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1 Stigmas 1-branched; fruits rounded or acuminate to a beak at the apex, elliptic, fusiform, or obovate, 1-4 mm broad; [subgenus Xanthosparganium].
..2 Leaves and inflorescence primarily emergent, with few or no leaves floating on water surfaces; leaves keeled throughout or at least basally.
....3 Rachis of inflorescence unbranched; fruit beak straight to curved; tepals reaching about half the length of fruit body; leaves often keeled distally; perianth segments essentially translucent and lacking an apical dark spot
....3 Rachis of inflorescence branched; fruit beak curved; tepals reaching about half or more the length of fruit body; leaves usually keeled only near bases (S. americanum) or from base to at least the middle of leaves (S. androcladum(); perianth segments not translucent, their apices with a dark brown or black pad of tissue.
......4 Mature fruits dull, finely pitted, the body 3-5 mm long; fruiting heads 1.5-2.5 cm in diameter; branches of the inflorescence with (0-) 1-3 pistillate heads (in addition to staminate heads); stigma 0.8-1.9 (-2.8 in the Coastal Plain) mm long; leaves erect but not stiffened
......4 Mature fruits shiny, smooth, the body 5.5-7 mm long; fruiting heads 2.5-3.5 cm in diameter; branches of the inflorescence with 0 (-1) pistillate heads (in addition to staminate heads); stigma 1.5-3 mm long; leaves stiff
..2 Leaves and inflorescence primarily floating, limp on the surface of water (sometimes with a few emergent stems); floating leaves usually without keels and mostly flattened or usually at least basally keeled (as in S. acaule).
........5 Rachis of inflorescence branched, the distal portion erect at water surface
........5 Rachis of inflorescence unbranched, either floating, the distal portion erect at water surface, or completely erect on entirely emergent plants.
..........6 Staminate heads 1; pistillate heads borne directly in axils of leaves or bracts; beak of fruit 0.5-1.5 mm long
..........6 Staminate heads 2 or more; pistillate heads (some or all) borne above the axils of leaves or bracts; beak of fruit 1.5-4.3 mm long
............ 7 Fruit beak straight to curved, 2-4.5 mm long, fruits green to reddish brown when fresh; floating leaves keeled at least basally; plants often a mix of (mostly) emergent and (some) floating leaves and inflorescences