# Inferring spatially varying animal movement characteristics using a hierarchical continuous-time velocity model

> Where do wildebeest hurry, and where do they linger? Using six years of GPS data from 31 Serengeti wildebeest, researchers built a model that maps how fast and how straight animals move across a landscape. It revealed the migration’s main routes and showed wildebeest moving fastest and most directly near drainage lines, where lions lie in wait, and near villages.

Summary by Kersey Lawrence, Original Wisdom. Updated 5 November 2026. Page: https://www.originalwisdom.com/tracking-literature/2022-paun-husmeier-inferring-spatially-varying-animal/

## Citation and access

- **Authors:** Ionut Paun, Dirk Husmeier, J. Grant C. Hopcraft, Majaliwa M. Masolele, Colin J. Torney
- **Year published:** 2022 (published online 18 October 2022)
- **Journal or source:** Ecology Letters 25(12): 2726–2738
- **Full citation:** Paun, I., Husmeier, D., Hopcraft, J.G.C., Masolele, M.M., and Torney, C.J. 2022. Inferring spatially varying animal movement characteristics using a hierarchical continuous-time velocity model. Ecology Letters 25(12): 2726–2738.
- **DOI:** https://doi.org/10.1111/ele.14117
- **Access status:** Open access (CC BY 4.0)
- **PDF:** https://www.originalwisdom.com/wp-content/uploads/2026/11/2022_Paun_and_Husmeier_etal_inferring-spatially-varying-animal-movement-characteristics.pdf

## Tags

- **Species:** Mammals > Blue wildebeest
- **Region:** Africa > Tanzania
- **Behaviour and ecology:** Behaviour; Human disturbance; Migration; Movement; Predation risk
- **Methods and technology:** Bayesian statistics; Correlated random walk; Gaussian processes; Global Positioning System (GPS) collars; Machine learning; Normalised Difference Vegetation Index (NDVI); Ornstein-Uhlenbeck process; Variational inference
- **Data type:** Existing data; Modelling or theoretical
- **Discipline:** Behaviour and ecology
- **Year published:** 2022

## Detailed keywords

- **Species:** Studied: blue wildebeest (Connochaetes taurinus), the migratory Serengeti population. Mentioned but not studied: lions, as the ambush predators linked to drainage lines.
- **Location and habitat:** Serengeti National Park, Tanzania, including the north-west of the park near its boundary, south of the Tanzania-Kenya border. Nutrient-rich short grass plains in the south-east, long grass plains in the centre, woodland in the Western Corridor. Also seasonal drainage lines, which stay dry most of the year and have thick vegetation, river confluences and erosion terraces.
- **Topics:** movement ecology, migration routes, directional persistence and speed, spatial patterns of movement, forage quality, predation risk, human disturbance, early warning signs of environmental change, big telemetry data sets, directing future field data collection.
- **Statistics or models:** A two-layer hierarchical Bayesian model built on Gaussian processes (GPs). The top layer is a continuous-time correlated velocity model: a correlated random walk based on an integrated Ornstein-Uhlenbeck (OU) process. It uses a new non-stationary covariance kernel, so movement parameters can change across the landscape. The lower layer holds two latent spatial fields, one for directional persistence (the timescale parameter) and one for speed (the variance parameter), estimated on a grid of locations. Fitted by stochastic variational inference with the Adam optimiser in TensorFlow Probability, using sparse variational GP methods. Trajectories were split into segments of 500 points, about 3 months each (a “mixture of GP experts”). Kernels: a radial basis function kernel for the wildebeest data and a periodic kernel for the simulated data. Environmental covariates: Normalised Difference Vegetation Index (NDVI, a measure of vegetation greenness), grass nitrogen, and distance to drainage lines.
- **Data type:** A new statistical method, tested first on simulated data and then on existing GPS data. Simulated data: 200 simulated animals with 500 locations each (100,000 locations); speed tests used up to 1.6 million locations. Wildebeest data: 31 GPS-collared wildebeest gave 84,000 locations between June 2013 and June 2019; J.G.C. Hopcraft collected the data. The data are on Dryad and the code is on Zenodo.

## Synopsis

### 1. What they did

How animals move changes from place to place. They may travel fast and straight through one area, and wander slowly while feeding in another. Altered movement and migration patterns are often an early warning sign of environmental disturbance and later population declines. The authors built a statistical model that maps, directly from GPS locations, two features of movement across a landscape: directional persistence (how straight an animal keeps going) and speed.

Most methods start from a list of habitat features the researcher chooses. This model can find the patterns from the locations alone, and can also test chosen features if wanted. It combines locations from many animals, and it is fast enough to handle millions of locations.

They first tested it on simulated animals moving through a made-up landscape where the true answer was known. Then they applied it to six years of GPS data from 31 migratory wildebeest in Serengeti National Park, Tanzania.

To test what drives the patterns, they added three features: greenness of the vegetation (from NDVI), grass nitrogen as a measure of forage protein, and distance to drainage lines as a measure of predation risk. Drainage lines have thick vegetation that hides ambush predators such as lions.

### 2. What they found

- Simulated data: the model closely recovered where the different movement zones were and their true values. The borders between zones came out blurred, because an animal’s movement takes time to change after entering a new zone. It handled 1.6 million locations in under 3.5 hours.

- The wildebeest data took about 22 minutes to process on a graphics processor.

- Migration routes: high directional persistence formed a circuit around the southern Serengeti: south along the east of the park, then north through the Western Corridor.

- Central long grass plains: wildebeest moved fast but not straight there. The authors expect this reflects quick travel between the nutrient-rich short grass plains in the south-east and the Western Corridor woodlands.

- North-west of the park: near the boundary, south of the Tanzania-Kenya border, wildebeest moved fast and straight, passing through directly and rapidly. This is an area of high human density, close to villages and human activity. The authors cannot show cause and effect, but say the results strongly suggest that human presence affects how wildebeest move.

- Certainty: uncertainty was low across most of the map, and high only at the edges of the migration range, where there was little data.

- Greenness: wildebeest moved more slowly where vegetation was greener, in high-quality forage.

- Grass nitrogen: only a weaker effect on speed. It also had a small effect on direction: movement was less directed where grass quality was high. The authors suggest this may come from wildebeest following short-lived resources in the wet season.

- Drainage lines: these had the strongest effects on both speed and direction. Wildebeest moved faster and more directly near drainage lines, where predation risk is higher.

### 3. What they concluded

- The model links two standard tools of statistical ecology, spatial random fields and correlated random walk movement models, in one framework.

- It can show which places are tied to which behaviours (migration routes, feeding areas, areas of high perceived risk) without first deciding which habitat features to include.

- Because it finds areas of unusual movement first, it can point researchers to where to collect environmental data next. This includes studying human disturbance where it is hard to measure, or where its effects reach beyond the immediate area.

- To use it well, GPS fix rates should be set so that each trajectory segment is much longer than the time over which an animal keeps its direction.

- A suggested next step is to compare wildebeest responses to natural predators with their responses to risk from people.

### 6. Other technologies, skills or innovations

- GPS collars on 31 wildebeest over six years

- Satellite-derived vegetation greenness (NDVI), grass nitrogen and drainage line maps as environmental layers

- Machine-learning software (TensorFlow Probability) run on a graphics processor (NVIDIA Quadro GP100), so very large data sets can be processed in hours

- Freely available code (Zenodo) and data (Dryad)

### 7. Implications for conservation (from the paper)

- Infrastructure, growing human populations, fences and roads are disrupting animal movement, and many far-ranging and migratory species are declining.

- Maps of where animals move fast, slow, straight or wandering can identify migration corridors, stop-over sites and feeding grounds that are vital to a species.

- They can also flag areas where human disturbance may be changing behaviour, as in the north-west Serengeti, before that disturbance has been measured directly.

### 8. Implications for tracking (Original Wisdom's observations)

_These are Original Wisdom's observations, not the authors'._

The model flags where animals move differently, but it cannot say why. Tracks and signs on the ground at those places could help explain what is going on. For example, predator tracks and kill sites along drainage lines would show whether the risk is real. Trail patterns and feeding signs would show whether wildebeest are passing through or feeding. Signs of people and livestock would show what is happening near villages.

## Cite this summary

Lawrence, K. 2026. Summary of: Inferring spatially varying animal movement characteristics using a hierarchical continuous-time velocity model (Paun and Husmeier et al., 2022). Original Wisdom, Tracking Literature. https://www.originalwisdom.com/tracking-literature/2022-paun-husmeier-inferring-spatially-varying-animal/