# anipaths: spline-based interpolation

## Animating animal trajectories

The package anipaths contains a collection of telemetry observations for turkey vultures originally analyzed in:

Dodge S, Bohrer G, Bildstein K, Davidson SC, Weinzierl R, Mechard MJ, Barber D, Kays R, Brandes D, Han J (2014) Environmental drivers of variability in the movement ecology of turkey vultures (Cathartes aura) in North and South America. Philosophical Transactions of the Royal Society B 20130195.

To animate the locations, we first need to create a time stamp variable of class numeric or POSIX. One advantage to using the POSIX class is that we can specify the gaps in the interpolation (delta.t) using convenient character strings like "hour" or "week".

library(anipaths)
vultures$POSIX <- as.POSIXct(vultures$timestamp, tz = "UTC")
vultures_paths <- vultures[format(vultures$POSIX, "%Y") == 2009, ] ## limit attention to 2009 delta.t <- "day" animate_paths(paths = vultures_paths, delta.t = delta.t, coord = c("location.long", "location.lat"), Time.name = "POSIX", ID.name = "individual.local.identifier") ### Using background maps Often it may be useful to add a map of the relevant study area. There are lots of ways to incorporate a map. The simplest way is to set background to TRUE, in which case anipaths will do the best it can to select a map based on the data. In the next example, we’ve changed the time step to help the animations load a little faster. library(ggmap) delta.t <- "week" animate_paths(paths = vultures_paths, delta.t = delta.t, coord = c("location.long", "location.lat"), Time.name = "POSIX", ID.name = "individual.local.identifier", background = TRUE) You can also give a long/lat location, zoom level (3-21; see ?ggmap::get_map()), and maptype (satellite, terrain, hybrid) to be passed to ggmap::get_map(), and anipaths will make a background for you. As shown below, the value of delta.t can be specified as a numeric, which will be interpreted in whatever units used by as.numeric(paths['Time.name']) (in our case, this is seconds). vultures_paths <- vultures[format(vultures$POSIX, "%Y") == 2009:2010, ]
delta.t <- 3600*24*2 ## number of seconds in two days
background <- list(center = c(-90, 10),
zoom = 3,
maptype = "satellite")
animate_paths(paths = vultures_paths,
delta.t = delta.t,
coord = c("location.long", "location.lat"),
Time.name = "POSIX",
ID.name = "individual.local.identifier",
background = background)

You can also supply your own background image. The projection and units should match the data.

delta.t <- "week"
background <- rworldmap::getMap(resolution = "coarse")
sp::proj4string(background) ## matches default projection in animate_paths()
animate_paths(paths = vultures_paths,
delta.t = delta.t,
coord = c("location.long", "location.lat"),
Time.name = "POSIX",
ID.name = "individual.local.identifier",
background = background)

The function animate_paths() must project the data to match Google’s map tiles, so if your data aren’t in long/lat format, make sure you update the paths.proj variable with the correct string.

If you have a covariate of interest for each individual, animate_paths() can display that information as a colored ring around each individual. We don’t have any natural individual-level covariates available for the vultures, so we’ll make one up for the purposed of demonstration. The following code assigns each individual a random interval for each of three behaviors: exploratory, directed, and stationary.

behaviors <- c("exploratory", "directed", "stationary")
set.seed(1)
vultures_paths$behavior <- unlist(sapply(unique(vultures_paths$individual.local.identifier), function(id){
v_id <- vultures_paths[vultures_paths$individual.local.identifier == id, ] switches <- c(0, sort(sample(1:nrow(v_id), 2)), nrow(v_id)) rep(behaviors[sample(1:3, 3)], diff(switches)) })) The covariates have now been appended to the paths data frame. We can let animate_paths() know we would like it to display this information by setting the argument covariate to match the name of the appropriate column in paths (i.e., behavior). The default colors are a gray scale. Any collection of colors can be provided (e.g., covariate.colors = viridis::viridis(3)) which will be turned into a palette to match the support of the covariate. delta.t <- "day" background <- rworldmap::getMap(resolution = "coarse") sp::proj4string(background) animate_paths(paths = vultures_paths, delta.t = delta.t, coord = c("location.long", "location.lat"), Time.name = "POSIX", covariate = "behavior", covariate.colors = viridis::viridis(3), ID.name = "individual.local.identifier", background = background, s_args = c(k = 80)) Note: if a covariate is represented numerically but should be treated as a factor, changing the class using as.factor() should prevent animate_paths() from interpolating to “intermediate” values (e.g., if male and female are coded as 0 and 1, defining the column of the data frame as a factor will constrain individuals to only take on values of 0 and 1). ### Animating synchronous data This situation may arise, for example, when a user wishes to employ anipaths to produce visualizations of realizations generated from a discrete-time movement model. To demonstrate how to use animate_paths() to animate already synchronous paths, bypassing the spline-based interpolation, we can use animate_paths() to produce synchronized paths (setting return.paths = TRUE), and then pretend we had those synchronized paths from the beginning. In this case, we will also pretend we have covariates associated with those synchronized times. delta.t <- 3600*24*3 ## 3 days between synchronized observations background <- rworldmap::getMap(resolution = "coarse") sp::proj4string(background) behaviors <- c("exploratory", "directed", "stationary") set.seed(1) vultures_paths$behavior <-
unlist(sapply(unique(vultures_paths$individual.local.identifier), function(id){ v_id <- vultures_paths[vultures_paths$individual.local.identifier == id, ]
switches <- c(0, sort(sample(1:nrow(v_id), 2)), nrow(v_id))
rep(behaviors[sample(1:3, 3)], diff(switches))
}))
synchro_paths <- animate_paths(paths = vultures_paths, s_args = c(k = 70),
delta.t = delta.t, covariate = "behavior",
coord = c("location.long", "location.lat"),
Time.name = "POSIX", ID.name = "individual.local.identifier",
return.paths = T)

Now we input our synchronized paths (a list of matrices all with the same number of rows) into the paths argument, the synchronized times in the times argument, and the synchronized covariates in the covariate argument. Naming the first element of the covariate list passes the label through to the legend in the animation.

names(synchro_paths$covariate.interp) <- "behavior" animate_paths(paths = synchro_paths$paths.interp, times = synchro_paths$time.grid, covariate = synchro_paths$covariate.interp,
covariate.colors = 1:3, background = background)

### Output formats

The default format for displaying the animation is an index.html file. This is great for broad functionality, and the generated images may be used as the basis of a variety of other animation formats (e.g., the “animate” package in LaTeX). If you have ffmpeg installed on your system, you can also set method = "mp4" to create a stand-alone video that is easy to share with others. For more information, see https://www.ffmpeg.org/.

## Checking the interpolation

As a way to check that anipaths is producing reasonable interpolations of the telemetry observations, a generic plot() function is provided that takes an argument of class paths_animation produced by calling animate_paths() with return.paths = TRUE. See example(plot.paths_animation). Adjusting the parameters of the interpolation can be done by modifying the s_args argument. As a general rule, if the interpolated paths look “too smooth”, try increasing the number of knots using s_args = c(k = ...).

### Showing location uncertainty (beta)

Uncertainty about the depicted location of each individual is computed as part of the interpolation procedure. Error ellipses representing a Gaussian approximation to the uncertainty can be added by specifying a quantile level for the argument uncertainty.level. These ellipses should really only be interpreted qualitatively, but may be useful for communicating when there is significant uncertainty about the location of an individual (perhaps due to sparse observations in time).

vultures_paths <- vultures[format(vultures$POSIX, "%Y") == 2009 & vultures$location.lat > 32 &
vultures$location.lat > 32, ] animate_paths(paths = vultures_paths, delta.t = delta.t, coord = c("location.long", "location.lat"), Time.name = "POSIX", ID.name = "individual.local.identifier", background = background, dimmed = c(1, 3, 5)) ### Showing relational information (beta) It is also possible to visualize dynamic pair-wise relational information with anipaths. This information needs to be coded as an array of adjacency matrices (binary and weighted edges allowed, no support yet for directed information). If the network information is on a different time scale than the position information, it will be interpolated using smoothing splines to match. We don’t have existing relationships among the vultures to display, so we’ll make some up for the purposes of demonstration. vultures_paths <- vultures[format(vultures$POSIX, "%Y") == 2009, ]
set.seed(1)
n_indiv <- length(unique(vultures_paths$individual.local.identifier)) change_pts <- 5 network.times <- seq(min(vultures_paths$POSIX), max(vultures_paths\$POSIX), l = change_pts + 2)
network <- array(NA, dim = c(n_indiv, n_indiv, length(network.times)))
for(time_i in 2:length(network.times)){
network_mat <- matrix(sample(1:0, n_indiv^2, prob = c(0.1, 0.9), replace = T),
n_indiv, n_indiv)
network_mat[lower.tri(network_mat)] <- t(network_mat)[lower.tri(network_mat)]
diag(network_mat) <- 1
network[, , (time_i - 1):time_i] <- network_mat
}
delta.t <- 3600*24*2
animate_paths(paths = vultures_paths,
delta.t = delta.t,
coord = c("location.long", "location.lat"),
Time.name = "POSIX",
ID.name = "individual.local.identifier",
background = background, network = network, network.times = network.times)