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Plants with amphitropical distributions have closely related populations in both Northern and Southern Hemispheres, but are absent from the intervening tropics. They provide a unique opportunity to study the constraints shaping the distribution of temperate lineages through time. Using grasses from the ecologically diverse supertribe Melicodae, an emerging study system with species distributed throughout the temperate regions, we test the hypothesis that geography and/or environmental niche constrain which lineages successfully cross the tropics to establish in the opposite hemisphere. Biogeographic and evolutionary modelling was conducted on well resolved plastid and nuclear phylogenies constructed from whole-genome sequencing of 178 accessions of 103 Melicodae species. Results show that species from cold regions are much less likely to successfully cross the tropics, with successful lineages all sharing warmer niches that evolved prior to their establishment in the opposite hemisphere. Evidence suggests that this result is explained both by the greater distances that high-latitude, cold-origin lineages must disperse to cross the tropics, and inherent limitations associated with colder thermal niches. In particular, our results suggest that traits allowing species to cope with cold winters, rather than an inability to cope with warm summers, limit their ability to establish in the opposite hemisphere, hinting at important trade-offs between cold-tolerance and biogeographic potential. These results provide insight into the drivers of the distribution and diversity of plants, and the challenges facing cold-origin lineages in a rapidly warming world. If cold-origin species occupy a smaller proportion of their potential range, and are unlikely to establish in new areas with suitable climates, their ability to track preferred habitat as climates warm may be worse than currently expected. 

Summary Grasses are exceptionally productive, yet their hydraulic adaptation is paradoxical. Among C₃grasses, a high photosynthetic rate (A_area) may depend on higher vein density (D_v) and hydraulic conductance (K_leaf). However, the higherD_vof C₄grasses suggests a hydraulic surplus, given their reduced need for highK_leafresulting from lower stomatal conductance (g_s).Combining hydraulic and photosynthetic physiological data for diverse common garden C₃and C₄species with data for 332 species from the published literature, and mechanistic modeling, we validated a framework for linkages of photosynthesis with hydraulic transport, anatomy, and adaptation to aridity.C₃and C₄grasses had similarK_leafin our common garden, but C₄grasses had higherK_leafthan C₃species in our meta‐analysis. Variation inK_leafdepended on outside‐xylem pathways. C₄grasses have highK_leaf : g_s, which modeling shows is essential to achieve their photosynthetic advantage.Across C₃grasses, higherA_areawas associated with higherK_leaf, and adaptation to aridity, whereas for C₄species, adaptation to aridity was associated with higherK_leaf : g_s. These associations are consistent with adaptation for stress avoidance.Hydraulic traits are a critical element of evolutionary and ecological success in C₃and C₄grasses and are crucial avenues for crop design and ecological forecasting. 

Abstract Allometric relationships among the dimensions of leaves and their cells hold across diverse eudicotyledons, but have remained untested in the leaves of grasses. We hypothesised that geometric (proportional) allometries of cell sizes across tissues and of leaf dimensions would arise due to the coordination of cell development and that of cell functions such as water, nutrient and energy transport, and that cell sizes across tissues would be associated with light‐saturated photosynthetic rate. We tested predictions across 27 globally distributed C₃and C₄grass species grown in a common garden. We found positive relationships among average cell sizes within and across tissues, and of cell sizes with leaf dimensions. Grass leaf anatomical allometries were similar to those of eudicots, with exceptions consistent with the fewer cell layers and narrower form of grass leaves, and the specialised roles of epidermis and bundle sheath in storage and leaf movement. Across species, mean cell sizes in each tissue were associated with light‐saturated photosynthetic rate per leaf mass, supporting the functional coordination of cell sizes. These findings highlight the generality of evolutionary allometries within the grass lineage and their interlinkage with coordinated development and function.