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

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.