• R: code to assess spatial independence of residuals of a model

This code is useful to check if the assumption of (spatial) independence between residuals of a model is met.

Useful because it can be applied to the residuals of any model we run

It generates a plot of bubbles located according to the X-Y coordinates of the corresponding residuals. The size of the bubbles represents the magnitude of the residuals, while the color indicates if they are positive or negative. If there is spatial independence of the residuals, no pattern should be observed in the disposition of the bubbles. NOTE: requires “sp” package

library(sp)                                                     #Load the sp package
Residuals<-resid(model)                          #Generates a vector with the residuals from the model
mydata <- data.frame(Residuals, RawData$XCooords, RawData$YCoords)    # Generate a data frame with the residuals and corresponding coordinates (obtained from the dataset in which the model was ran)
colnames(mydata)<-c(“Residuals”,”X”, “Y”)                   #Assign names to the columns
coordinates(mydata) <- c(“X”,”Y”)                                    #Identify which columns correspond to the coordinates

bubble (data, “Residuals“, col = c(“black”,”grey”), xlab = “X-coordinates”, ylab = “Y-coordinates”)   #Plot the bubbles

• ArcGIS: Iterator option in Model Builder

This option allows to run the same function over all the files contained inside a folder, freeing the user from doing repetitive tasks.

Radiotelemetry is a common tool for studying animal movement, consisting of attaching a radio tag to an individual and tracking it either remotely with a GPS system or at shorts distances using hand-held antennas.
Until recently, hummingbird movement patterns hadn’t been able to be studied due to lack of transmitters small enough to be carried by such a light animal. The development of miniaturized radio-telemetry devices changed this. Using them, Hadley & Betts were able to conduct a translocation experiment in 2008, while I, in 2012, gathered information on natural (within the home range) movement patterns. This information consisted in time-stamped location points, which seemed perfect for the application of spatio-temporal statistics. In particular, I wanted to see if certain characteristics of the observed movement paths (speed, turning angle) could be used to assess behavioral changes associated to characteristics of the terrain (presence of forest).
As my previous posts show, I was unsuccessful in doing this, as none of the tools or analyses I tried showed evidence of pattern, neither in space or time. It is possible that due to the very high flight speed of these birds (average= 30 mi [48 km]/ hour), we weren’t able to keep up with them while tracking them, leading to un-realistic speed estimates (1.2km/hour).
Even when my data doesn’t have enough precision to answer point-level questions the information on general movement rates of the individuals can still give an insight on how behavior can be affected by the context in which the animals are moving. The advantage of the lack of temporal and spatial correlation between the data points is that I will be able to use traditional statistics to run these analyses.
I also explored a new tool for analyzing telemetry data points: the Dynamic Brownian Bridge Model (dBBMM). This model predicts the areas probably used by the individuals based on their overall movement paths, taking into account not only the location of points but also the sequence in which they took place, incorporating temporal autocorrelation in their calculations. The dBBMM also estimates a parameter (“Brownian motion variance”) that can be used to evaluate the existence heterogeneous behavior along the tracks. High values of Brownian motion variance would indicate more complex paths (and consequent more active behavior), while low values would indicate less variation in the way the individual is moving. I tried to apply this model to my data, but wasn’t able to find a way of estimating the Brownian motion variance. What I was able to do though was generating rasters showing the probability distribution of individuals in space, that’s to say, the areas where it as likely for the birds to be present.

Figure 1. Map showing the probability of observing a particular individual in space, based on data points obtained through radio-telemetry. This particular bird seems to have two centers of activity, joined by a transit area

The code to run this model (in R) can be found at http://www.computational-ecology.com/main-move.html.