Estimation of the spatial autocorrelation function: consequences of sampling dynamic populations in space and time

The estimation of spatial autocorrelation in spatially- and temporally-referenced data is fundamental to understanding an organism's population biology. I used four sets of census field data, and developed an idealized space-time dynamic system, to Study the behavior of spatial autocorrelation estimates when a practical method of sampling is employed. Estimates were made using both a classical geostatistical approach and a recently developed non-parametric approach. In field data, the estimate of the local spatial autocorrelation (i.e. autocorrelation as the distance between pairs of sampling points approaches 0), was greatly affected by sample size, while the range of spatial dependence (i.e. the distance at which the autocorrelation becomes negligible) was fairly stable. Similar patterns were seen in the theoretical system, as well as greater variability in local spatial autocorrelation during the invasion stage of colonization. When sampling for the purposes of quantifying spatial patterns, improved estimates of spatial autocorrelation may be obtained by increasing the number of pairs of points that are close in space at the expense of attempting to cover the entire region of interest with equidistant sampling points. Also, results from the theoretical space-time system suggested that greater resolution in sampling may be required in newly establishing populations relative to those already established.