Understanding the spatiotemporal pattern of grazing cattle movement

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 high-frequency movement dataset for a group of grazing cattle and investigate their spatiotemporal patterns using a simple two-state 'stop-and-move' 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 scale-invariant below a certain cut-off and is best described by a truncated power-law distribution, suggesting that the non-moving state is governed by time-varying 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 decision-making 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.

Figure 1. A schematic diagram of the spatiotemporal pattern under the two-state ‘stop-and-move’ representation.

(a) The temporal spectrum of activities illustrated in a spike train. Colour segments on the time-axis represent alternating waiting (white) and moving (red) activities over time. (b) The raw trajectory of an individual cow before processing. The two-dimensional x-y plane here represents the grazing area (in meters). (c) The spatial pattern extracted from the raw trajectory in panel (b) can be projected as a transition graph, where the waiting locations for non-moving segments are represented by red dots and the trips are represented by blue solid lines.

Figure 2. The statistics for the moving state with Δr = 5 m.

Panels (a–c) are the cumulative distributions P(l) for trip length with Δt = 1, 2 and 5 mins (from left to right). Panels (d–f) are the cumulative distributions P(τ_m) for trip time with Δt = 1, 2 and 5 mins (from left to right). The solid red lines represent the best fitted mixture exponential obtained by the maximum-likelihood method using an expectation-maximisation algorithm.

Figure 3. The visualisation of clusters extracted by the DBSCAN algorithms and the corresponding inter-cluster trips.

Dots with different colours represent different clusters (the lightest colour represent outliers). Blue solid lines indicate inter-cluster trips.

Figure 4. The trip length distribution for intra-cluster movements and inter-cluster movements.

Both of them are well described by a single exponential distribution p(l) ~ exp(−l/l₀) (red solid lines). The black solid line in panel (a) indicates the mixture exponential fitting using Eq. 1. The mixture exponential is still the best candidate model for the intra-cluster trip length distribution according to the AIC weight. However the difference between the two components in the mixture model is comparably small, suggesting that a single exponential could be a reasonable alternative.

Figure 5. The statistics for the non-moving state with Δr = 5 m.

Panels (a–c) are the cumulative distributions P(τ_w) for waiting time with Δt = 1, 2 and 5 mins (from left to right). The solid red lines represent the best fitted truncated power-law obtained by the maximum-likelihood method.