Quantifying the scale dependence of primary productivity-species-richness relationships.

Vegetation productivity is expected to correlate with species richness, but there is debate about whether the relationship form (non-existent, negative, positive, unimodal) of productivity-species-richness relationships (PSRR) depends on the spatial extent and productivity measure used. Previous assessments employed coarse distance categories to examine scale dependence and did not consider scale dependence for alternative productivity measures. I used spatially varying coefficient models to precisely estimate the distances over which PSRRs change and to map spatial patterns of form for breeding birds across the conterminous United States. I created separate models for three measures summarizing intra-annual estimates of gross primary productivity: sum, minimum, and seasonality (coefficient of variation). Models demonstrated that PSRRs were scale-dependent, and PSRR relationships changed at median distances ranging from 1,010 to 2,184 km depending on the productivity measure. Previously used coarse distance categories would not have resolved the modeled distance estimates. Differences in median distance estimates across productivity measures were not statistically important. Across measures, PSRR form generally alternated between non-existence and positive, but there were pockets where seasonality negatively related to species richness in the western United States. While spatial patterns of form differed across measures, species richness in a small region of the western United States displayed a positive association with all three measures. Spatial patterns were related to prevailing productivity conditions. For example, sum tended to have a positive association with bird species richness in areas characterized by low annual productivity. This study novelly applies spatially varying coefficient models to address the long-debated scale-dependence of PSRR form, and the same approach is broadly applicable across geographies and taxonomic groups.