Accuracy of fractal dimension estimates for small samples of ecological distributions

We carry out a simulation study of the estimation of fractal dimension in a grid-based setting typical of ecological species distributions, using null landscape models. We calculate the box-counting dimension for samples taken in various types of sampling geometry. Sampler geometries include simple blocks,Cantor grids and line transects. This method may be used to measure fractal dimension of a species distribution, but the accuracy depends on a number of criteria. The most important is sampling effort: any estimate will be inaccurate if the sampling effort is low. We also find the geometry of the sampler to be important. For a given sampling effort, schemes based on the Cantor grids performed better than either line transects or simple blocks. Sampling effort can be improved either by using a bigger sampler over a larger area or by repeated sampling of a smaller area: optimum performance is often a trade-off between these two mechanisms. However, performance is also highly sensitive to the type of fractal object being sampled, with certain types of object requiring a much greater effort for an accurate estimate of fractal dimension. These results raise the possibilities of using novel sampling techniques to estimate fractal dimension, when confronted with limited resources and time, but underline also the need for an understanding of the “type” of fractality expected in ecological situations. This revised version was published online in July 2006 with corrections to the Cover Date.