Given a ctmm movement model and telemetry data, speed simulates multiple realizations of the individual's trajectory to estimate the time-averaged speed, which is proportional to distance traveled, while speeds estimates instantaneous speeds at a specified array of times t. Both tortuosity (non straight-line motion between the data) and telemetry error can be accounted for. Given only a ctmm movement model and no data, speed calculates the mean speed of the Gaussian movement process. All methods are described in Noonan & Fleming et al (2019).

speed(object,...)

# S3 method for ctmm
speed(object,data=NULL,t=NULL,level=0.95,robust=FALSE,units=TRUE,prior=TRUE,fast=TRUE,
cor.min=0.5,dt.max=NULL,error=0.01,cores=1,...)

# S3 method for telemetry
speed(object,CTMM,t=NULL,level=0.95,robust=FALSE,units=TRUE,prior=TRUE,fast=TRUE,
cor.min=0.5,dt.max=NULL,error=0.01,cores=1,...)

speeds(object,...)

# S3 method for ctmm
speeds(object,data=NULL,t=NULL,cycle=Inf,level=0.95,robust=FALSE,prior=FALSE,fast=TRUE,
error=0.01,cores=1,...)

# S3 method for telemetry
speeds(object,CTMM,t=NULL,cycle=Inf,level=0.95,robust=FALSE,prior=FALSE,fast=TRUE,
error=0.01,cores=1,...)

## Arguments

object A ctmm movement-model or telemetry object, which requires an additional CTMM argument. Optional telemetry object on which the simulations will be conditioned. Movement model object. Array of times to estimate instantaneous speeds at, or range of times to estimate mean speed over. Average over time t indices modulo cycle. E.g., for t sequenced by hours, cycle=24 gives daily the cycle of speeds. (Not yet supported.) Confidence level to report on the estimated average speed. Use robust statistics for the ensemble average and its confidence intervals (see Details). Convert result to natural units. Account for model parameter uncertainty. Whether or not to invoke the central-limit theorem when propagating parameter uncertainty (see emulate). Velocity correlation threshold for skipping gaps. Absolute gap sizes to skip (in seconds), alternative to cor.min. Target (relative) standard error. Number of simulations to run in parallel. cores=0 will use all cores, while cores<0 will reserve abs(cores). Arguments passed to emulate.

## Details

The cor.min or dt.max arguments are used to constrain the estimate to be derived from simulations near the data, and therefore ensure that the estimate is more reflective of the data than the model.

If data quality is poor and velocity can barely be resolved, then the sampling distribution may occassionally include impersistent motion and its mean will be infinite. In these cases robust=TRUE can be used to report the sampling distribution's median rather than its mean. The time average of speed, in either case, is still the mean average of times and the resulting quantity is still proportional to distance traveled. Furthermore, note that medians should be compared to medians and means to means, so the robust option should be the same for all compared individuals.

## Value

Returns the estimated mean speed of the sampled trajectory with CIs by default. If level=NULL, then the ensemble of mean speeds is returned instead.

## References

M. J. Noonan, C. H. Fleming, T. S. Akre, J. Drescher-Lehman, E. Gurarie, A.-L. Harrison, R. Kays, Justin Calabrese, Scale-insensitive estimation of speed and distance traveled from animal tracking data'', Movement Ecology, 7:35 (2019).

C. H. Fleming.

## Note

The average speeds estimated here are mean speeds. The speeds reported by summary.ctmm are root-mean-square (RMS) speeds. These quantities are sometimes proportional, but not equivalent.

emulate, simulate

## Examples

# \donttest{
library(ctmm)
data(buffalo)
Gabs <- buffalo\$Gabs

GUESS <- ctmm.guess(Gabs,interactive=FALSE)
FIT <- ctmm.fit(Gabs,GUESS)

# stationary Gaussian estimate
speed(FIT)
#>                             low      est     high
#> speed (kilometers/day) 11.82123 12.16713 12.51548
# conditional estimate
speed(FIT,Gabs)
#>
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|======================================================================| 100%#>                             low      est     high
#> speed (kilometers/day) 11.03669 11.46068 11.88858# }