In a previous study, we showed that n independent locational observations contain more spatial information than n autocorrelated observations. We also developed a statistical test of the null hypothesis that successive observations are independent. Here, we expand our discussion of testing for independence by clarifying assumptions associated with the tests. Specifically, the tests are robust when used with data collected from utilization distributions that are not normal, but they are sensitive to nonstationary distributions induced by shifts in centers of activity or variance-covariance structure. We also used simulations to examine how negative bias in kernel and polygon estimators of home-range size is influenced by level of autocorrelation, sampling rate, sampling design, and study duration. Relative bias increased with increasing levels of autocorrelation and reduced sample sizes. Kernel (95%) estimates were less biased than minimum convex polygon estimates. The effect of autocorrelation is greatest when low levels of bias ( -5%) are desired. For percent relative bias in the range of -20% to -5%, though, collection of moderately autocorrelated data bears little cost in terms of additional loss of spatial information relative to an equal number of independent observations. Tests of independence, when used with stationary data, provide a useful measure of the rate of home-range use and a means of checking assumptions associated with analyses of habitat use. However, our results indicate that exclusive use of independent observations is unnecessary when estimating home-range size with kernel or polygon methods.

Key Words
Autocorrelation; Bias; Home range; Migration; Randomization; Stationary distribution; Statistical independence.

Robert K. Swihart is Associate Professor of Wildlife Ecology, Department of Forestry and Natural Resources, Purdue University, W. Lafayette, IN 47907-1159. Norman A. Slade is Professor and Curator of Mammals, Department of Systematics and Ecology, and Museum of Natural History, University of Kansas, Lawrence, KS 66045-2454.