Temporal autocorrelation functions for movement rates from global positioning system radiotelemetry data

Abstract

Autocorrelation has been viewed as a problem in telemetry studies because sequential observations are not independent in time or space, therefore violating assumptions for statistical inference. Yet nearly all ecological and behavioural data are autocorrelated in both space and time. We argue that there is much to learn about the structure of ecological and behavioural data from patterns of autocorrelation. Such patterns include periodicity in movement and patchiness in spatial data, which can be characterized by an autocorrelogram, semivariogram or spectrum. We illustrate the utility of temporal autocorrelation functions (ACFs) for analysing step-length data from GPS telemetry of wolves (Canis lupus), cougars (Puma concolor), grizzly bears (Ursus arctos) and elk (Cervus elaphus) in western Alberta. ACFs often differ by season, reflecting differences in foraging behaviour. In wilderness landscapes, step-length ACFs for predators decay slowly to apparently random patterns, but sometimes display strong daily rhythms in areas of human disturbance. In contrast, step lengths of elk are consistently periodic, reflecting crepuscular activity.

Figure 1.

Autocorrelation function of step length for a female grizzly bear (G027) with 4-h interval between GPS telemetry fixes. Observations were from a heavily roaded area in the vicinity of the Cheviot Mine near Hinton, Alberta during late summer and autumn, 15 July to denning.

Figure 2.

(a) ACF of step length for a female grizzly bear with cubs (G077) from den emergence until 15 July 2008 and 2009 with essentially all positive correlations. The bear occupied agricultural lands in southwest Alberta on the east front of the Rocky Mountains. The daily rhythm is driven by regular nocturnal movements averaging 800 m h⁻¹ at 23.00 h and 24.00 h. Autocorrelations are essentially zero at other lags indicating no periodicity in movements beyond the midnight movements for this bear. (b) Step-length ACF for the same bear (G077) during autumn, 15 July to denning, showing a distinctive crepuscular pattern with two peaks in activity per day, with longest steps occurring at 07.00 h and 19.00 h.

Figure 3.

Wolf step-length ACF across three packs in southwest Alberta in an area of high livestock conflict. Although there is a weak peak in the ACF of step length with a 24 h rhythm, the correlation is not strong.

Figure 4.

(a) Cougar step-length ACFs from an area near Nordegg, Alberta. (b,c) The same data decomposed into (b) searching steps and (c) prey handling steps near kill sites.

Figure 5.

(a) Elk ACF over all seasons during 2007–2008 in the Pincher Creek area of southwest Alberta. (b) Step-length ACF by season for 52 elk in southwestern Alberta (filled diamonds, filled squares, filled triangles and crosses symbolize spring, summer, autumn and winter, respectively).

Figure 6.

Average absolute value of autocorrelation in elk step lengths as a function of road density near Pincher Creek, Alberta.