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

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]

γ - drift term

Northern fur seal (Callorhinus ursinus)

R package crawl [18] with state-

McClintock et al. 2014 [3]

β - autocorrelation parameter

Harbor seal (Phoca vitulina)

space observation error

σ - white noise variance term

5

Gurarie et al. 2011 [14]

τ _a ,τ _o - characteristic time scales ^∗

Dinoflaggelate (Heterosigma akashiwo)

[15] adapted to 3D helical movement:

σ _a ,σ _o - white noise term variance ^∗

* - a and o refer to advective and

μ - 3-D mean velocity

oscillatory components, respectively)

ω - mean angular speed

6

Gurarie and Ovaskainen 2011 [9]

τ - characteristic time scale

Encounter rate theory

Gurarie and Ovaskainen 2013 [16]

σ - characteristic spatial scale

ν - mean tangential speed

7

Zattara et al. 2016 [33]

τ and ν as above

Regenerating cells in Pristina leidyi

8

Calabrese et al. 2016 [17]

τ _v - time scale of velocity autocorrelation

Presented as limiting case of OUF model [13]

R package ctmm [19]