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Table 1 Summary of studies that develop or apply versions of the integrated Ornstein-Uhlenbeck process for modeling biological movement. Numbers 3 [34] and 5 [9] are extensions to spherical coordinates and for three-dimensional helical movement, respectively. The remaining models all correspond to one of more of the CVM family of models presented here

From: Correlated velocity models as a fundamental unit of animal movement: synthesis and applications

  Authors Nomenclature Parameterization Application Comments
1 Dunn and Brown 1987 [32]   α - white noise spectrum General cell motility  
    β - relaxation term   
2 Alt 1990 [15]   T - persistence time Unicellular organisms and individual cells  
    ω - mean angular speed   
    μ - mean advective speed   
    \(\sigma _{V}^{2}\) - variance of velocity   
3 Brillinger and Stewart 1998 [34] - β - dynamical friction Elephant seal (Mirounga angustirostris) Spherical coordinates
    σ - Brownian motion variance term   
    δ- speed of attraction to center   
4 Johson et al. 2008 [12] Continuous Time γ - drift term Northern fur seal (Callorhinus ursinus) R package crawl [18] with state-
  McClintock et al. 2014 [3] Correlated Random Walk β - autocorrelation parameter Harbor seal (Phoca vitulina) space observation error
   (CTCRW) σ - white noise variance term   
5 Gurarie et al. 2011 [14] Correlated Velocity τ a ,τ o - characteristic time scales Dinoflaggelate (Heterosigma akashiwo) [15] adapted to 3D helical movement:
   Helical Movement σ a ,σ o - white noise term variance   * - a and o refer to advective and
   (CVHM) μ - 3-D mean velocity   oscillatory components, respectively)
    ω - mean angular speed   
6 Gurarie and Ovaskainen 2011 [9] Correlated Velocity τ - characteristic time scale Encounter rate theory  
  Gurarie and Ovaskainen 2013 [16] Movement (CVM) σ - characteristic spatial scale   
    ν - mean tangential speed   
7 Zattara et al. 2016 [33] CVM τ and ν as above Regenerating cells in Pristina leidyi  
8 Calabrese et al. 2016 [17] Integrated Ornstein- τ v - time scale of velocity autocorrelation Presented as limiting case of OUF model [13] R package ctmm [19]
   Uhlenbeck (IOU)