Ecological application of wavelet analysis in the scaling of spatial distribution patterns of Ceratoides ewersmanniana

Ecological experiments are usually conducted on small scales, but the ecological and environmental issues are usually on large scales. Hence, there is a clear need of scaling. Namely, when we deal with patterns and processes on larger scales, a special connection needs to be established on the small scales that we are familiar with. Here we presented a wavelet analysis method that could build relationships between spatial distribution patterns on different scales. With this method, we also studied how spatial heterogeneity and distribution patterns changed with the scale. We investigated the distribution and the habitat of C. ewersmanniana in two plots (200 m × 200 m; the distance between these two plots is 15 km) at Mosuowan desert. The results demonstrated that spatial heterogeneity and distribution patterns were incorporated into larger scales when the wavelet scale varied from one (5 m) to four (20 m). However, if the wavelet scale was above five (25 m), the spatial distribution patterns varied placidly, the oscillation frequency of landforms stabilized at 110 m, and the dynamic quantity period of C. ewersmanniana stabilized at 115–125 m. We also identified signal mutation points with wavelet analysis and verified the heterogeneity degree of local space with position variance. We found that position variance decomposed the distribution patterns on large scales into small sampling plots, and the position with the largest variance also had the strongest heterogeneity. In a word, the wavelet analysis method could scale-up spatial distribution patterns and habitat heterogeneity. With this method and other methods derived from this one, such as wavelet scale, wavelet variance, position variance and extremely direct-viewing graphs, wavelet analysis could be widely applied in solving the scaling problem in ecological and environmental studies.