Elephants in space and time

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Abstract
Autocorrelation in animal movements can be both a serious nuisance to analysis and a source of valuable information about the scale and patterns of animal behavior, depending on the question and the techniques employed. In this paper we present an approach to analyzing the patterns of autocorrelation in animal movements that provides a detailed picture of seasonal variability in the scale and patterns of movement. We used a combination of moving window Mantel correlograms, surface correlation and crosscorrelation analysis to investigate the scales and patterns of autocorrelation in the movements of three herds of elephants in northern Botswana. Patterns of autocorrelation of elephant movements were long‐range, temporally complicated, seasonally variable, and closely linked with the onset of rainfall events. Specifically, for the three elephant herds monitored there was often significant autocorrelation among locations up to lags of 30 days or more. During many seasonal periods there was no indication of decreasing autocorrelation with increasing time between locations. Over the course of the year, herds showed highly variable and complex patterns of autocorrelation, ranging from random use of temporary home ranges, periodic use of focal areas, and directional migration. Even though the patterns of autocorrelation were variable in time and quite complex, there were highly significant correlations among the autocorrelation patterns of the different herds, indicating that they exhibited similar patterns of movement through the year. These major patterns of autocorrelation seem to be related to patterns of rainfall. The strength of correlation in movement patterns of the different herds decreased markedly at the cessation of major rain events. Also, there was a strong crosscorrelation between strength of autocorrelation of movement and rainfall, peaking at time lags of between three and four weeks. Overall, these approaches provide a powerful way to explore the scales and patterns of autocorrelation of animal movements, and to explicitly link those patterns to temporally variable environmental attributes, such as rainfall or vegetation phenology.