Disentangling the origin of species-genetic diversity correlations (SGDCs) is a challenging task that provides insight into the way that neutral and adaptive processes influence diversity at multiple levels. Genetic and species diversity are comprised by components that respond differently to the same ecological processes. Thus, it can be useful to partition species and genetic diversity into their different components to infer the mechanisms behind SGDCs. In this study, we applied such an approach using a high-elevation Andean wetland system, where previous evidence identified neutral processes as major determinants of the strong and positive covariation between plant species richness and AFLP genetic diversity of the common sedge Carex gayana. To tease apart putative neutral and non-neutral genetic variation of C. gayana, we identified loci putatively under selection from a dataset of 1,709 SNPs produced using restriction site-associated DNA sequencing (RAD-seq). Significant and positive relationships between local estimates of genetic and species diversities (alpha-SGDCs) were only found with the putatively neutral loci datasets and with species richness, confirming that neutral processes were primarily driving the correlations and that the involved processes differentially influenced local species diversity components (i.e., richness and evenness). In contrast, SGDCs based on genetic and community dissimilarities (beta-SGDCs) were only significant with the putative non-neutral datasets. This suggests that selective processes influencing C. gayana genetic diversity were involved in the detected correlations. Together, our results demonstrate that analyzing distinct components of genetic and species diversity simultaneously is useful to determine the mechanisms behind species-genetic diversity relationships.