Hierarchical decomposition of the species-energy relationship by scale

Background/Question/Methods

Understanding the determinants of global patterns of species richness provide insight into the complex process of community organization and may be critical for maintaining community diversity, stability, and ecosystem functioning.  One possible driver of richness patterns is energy.  Many energy-associated variables (such as evapotranspiration, net primary production, temperature, and precipitation) have been widely recognized to correlate with richness patterns.  Most studies analyze the species-energy relationship at one discrete spatial scale or vary spatial scale by averaging over quadrats or circles with increasing area. This form of nested data manipulation is less sensitive to thresholds and patterns appearing over a narrow scale range, and important species-energy associations that manifest may be missed. Current understanding of scale-dependent patterns is limited owing to a lack of methods that incorporate scale explicitly and in a consistent manner. We present a newly developed method based on wavelet lifting to analyze the effect of scale on irregularly sampled data in two dimensions. We explore the scale dependence of the relationship between breeding avian richness from 1990 - 2005 and four energy-associated variables (evapotranspiration, net primary production, temperature and precipitation). Wavelet lifting was used to create scale specific decompositions of the dependent and each independent variable.  Wavelet coefficient regression was used to determine how the richness-energy relationship changes with scale and identify at what scale (or scales) these four energy forms contribute to the observed pattern of avian richness.

Results/Conclusions

The rate, at which species richness changes, varies as a function of each energy variable and spatial scale.  Different energy-associated variables emerge as significant predictors at different spatial scales.  Net primary production explains the most variation (40%) in species richness at an intermediate spatial scale, ranging from 292.1 - 371.1 km.  Energy predictors explain the most variation in species richness at an intermediate to large spatial scales, and energy predictors at smallest and largest scales explain very little of the species richness pattern. The species-energy relationship changes with scale thus inhibiting the ability to make cross-scale predictions. Flexible scale sensitive methods can be used to gain a better understanding of scale dependent ecological patterns and processes.