| 1. Plants with both submersed and floating leaves; floating leaves generally elliptic to ovate, generally leathery; submersed leaves linear to ovate, membranous |
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| 2. Submersed leaves lanceolate to ovate, generally 17 cm wide, sometimes linear |
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| 3. Submersed leaves generally lanceolate to ovate, curved, generally folded along midrib, sessile or short-petioled, blade veins 2040; floating leaves elliptic to ovate, blade veins 3050 |
| P. amplifolius |
| 3' Submersed leaves linear to lanceolate, not curved, flat, upper long-petioled, lowermost sessile (all sessile in P. gramineus); all leaf blades with < 30 veins |
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| 4. Submersed leaves with 8+ veins, long-petioled |
| 2 P. nodosus |
| 4' Submersed leaves generally with 7 veins, all or lowermost sessile |
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| 5. Margin of submersed leaves finely serrate near tip |
| 2 P. illinoensis |
| 5' Margin of submersed leaves entire |
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| 6. Leaves reddish; submersed leaf width = floating leaf width; submersed leaves ± all on central stem; floating leaves short-petioled |
| 2 P. alpinus subsp. tenuifolius |
| 6' Leaves green; submersed leaves narrower than floating leaves; submersed leaves on short, axillary branches; floating leaves long-petioled |
| P. gramineus |
| 2' Submersed leaves linear, < 1 cm wide |
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| 7. Stipules fused to leaf base; inflorescences of 2 kinds, lowermost spheric, submersed, short-peduncled, uppermost cylindric, emergent, long-peduncled; fruit clearly compressed lateral keels low |
| P. diversifolius |
| 7' Stipules free from leaf base; inflorescences all emergent, ± cylindric; fruit plump to slightly compressed |
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| 8. Submersed leaves ribbon-like, 210 mm wide, with a clearly net-like band along the midrib |
| P. epihydrus subsp. nuttallii |
| 8' Submersed leaves without a net-like band, cylindric, often petiole-like, < 2 mm wide, or linear to elliptic-lanceolate, 1040 mm wide |
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| 9. Floating leaf blade oblong to widely elliptic, base slightly lobed, jointed to petiole; fruit smooth or faintly keeled, sides concave |
| P. natans |
| 9' Floating leaf blade elliptic to ovate, base tapered to petiole, not jointed to petiole; fruit 3-keeled, sides flat |
| 2 P. nodosus |
| 1' Plants with all leaves submersed |
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| 10. Leaves lanceolate, elliptic, oblong, or ovate, sessile, base tapered to clasping (short-petioled in P. illinoensis) |
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| 11. Leaf blade margin finely serrate; fruit with long, slender beak 23 mm |
| P. crispus |
| 11' Leaf blade margin entire (finely serrate near tip in P. illinoensis); fruit short-beaked |
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| 12. Leaf base tapered, not clasping |
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| 13. Upper leaves generally sessile; blade margins entire; leaves reddish |
| 2 P. alpinus subsp. tenuifolius |
| 13' Upper leaves short-petioled; blade margin finely serrate near tip; leaves green |
| 2 P. illinoensis |
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| 14. Blades lanceolate to ovate, 520 cm, tip hood-like, splitting when dry; stipules 28 cm, persistent, whitish; stems zigzag; fruit 45 mm, sharply 3-keeled |
| P. praelongus |
| 14' Blades narrowly ovate, 112 cm, tip not hood-like, flat, margin crinkly, not splitting when dry; stipules < 2 cm, becoming fibrous; stems straight; fruit 24 mm, faintly 3-keeled |
| P. richardsonii |
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| 15. Stipules fused to leaf base, sheath-like below, sheath 1+ cm |
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| 16. Leaves 28 mm wide; stipules fused above junction with blade, ligule-like |
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| 17. Leaf margin entire; ligule entire; leaf blade not appendaged at junction with sheath; fruit smooth or faintly keeled |
| P. latifolius |
| 17' Leaf margin finely serrate; ligule generally cut to fibrous; leaf blade often appendaged at junction with sheath; fruit clearly keeled |
| P. robbinsii |
| 16' Leaves linear to thread-like, < 3 mm wide; stipules free above junction with blade |
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| 18. Stigma sessile; fruit 22.7 mm, not beaked; sheath partly closed; stem branched below, few-branched above |
| P. filiformis |
| 18' Stigma raised on minute style, head-like, persisting in fruit as minute beak; fruit 2.55 mm; sheath open to base; stem with many, forked branches above |
| P. pectinatus |
| 15' Stipules free from leaf or fused to leaf base for 12 mm |
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| 19. Leaves 25 mm wide, veins 935, somewhat rigid; stems clearly flattened, winged, width at least 1/2 leaf width |
| P. zosteriformis |
| 19' Leaves < 3 mm wide, veins 17, weak; stem not flattened or winged |
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| 20. Keel of fruit back wing-like, wavy; glands at leaf base 0 or faint |
| P. foliosus |
| 21. Stipules coarsely veined and ciliate, rigid, breaking apart into fibers; inflorescence generally interrupted; fruit pale green, 1.41.7 mm, 1.11.2 mm wide, keel on back generally < 0.2 mm high, beak < or = 0.2 mm |
| var. fibrillosus |
| 21' Stipules finely veined, not coarsely ciliate, decaying early; inflorescence generally not interrupted; fruit olive to greenish brown, 1.52.7 mm, 1.22.2 mm wide, keel on back generally 0.20.4 mm high, beak 0.20.6 mm |
| var. foliosus |
| 20' Fruit back rounded, not keeled; glands at base of some or all leaves 2, prominent |
| P. pusillus |
| 22. Fruit sides concave, tip beaked at top of central axis; inflorescence clearly interrupted, with 24 whorls; stipules fused below middle |
| var. pusillus |
| 22' Fruit sides rounded, tip oblique, beak to 1 side of central axis; inflorescence with 12 whorls; stipules free, flat or margins inrolled |
| var. tenuissimus
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