Measures of preferred direction for environmental and ecological circular data

Circular or angular variables indicating direction or cyclical time can be of great interest to scientists studying ecology, biology or environmental issues. A common problem of interest in circular data is estimating a preferred direction and its corresponding distribution. This problem is complicated by the so-called “wrap-around effect” on the circle, which exists because there is no natural minimum or maximum. The usual statistics employed for linear data are inappropriate for directional data, as they do not account for its circular nature. Three choices for summarizing the preferred direction (the sample circular mean, sample circular median and a circular analog of the Hodges–Lehmann estimator) are discussed, with examples from environmental and ecological applications. Similar to the linear data case, the relative emphases of different methods sometimes yield different measures of preferred direction in the presence of outliers or lack of symmetry in the original data. Received: November 2003 / Revised: June 2004