Aim Across angiosperm families, the area occupied by a family is strongly correlated with its richness. We explore the causes of this area‐richness correlation using the cosmopolitan family, Cyperaceae Juss., as a model. We test the hypothesis that, despite a proposed tropical origin, temperate lineages in the family diversified at elevated rates. We test the hypothesis that the area‐richness correlation is maintained within intrafamilial clades, and that this relationship could be described as a function of niche space. We also test the hypothesis that the partitioning of geographical and ecological space, not the extent of this space, is the factor most closely associated with clade richness. Location Cosmopolitan. Methods We use molecular data from four genes sequenced in 384 taxa to develop a chronogram of Cyperaceae. We then develop a model of ancestral ranges and measure rates of diversification throughout the history of the family. Integrating data from over 4,800,000 digitized herbarium records, we characterize the range and niche of more than 4500 species and test for correlations of the species richness maintained within clades with range size, range partitioning, range overlap, niche, clade age and rate of diversification. Results Cyperaceae originated in South America in the late Cretaceous and subsequently dispersed throughout the globe. Of three increases in diversification rate, two occurred in the temperate Northern Hemisphere. The variable most closely associated with clade richness is the partitioning of geographical space by species within each clade. Main conclusions We show that species‐rich clades in Cyperaceae are not only more widespread, occupy more niche space, and diversify more quickly, but also exhibit patterns that are consistent with the partitioning of geographical and ecological space as a major correlate to diversification.

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The role of geography and ecology in speciation are often discussed in the context of phylogenetic niche conservatism (PNC), the propensity of lineages to retain ancestral niche related traits. However, a recent paradigm shift focuses instead on measuring divergence of these traits in conjunction with patterns of speciation. Under this framework, we analyzed the diversification of North America's third most diverse family, Cyperaceae ("sedges"), using a modified Parsimony Analysis of Endemicity approach to identify floristic regions and ordination statistics to quantify species distribution in a continuous manner. Utilizing over 200,000 georeferenced specimens, we characterized the geographical distribution and climatic and edaphic niche space occupied by each species. We constructed a supermatrix phylogeny of the North American sedge flora, aided in part by the sequencing of all sedges of Wisconsin, and employed a multifaceted approach to assess the role of geographical and ecological divergence on lineage diversification. In addition to measuring phylogenetic signal for these traits, we also measured pairwise phylogenetic distance of species within floristic regions, calculated rates of speciation, and tested for correlations of speciation rate to tempo of geographical and ecological evolution. Our analyses consistently show that evolutionarily related species tend to be geographically unrelated. Rates of geographical and ecological diversification are closely linked to tempo of speciation, and exploration of geographical place coincides with divergence in ecological niche space. We highlight the benefits of treating geography in a continuous manner, and stress the importance of employing a diverse suite of analytical approaches in testing hypotheses regarding the evolution of range and niche.

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