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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.