# A moving–resting process with an embedded Brownian motion for animal movements

> Animals do not move all the time, yet many models of GPS data assume they do. Jun Yan, Kersey Lawrence (published as Kirstin Lawrence-Apfel) and colleagues built a “moving–resting” model that lets animals stop, and tested it on a Wyoming mountain lion. She spent about ten times longer resting than moving, often staying for days near her kills.

Summary by Kersey Lawrence, Original Wisdom. Updated 9 November 2026. Page: https://www.originalwisdom.com/tracking-literature/2014-yan-chen-moving-resting-process-animal-movements/

## Citation and access

- **Authors:** Jun Yan, Yung-wei Chen, Kirstin Lawrence-Apfel (now Dr. Kersey Lawrence), Isaac M. Ortega, Vladimir Pozdnyakov, Scott Williams, Thomas Meyer
- **Year published:** 2014
- **Journal or source:** Population Ecology 56(2): 401–415
- **Full citation:** Yan, J., Chen, Y., Lawrence-Apfel, K., Ortega, I.M., Pozdnyakov, V., Williams, S., and Meyer, T. 2014. A moving–resting process with an embedded Brownian motion for animal movements. Population Ecology 56: 401–415.
- **DOI:** https://doi.org/10.1007/s10144-013-0428-8
- **Access status:** Hosted with permission
- **PDF:** https://www.originalwisdom.com/wp-content/uploads/2026/11/2014_Yan_and_Chen_etal_a-moving-resting-process-with-an-embedded-brownian-motion-for-animal-movements.pdf

## Tags

- **Species:** Mammals > Mountain lion
- **Region:** North America > United States
- **Tracking:** Feeding signs; Kill sites; Tracking; Tracks and signs identification
- **Behaviour and ecology:** Behaviour; Feeding; Home range; Movement; Resting
- **Methods and technology:** Brownian bridge movement model (BBMM); Composite likelihood; Global Positioning System (GPS) collars; Moving–resting process; Simulation; Utilization distribution
- **Data type:** Existing data; Modelling or theoretical
- **Observer qualification:** Not reported
- **Discipline:** Behaviour and ecology; Wildlife tracking
- **Year published:** 2014

## Detailed keywords

- **Species:** Studied: one mature female mountain lion (Puma concolor), with GPS data supplied by Dr. Mark Elbroch. Mentioned only: elk (Cervus elaphus), as an example of an animal that keeps its head still while moving; wood frog (Lithobates sylvaticus), as an example of an animal whose home range may be too small for the method; sharks; and fish fitted with radio transmitters.
- **Location and habitat:** Gros Ventre Mountain Range near Jackson, Wyoming, United States.
- **Topics:** Author note: Kirstin Lawrence-Apfel is a previous name of Dr. Kersey Lawrence, founder of Original Wisdom. Animal movement modelling between GPS fixes; resting and inactivity periods; time spent moving versus resting; home range and utilization distribution; occupation time (probability of being at a place during a time interval); kill or consumption sites seen as "plateaus" in GPS data; sallying movements around a kill; GPS sampling interval and the trade-off between fix frequency and battery life; GPS position error (citing Lawrence-Apfel et al. 2012); accelerometers for detecting resting; measurement error; terrain boundaries.
- **Statistics or models:** A moving–resting process: an alternating renewal (telegraph, or on–off) process with exponentially distributed moving and resting periods, and Brownian motion during moving. Closed-form distributions for one increment and two consecutive increments; a moving–resting bridge model given start and end points; occupation time density with 50%, 80% and 90% highest-density contours. Maximum likelihood (when moving or resting state is known) and maximum composite likelihood estimation (when it is not). Validation with 10,000 simulated replicates and bivariate kernel smoothing; a simulation study of 500 datasets of 1,000 observations each. Comparison with a Brownian motion model and the Brownian bridge movement model (BBMM). Implemented in the R package smam.
- **Data type:** Modelling or theoretical, illustrated with existing GPS collar data: 3,917 fixes from one female mountain lion, 2009 to 2012. The collar was set for one fix every 8 hours, but intervals ranged from 0.5 to 120 hours.

## Synopsis

### 1. What they did

GPS collars record where an animal is only at set times, so researchers have to estimate where it went in between. A common method, the Brownian bridge movement model (BBMM), treats the animal as always on the move between fixes. But animals spend much of their time still: sleeping, resting, ruminating, watching, or feeding at a kill. Some mammals are inactive for as much as 75% of the time.

The authors, statisticians and wildlife researchers at the University of Connecticut, built a new mathematical model, the moving–resting process. In it, an animal switches at random between moving (wandering in a random, Brownian pattern) and resting (not moving at all). They worked out its mathematical properties, checked their formulas with computer simulations, and showed how to estimate the model from real GPS data.

They then applied it to GPS data from a mature female mountain lion in the Gros Ventre Mountains near Jackson, Wyoming, collared from 2009 to 2012 (3,917 positions).

### 2. What they found

- The moving–resting model predicts that an animal's likely locations between two fixes are more tightly bunched than the always-moving model predicts, with a real chance that the animal simply stayed at the start or end point.

- In simulations, the estimation method recovered the true values of how long animals moved and rested and how fast they moved.

- The mountain lion's track showed many “plateaus” where she stayed close to one place for several days. Field personnel investigated some of these and found they were places where she had eaten prey. She typically stayed within 250 m of the site, making short sallies out and back in different directions.

- The model estimated that she spent about 10.7 times as much time resting as moving, and that when she moved, she moved about twice as fast as the always-moving model suggested.

- For an 8-hour interval, the two models gave similar outer (95%) ranges, but the moving–resting model gave a 0.48 probability that she stayed at one of the two end points.

### 3. What they concluded

- Allowing animals to stay still gives a more realistic picture of behaviour, and tighter, more realistic home range estimates, than models that assume constant movement.

- The model needs only three values: how mobile the animal is when moving, and how often it switches between moving and resting.

- If collars could tell when an animal is resting, estimation would be simple, but closely spaced GPS fixes are too noisy, and accelerometer data can be confusing: elk keep their heads still while moving, grazers lift their heads to scan, and cats wake briefly to groom.

- Choosing how often to take GPS fixes is a trade-off between detail and battery life; realistic movement models are the best way to estimate where an animal was between fixes.

- The method suits any animal whose home range is much larger than GPS error (tens of metres), and works with other positioning methods too.

- Future work includes measurement error, changing behaviour over time, terrain boundaries and memory in movement.

### 4. How tracking was or was not used

The model is built from GPS data. Field personnel investigated some of the places where the mountain lion stayed still and found they were sites where she had eaten prey. The paper does not describe how these sites were identified.

### 5. Tracker or observer certification

Not reported. The paper does not say who investigated the consumption sites or how they were identified, although the interpretation of the plateaus as resting at kills rests on those visits.

### 6. Other technologies, skills or innovations

- GPS collar data.

- A new movement model with exact formulas, and a computer method for drawing possible paths between two known locations.

- The R package smam (Statistical Modeling of Animal Movements).

- A discussion of accelerometers and high-frequency GPS fixes for detecting resting.

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

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

- Many movement models used with GPS data, such as the Brownian bridge movement model, assume that animals are always moving and do not take resting into account. Yet animals stop for many reasons, including feeding at a kill, sleeping, ruminating, keeping watch and simply resting.

- Deciding that a GPS plateau is a place where the lion ate prey means reconstructing an event from what is found on the ground, which requires speculative tracking, even though the paper does not name it.

- In GPS data, a resting animal and a feeding animal can look the same. Tracks and signs at the site are what tell them apart.

## Cite this summary

Lawrence, K. 2026. Summary of: A moving–resting process with an embedded Brownian motion for animal movements (Yan and Chen et al., 2014). Original Wisdom, Tracking Literature. https://www.originalwisdom.com/tracking-literature/2014-yan-chen-moving-resting-process-animal-movements/