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. |