Fruits and male flowers are often necessary for positive determination of these highly variable aquatics.
1. Sepals closely appressed; pedicels thick (the lower ca. 3–5 mm in diameter); leaves very broadly sagittate, much broader than long; lowermost flowers mostly bisexual.
1. Sepals of mature pistillate flowers reflexed; pedicels more slender; leaves various; lowermost flowers ordinarily pistillate.
2. Filaments pubescent with ± flattened or scale-like hairs; leaves not sagittate (or small basal lobes occasionally present in S. rigida).
3. Pistillate (lower) flowers sessile or nearly so; axis of the inflorescence strongly bent above the lowest flowers; achenes with beak ca. 1–1.5 mm long.
3. Pistillate and staminate flowers pediceled; axis of inflorescence straight; achenes with beak ca. 0.2–0.8 mm long.
4. Achenes with beak 0.4–0.6 mm long; anthers clearly shorter than the filaments.
4. Achenes with beak minute, scarcely discernable, ca. 0.2 mm long; anthers as long as or longer than filaments.
2. Filaments glabrous; leaves usually sagittate when emersed.
5. Mature achenes with a ± horizontal beak projecting to one side and attaining 0.5–1.5 (–2.3) mm in length; faces of achene not winged, at most with a visible resin duct; bracts 4–9 mm long (or up to 11 mm in some robust plants).
5. Mature achenes with an erect or curved apical beak up to ca. 0.7 mm long; faces of achene sometimes with a low wing or ridge; bracts usually (8–) 10–16 mm long.
6. Achenes with beak ca. 0.4–0.7 mm long, appearing as a continuation of the ± straight margin of the achene, straight or curved outward or over apex of achene.
6. Achenes with a very tiny erect beak scarcely 0.2–0.3 mm long, terminating a swollen or convex margin of the achene and thus appearing to project from summit of the achene, definitely set in from the margin.