobility in the real world and cyberspace. New Journal of Physics 18(5), 053025 (2016).
Bartumeus, F., Da Luz, M. G., Viswanathan, G. M. & Catalan, J. Animal search strategies: a quantitative randomwalk analysis. Ecology 86, 3078–87 (2005).
Codling, E. A., Plank, M. J. & Benhamou, S. Random walk models in biology. Journal of the Royal Society Interface 5, 813–834 (2008).
Reynolds, A. M. & Rhodes, C. J. The Lévy flight paradigm: random search patterns and mechanisms. Ecology 90, 877–887 (2009).
Bullock, J. M., Kenward, R. E. & Hails, R. S. Dispersal ecology: 42nd symposium of the British ecological society (No. 42). Cambridge University Press (2002).
Brockmann, D., Hufnagel, L. & Geisel, T. The scaling laws of human travel. Nature 439, 462–465 (2006).
Reynolds, A. M. et al. Displaced honey bees perform optimal scalefree search flights. Ecology 88, 1955–1961 (2007).
Sims, D. W. et al. Scaling laws of marine predator search behaviour. Nature 451, 1098–1102 (2008).
Viswanathan, G. M. et al. Lévy flight search patterns of wandering albatrosses. Nature 381, 413–415 (1996).
Humphries, N. E., Weimerskirch, H., Queiroz, N., Southall, E. J. & Sims, D. W. Foraging success of biological Lévy flights recorded in situ. Proc Natl Acad Sci USA 109, 7169–7174 (2012).
RamosFernández, G. et al. Lévy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi). Behavioral Ecology and Sociobiology 55, 223–230 (2004).
González, M. C., Hidalgo, C. A. & Barabási, A. L. Understanding individual human mobility patterns. Nature 453, 779–782 (2008).
Edwards, A. M. et al. Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. Nature 449, 1044–1048 (2007).
Benhamou, S. How many animals really do the Lévy walk? Ecology 88, 1962–1969 (2007).
Clauset, A., Shalizi, C. R. & Newman, M. E. J. Powerlaw distributions in empirical data. SIAM review 51, 661–703 (2009).
Rhee, I. et al. On the lévywalk nature of human mobility. IEEE/ACM transactions on networking (TON) 19, 630–643 (2011).
Amy, J. & Robertson, A. I. Relationships between livestock management and the ecological condition of riparian habitats along an Australian floodplain river. Journal of applied ecology 38, 63–75 (2001).
Daszak, P., Cunningham, A. A. & Hyatt, A. D. Emerging infectious diseases of wildlife–threats to biodiversity and human health. Science 287, 443–449 (2000).
Sommer, P. et al. Information Bang for the Energy Buck: Towards Energyand MobilityAware Tracking. In Proceedings of The International Conference on Embedded Wireless Systems and Networks (EWSN), 193204 (2016).
Jurdak, R., Corke, P., Dharman, D. & Salagnac, G. Adaptive GPS duty cycling and radio ranging for energyefficient localization. In Proceedings of the 8th ACM Conference on Embedded Networked Sensor Systems, 57–70 (2010).
Godsk, T. & Kjærgaard, M. B. High classification rates for continuous cow activity recognition using lowcost GPS positioning sensors and standard machine learning techniques. In Advances in Data Mining. Applications and Theoretical Aspects, 174188 (2011).
Petrovskii, S., Mashanova, A. & Jansen, V. A. Variation in individual walking behavior creates the impression of a Lévy flight. Proc Natl Acad Sci USA 108, 8704–8707 (2011).
Harris, T. H. et al. Generalized Lévy walks and the role of chemokines in migration of effector CD8+ T cells. Nature 486, 545–548 (2012).
Karsai, M., Kaski, K., Barabási, A. L. & Kertész, J. Universal features of correlated bursty behaviour. Scientific reports 2, 397 (2012).
Ginelli, F. et al. Intermittent collective dynamics emerge from conflicting imperatives in sheep herds. Proc Natl Acad Sci USA 112, 12729–12734 (2015).
Zhao, K., Stehlé, J., Bianconi, G. & Barrat, A. Social network dynamics of facetoface interactions. Physical review E 83, 056109 (2011).
Zhao, K. & Bianconi, G. Social interactions model and adaptability of human behavior. Frontiers in Physiology 2, 101 (2011).
Garrett, W. N., Meyer, J. H. & Lofgreen, G. P. The comparative energy requirements of sheep and cattle for maintenance and gain. Journal of Animal Science 18(2), 528–547 (1959).
Yan, X. Y., Han, X. P., Wang, B. H. & Zhou, T. Diversity of individual mobility patterns and emergence of aggregated scaling laws. Scientific reports 3, 2678 (2013).
Kölbl, R. & Helbing, D. Energy laws in human travel behaviour. New Journal of Physics 1, 48 (2003).
Hu, Y., Zhang, J., Huan, D. & Di, Z. Toward a general understanding of the scaling laws in human and animal mobility. Europhysics Letters 96(3), 38006 (2011).
Sun, G. Q. Pattern formation of an epidemic model with diffusion. Nonlinear Dynamics 69(3), 1097–1104 (2012).
Sun, G. Q., Wang, S. L., Ren, Q., Jin, Z. & Wu, Y. P. Effects of time delay and space on herbivore dynamics: linking inducible defenses of plants to herbivore outbreak. Scientific Reports 5 (2015).
Jiang, S. et al. A review of urban computing for mobile phone traces: current methods, challenges and opportunities. In Proceedings of the 2nd ACM SIGKDD international workshop on Urban Computing (2013).
Acknowledgements
K.Z. was funded by a CSIRO Office of the Chief Executive Postdoctoral Fellowship Award. R.J. was supported by the CSIRO Sensors and Sensor Networks Transformational Capability Platform.
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K.Z. and R.J. conceived and designed the experiment. K.Z. conducted the experiment and analysed the results. K.Z. and R.J. wrote the manuscript.
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Zhao, K., Jurdak, R. Understanding the spatiotemporal pattern of grazing cattle movement. Sci Rep 6, 31967 (2016). https://doi.org/10.1038/srep31967
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DOI: https://doi.org/10.1038/srep31967
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