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Table 1 Glossary

From: When to be discrete: the importance of time formulation in understanding animal movement

Term

Definition

Synonyms

Behavioral state

A discrete (and typically latent) behavior associated with a specific type of movement.

Behavior; behavioral mode

Brownian motion

A simple random walk in continuous time, i.e., a diffusion model with no centralizing tendency.

Wiener process

Central tendency

A tendency to move back towards a central location (e.g., the center of a home range or patch) as a result of directed movement.

Mean-reverting

Correlated movement

Short-term directional persistence resulting from a tendency to continue moving in a similar direction (or velocity) as previous moves.

 

Directed movement

Systematic, non-random movement in a particular direction. Directed movement associated with a particular location or gradient, such as a “center of attraction,” can result in long-term directional persistence and/or central tendency.

Biased or oriented movement (discrete time); drift or advection (continuous time)

Directional persistence

A tendency for successive movements to be in a similar direction.

 

Hidden Markov model

A special class of state-space models with a finite number of hidden (e.g., behavioral) states.

 

Markov process

A stochastic process where state transitions are dependent only on the current state (first-order Markov process) or current and immediately previous states (higher-order Markov process).

 

Multistate model

A mixture of random walk models corresponding to different movement behavior states.

Mixture model, switching model

Ornstein-Uhlenbeck (OU) process

A diffusion model with centralizing tendency that accounts for dependence between observations. With no central tendency, Brownian motion is obtained as a limiting case.

 

Random walk

Given an initial starting position, a mathematical model for generating a stochastic movement trajectory in space. Random walks are often Markov processes and can be formulated in discrete or continuous time. They have no directional persistence or bias.

 

State-space model

A conditionally specified hierarchical model consisting of a latent system process model and an observation model.