1a. Lower, carpellate flowers sessile or, if pedicellate, pedicels evidently thickened: either at least half as thick as the main axis of the inflorescence or distinctly thicker than the pedicels of the staminate flowers ... 2

1b. Lower, carpellate flowers pedicellate, pedicels less than half the diameter of the main axis of the inflorescence (often much thinner), and not distinctly thicker than the pedicels of the staminate flowers ... 3

2a. Lower flowers ± long-pedicellate, pedicels of staminate flowers subequally as thick as those of the carpellate flowers; filaments longer than anthers; sepals of mature, carpellate flowers tightly appressed to or enclosing the fruiting head ... S. montevidensis

2b. Lower flowers sessile or very short-pedicellate, if present, those of the carpellate flowers thicker than those of the staminate flowers; filaments shorter than anthers; sepals of mature, carpellate flowers spreading to reflexed, or only appressed to base of fruiting head but not enclosing it ... S. rigida

3a. Filaments glabrous; emersed leaf blades with distinct basal lobes present, sagittate or hastate ... 4

3b. Filaments with scales or flattened hair; emersed leaf blades lacking distinct basal lobes, bases attenuate, rounded, truncate or only slightly cordate ... 6

4a. Tips of achene beaks pointing perpendicular to the long axis of the achene body, beaks arising laterally or obliquely, beaks usually greater than 0.4 mm long ... S. latifolia

4b. Tips of achene beaks pointing more or less parallel with the long axis of the achene body, beaks arising from or near to the apex, beaks 0.2–0.7 mm long ... 5

5a. Beak of achene minute, 0.2–0.3 mm long, apically attached but definitely set in from the margin ... S. cuneata

5b. Beak of achene 0.4–0.7 mm long, laterally or obliquely attached, appearing as a continuation of the margin of the achene, straight or curved outward or over apex of achene ... S. brevirostra

6a. Beak of achene 0.4–0.6 mm long; anthers clearly shorter than the filaments ... S. cristata

6b. Beak of achene minute, ca. 0.2 mm long; anthers as long as or longer than the filaments ... S. graminea