In my last blog post, I analyzed spatial autocorrelation in the whale movement parameters swimming speed and turning angles between consecutive segments of the whale’s trajectory for a single whale. In this update, I am expanding on this analysis by analyzing over a range of distances the spatial autocorrelation in swimming speed and turning angles in the trajectories of three foraging whales in the Stellwagen Bank National Marine Sanctuary. Positive autocorrelation in either parameter would mean that, when comparing two trajectory segments, the values for this parameter are similar between the two segments, and negative autocorrelation would mean that they are not similar. A correlogram shows the values of the autocorrelation coefficient for a range of distances between the trajectory segments. Here, I am presenting results from the analysis of the whale trajectories using the R CRAN adehabitatLT package (Calenge 2011).
The correlogram below shows the Moran’s I autocorrelation coefficient for the swimming speeds of three whales. Two whales show significant autocorrelation in swimming speed over short distances (<1000 m) (p<0.05, indicated by red circles). This means that during segments of the whale’s trajectories that are within 1000 m of each other, the whales maintained similar speeds. This is not surprising because generally it does not seem likely that the whales would abruptly change their swimming speed over such short distances.
After converting the turning angles to radians, the analysis of autocorrelation in turning angles (Moran’s I) revealed that the turning angles of only one trajectory were significantly positively autocorrelated at distances of 1000 and 2000 m (p<0.05, indicated by red circles).
Next, I used the R CRAN package adehabitatLT (Calenge 2011) to calculate first-passage time (Fauchald & Tveraa 2003) as metric for the search effort along each whale’s trajectory, and used linear regression to relate first-passage time to the environmental variables water depth and seafloor slope. The image below shows the three trajectories (in turquoise: 195b, purple: 188b_f, red: 188a) on a slope chart of the Stellwagen Bank National Marine Sanctuary area (USGS/NOAA).
Basend on the description by Fauchald & Tveraa (2003), for each trajectory, first-passage time quantifys the spatial scale of the animal’s foraging effort. The values of first-passage time at this spatial scale distinguish areas with high foraging effort (long first-passage time) from areas with low foraging effort (short first-passage time). The color-coded figure below shows first-passage time for whale 188b_f relative to seafloor slope (red: long first-passage time, green: short first-passage time).
Simple linear regression revealed that depth explained 17.2% of the variance in first-passage time for the trajectory of whale 188a (p=0.001). Separately, depth and slope explained 14.2 and 29.2 %, respectively, of the variance in first-passage time for the trajectory of whale 188b_f (each p<0.0005) (see figures below). For the trajectory of whale 195b, neither depth nor slope were significant predictors of first-passage time (each p>0.2).
Some authors (see Calenge 2011 for details) have suggested the analysis of autocorrelation of movement parameters of an animal’s trajectory following the standardization of the segment lengths. I will investigate this method in a follow-up analysis. Furthermore, I will re-analyze autocorrelation in turning angles using the absolute values of the turning angles instead of radians to facilitate the interpretation of the results.
Literature cited:
Calenge, C. 2011. “Analysis of Animal Movements in R: The adehabitatLT Package.” Saint Benoist, Auffargis, France: Office Nationale de La Chasse. http://cran.gis-lab.info/web/packages/adehabitatLT/vignettes/adehabitatLT.pdf.
Fauchald, P. & T. Tveraa. 2003. “Using First-Passage Time in the Analysis of Area-Restricted Search and Habitat Selection.” Ecology 84 (2): 282–88.
