Scale-specific inference using wavelets

Understanding of spatial pattern and scale has been identified as a key issue in ecology, yet ecology has traditionally lacked necessary tools for making inference about relationships between scale-specific patterns. We introduce wavelet-coefficient regression, in which the dependent and independent variables are wavelet transformed prior to analysis, as a means to formalize scale-specific relationships in ecological data. We apply this method to data on vegetation and environmental factors related to water availability from Sequoia-Kings Canyon National Park (California, USA). We find that the wavelet transform and wavelet-coefficient regression efficiently characterize scale-specific pattern in these data. We also find that different environmental factors show up as good predictors of vegetation growth at different scales and that these differences in scale greatly facilitate interpretation of the mechanisms relating water availability to vegetation growth.