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.

The goal of this exercise was to investigate spatial autocorrelation in the movement parameters of a foraging humpback whale. I used location points of sightings of the whale at the water surface between consecutive dives to infer the path of the whale (Friedlaender et al., 2009). To facilitate the analysis, I assumed linear travel of the whale below the surface between consecutive surfacings. I projected the location points and used the adehabitatLT package in R CRAN (Calenge, 2011) to plot the location points of the whale as well as the linear travel segments between these points (see graph below).

The blue triangle indicates the first, the red square the last observation of the whale at the surface.

Using projected data, the adehabitatLT package calculates the distance traveled by the whale between consecutive observations, the turning angle between consecutive linear segments of the whale’s path as well as the duration between the observations. Using the distance and duration data I calculated the swimming speed of the whale.

Then I calculated the spatial autocorrelation in swimming speed and turning angles using Moran’s I for the entire path, and also for a small section of the path which I assumed to be a foraging area of the whale (cluster of points southeast of the blue triangle). In this small area, the whale spent a comparatively large amount of its time and swam shorter distances between consecutive surfacings, possibly indicating foraging activity.

A small p-value in one of the parameters would provide convincing evidence for the hypothesis that the movement of the whale is autocorrelated in the respective parameter, i.e. that neighboring locations have more similar values than locations that are further apart.

The results from the current analysis (see table below) provide moderate evidence for spatial autocorrelation in swimming speed for the analysis of the entire path, indicating that the whale swam slower in certain parts of its path and faster in other parts (Calenge 2011). However there was no evidence to suggest that travel speed in the small foraging area was autocorrelated. This could be explained by the fact that in the foraging area, the whale swam at a constant, slow speed to the probability of prey detection or encounter (Benhamou, 1992). When leaving this foraging area, the whale is likely to increase its speed, resulting in separate areas of the whale’s path with lower and higher swimming speeds, which would explain the autocorrelation in swimming speed observed for the entire path.

Benhamou, S. (1992). Efficiency of area-concentrated searching behaviour in a continuous patchy environment. Journal of Theoretical Biology – J THEOR BIOL, 159(1), 67–81. http://doi.org/10.1016/S0022-5193(05)80768-4

Calenge, C. (2011). Analysis of Animal Movements in R: the adehabitatLT Package. Saint Benoist, Auffargis, France: Office Nationale de La Chasse. Retrieved from http://cran.gis-lab.info/web/packages/adehabitatLT/vignettes/adehabitatLT.pdf

Friedlaender, A. S., Hazen, E. L., Nowacek, D. P., Halpin, P. N., Ware, C., Weinrich, M. T., Hurst, T., Wiley, D. (2009). Diel changes in humpback whale Megaptera novaeangliae feeding behavior in response to sand lance Ammodytes spp. behavior and distribution. Marine Ecology Progress Series, 395, 91–100. http://doi.org/10.3354/meps08003

My research objective is to investigate two spatial aspects of humpback whale (Megaptera novaeangliae) surface feeding in and around the Stellwagen Bank National Marine Sanctuary in the southern Gulf of Maine, USA. Specifically, I aim to:

• Quantify the spatial scale of this behavior.
• Investigate whether this behavior is more frequently observed in certain areas of the study region.

Most studies investigating the spatial scale of humpback whale movement have focused on large spatial and temporal scales, using 1-2 location points per day over the course of several days or weeks during which the animals traveled hundreds or thousands of kilometers (Dalla Rosa et al. 2008; Heide-Jorgensen and Laidre 2007; Kennedy et al. 2013). In contrast, the proposed study aims at investigating the detailed movement of these whales on the temporal and spatial scales of daily bouts of foraging events. Analyzing such fine-scale foraging movement patterns can contribute to our knowledge of how marine predators search for patchily distributed resources (Levin 1992; Pinaud and Weimerskirch 2005).

The existing data for this analysis stems from a long-term study investigating humpback whale behavior and ecology in the southern Gulf of Maine, USA, (for more details, see Friedlaender et al. 2009). Almost every summer since 2004, whales were equipped with non-invasive tags that recorded detailed information on the underwater movement of the whales or collected video-footage of the behavior of the tagged animal and associated whales. During daylight deployments that usually lasted for up to 8 hours, focal follows were conducted from a small boat following the tagged whale, during which detailed information on the behavior of the tagged whale at the water surface was collected. Because the tags did not contain a GPS, range and bearing information on the whale were also collected at least once when the whale was observed at the surface in between consecutive dives, usually resulting in the collection of one location point every 3-5 min. Continuous GPS locations of the boat were automatically collected. Based on the time stamps of the range/bearing data and the boat GPS data, the GPS location collected at or close to the time the range and bearing data was collected, were identified and together this data was used to calculate the location of the whale.

The analysis proposed here will use the whale behavioral observation data to identify focal follows during which surface feeding was observed. The location data of these focal follows will be used for the following analysis. For each focal follow of a surface feeding whale, I will use the R package adehabitat (Calenge 2011) to implement first-passage time analysis to calculate the spatial scale of surface feeding, and to identify areas of intense foraging effort. The following description of the method is based on Fauchald & Tveraa (2003). First-passage time is a metric used to quantify search effort along an animal movement path. Around each location point, a circle of a given radius is created, and the amount of time the animal spent within the area of the circle is measured. The measurement is then repeated for each location point of the animal’s path with successively increasing circle radii. Increasing the radii will increase the amount of time the animal spent within the circle, but the increase in time will be greater in areas of intense search effort compared to areas through which the animal was simply traveling. The radius at which the variance in first-passage time between the different location points is greatest represents the spatial scale of foraging effort. I intend to statistically test for differences in the spatial scales of surface feeding between individuals and as a function of group size. At the radius representing the spatial scale of foraging, those circles with the longest first-passage times identify areas where foraging effort is concentrated (Bailey & Thompson 2006). Comparing the locations of intense foraging effort between individuals, areas within the study region can be identified that represent suitable foraging habitat (Bailey & Thompson 2006). The expected outcome of this part of the analysis is a map of the study region displaying locations of suitable foraging habitat based on first-passage time calculation.

I expect to find that different individuals have a similar spatial scale of surface feeding, as I anticipate that the spatial scale of foraging is correlated with spatial metrics of prey schools (Benoit-Bird et al. 2013). Because the spatial scale of search effort is likely to be larger than the spatial scale of the prey patches themselves, I expect the spatial scale of foraging for all individuals to be larger than the average prey school length in the area, which is ca. 139 m (Hazen et al. 2009). I expect to find a positive correlation between the spatial scale of surface feeding and group size because I anticipate that larger groups will cover a wider area during their search. I expect to see a concentration of surface feeding locations in the western part of the sanctuary region as this has been found to be an important feeding area in a previous study using a subset of the data I am planning on analyzing here (Hazen et al. 2009). This is due to the substrate type, topography and oceanographic conditions in this area which serve to attract and aggregate prey (Hazen et al. 2009).

I currently have basic knowledge of ArcMap and R and no experience with Python or Modelbuilder.

Literature cited:

Bailey, H. & P. Thompson. 2006. “Quantitative Analysis of Bottlenose Dolphin Movement Patterns and Their Relationship with Foraging: Movement Patterns and Foraging.” Journal of Animal Ecology 75 (2): 456–65. doi:10.1111/j.1365-2656.2006.01066.x.

Benoit-Bird, K.J., B.C. Battaile, C.A. Nordstrom, and A.W. Trites. 2013. “Foraging Behavior of Northern Fur Seals Closely Matches the Hierarchical Patch Scales of Prey.” Marine Ecology Progress Series 479 (April): 283–302. doi:10.3354/meps10209.

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.

Dalla Rosa, L., E. R. Secchi, Y. G. Maia, A. N. Zerbini, and M. P. Heide-Jørgensen. 2008. “Movements of Satellite-Monitored Humpback Whales on Their Feeding Ground along the Antarctic Peninsula.” Polar Biology 31 (7): 771–81. doi:10.1007/s00300-008-0415-2.

Fauchald, P. & T. Tveraa. 2003. “Using First-Passage Time in the Analysis of Area-Restricted Search and Habitat Selection.” Ecology 84 (2): 282–88.

Friedlaender, A.S., E.L. Hazen, D.P. Nowacek, P.N. Halpin, C. Ware, M.T. Weinrich, T. Hurst, and D. Wiley. 2009. “Diel Changes in Humpback Whale Megaptera Novaeangliae Feeding Behavior in Response to Sand Lance Ammodytes Spp. Behavior and Distribution.” Marine Ecology Progress Series 395 (December): 91–100. doi:10.3354/meps08003.

Hazen, E.L., A.S. Friedlaender, M.A. Thompson, C.R. Ware, M.T. Weinrich, P.N. Halpin, and D.N. Wiley. 2009. “Fine-Scale Prey Aggregations and Foraging Ecology of Humpback Whales Megaptera Novaeangliae.” Marine Ecology Progress Series 395 (December): 75–89. doi:10.3354/meps08108.

Heide-Jorgensen, M. P., and K. L. Laidre. 2007. “Autumn Space-Use Patterns of Humpback Whales (Megaptera Novaeangliae) in West Greenland.” Journal of Cetacean Research and Management 9 (2): 121.

Kennedy, A.S., A.N. Zerbini, O.V. Vásquez, N. Gandilhon, P.J. Clapham, and O. Adam. 2013. “Local and Migratory Movements of Humpback Whales (Megaptera Novaeangliae) Satellite-Tracked in the North Atlantic Ocean.” Canadian Journal of Zoology 92 (1): 9–18. doi:10.1139/cjz-2013-0161.

Levin, S.A. 1992. “The Problem of Pattern and Scale in Ecology: The Robert H. MacArthur Award Lecture.” Ecology 73 (6): 1943. doi:10.2307/1941447.

Pinaud, D.D. & H. Weimerskirch. 2005. “Scale-Dependent Habitat Use in a Long-Ranging Central Place Predator.” Journal of Animal Ecology 74 (5): 852–63. doi:10.1111/j.1365-2656.2005.00984.x.