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Keyed in multiple places:

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Key to Sapindaceae

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1 Leaves opposite; leaves either palmately compound, or simple (and then palmately lobed and/or toothed), or pinnately compound.
  2 Leaves either simple (and palmately lobed and/or toothed) or pinnately compound; flowers radially symmetrical; fruit a schizocarp of 2 samaroid mericarps; [subfamily Hippocastanoideae, tribe Acereae]
  2 Leaves palmately compound; flowers bilaterally symmetrical; fruit a capsule, usually with single large “nut-like” seed; [subfamily Hippocastaoideae, tribe Hippocastaneae]
1 Leaves alternate; leaves compound (if unifoliolate and thus appearing simple [Dodonaea], then unlobed and with entire margins).
    3 Leaves unifoliolate, appearing simple; [subfamily Dodonaeoideae, tribe Dodonaeae]
    3 Leaves compound.
      4 Herbaceous vines or lianas; leaves 3-foliolate or otherwise compound (biternately or pinnately compound); [subfamily Sapindoideae, tribe Paullinieae]
        5 Leaves 3-foliolate
        5 Leaves pinnately to biternately compound.
          6 Fruit a schizocarp with 3 winged mericarps; seeds lacking a pseudohilum
          6 Fruit an inflated, papery capsule; seeds with a white or pale tan heart-shaped or kidney-shaped mark (pseudohilum)
      4 Tree or shrub; leaves 3-foliolate or pinnately or bipinnately compound.
             7 Leaves palmately 3-foliolate; [subfamily Dodonaeoideae, tribe Doratoxyleae]
             7 Leaves pinnately or bipinnately compound, with 5 or more leaflets.
                 9 Fruits 1 (-2)-coccate, with (1-) 2 rudimentary cocci, tardily schizocarpic, separating into indehiscent globose mericarps, with fleshy pericarp containing much saponin; seeds globose, lacking an aril
                 9 Fruits ellipsoid or nearly globose, usually with a single locule; seeds arillate or sarcotestal.
                   10 Leaves with (4) 8-10 (-18) leaflets; fruits light brown; seeds with a thin, translucent-white, fleshy aril, easily removable to show a shiny dark brown testa
                   10 Leaves with (2-) 4 leaflets; fruits green; seeds with a fleshy testa; petals usually with 2 marginal projections or appendages on or above the base, or lacking appendages
               8 Fruits dehiscent, a capsule with papery, membranaceous, coriaceous, or woody valves.
                     11 Leaves mostly odd-pinnate (with a definite terminal leaflet); [subfamily Sapindoideae, tribe Koelreuterieae]
                       12 Petals yellow; capsules papery or crustaceous, inflated (the capsule wall , with incomplete septae; seeds < 7 mm in diameter; [non-native, collectively widespread in our region]
                       12 Petals pink; capsules coriaceous, the capsule wall closely invested around the seeds, with complete septae; seeds 10-15 mm in diameter; [native, TX]
                          13 Leaflet margins serrate; [subfamily Sapindoideae, tribe Cupanieae]
                            14 Locule 2- to several-seeded; [subfamily Dodonaeoideae, tribe Dodonaeae]

Key I: woody plants with opposite, compound leaves

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1 Leaves 2-3-foliolate.
  2 Leaves 2-foliolate, with a branched tendril in the terminal position (this sometimes not developed, or withered); liana
  2 Leaves 3-foliolate, lacking tendrils; shrub, liana, or tree.
    3 Upright shrub or tree.
      4 Leaflets entire, glandular-dotted; [n. FL southwards
      4 Leaflets serrate or serrulate, not glandular-dotted; [collectively widespread].
        5 Leaflets 3-5 (-7), coarsely and jaggedly serrate, with < 5 teeth per leaflet side; fruit a schizocarp of 2 samaroid mericarps (maple “keys”)
        5 Leaflets 3, evenly serrulate, with > 10 teeth per leaflet side; fruit an inflated capsule
          6 Flowers yellow with fused petals; stems stiff, green
          6 Flowers either white, radially symmetrical, with separate petaloid sepals (Clematis), or blue, bilaterally symmetrical, with fused petals (Vitex).
             7 Leaves 3-more-foliolate; flowers white, radially symmetrical, uniseriate, with white petaloid sepals and no petals
             7 Leaves 1 (-3) foliolate; flowers blue, bilaterally symmetrical, biseriate, with green calyx and blue corolla
1 Leaves 4-15-foliolate.
                 9 Leaflets serrate; flowers white, yellow, or red; fruit a leathery capsule, irregularly spheroidal, 2-9 cm in diameter, with 1-3 (-6) large seeds, each with a large pale hilum contrasting with the dark brown color of the rest of the seed
                 9 Leaflets entire; flowers blue, pink, or purple; fruit either a 4-seeded drupe, < 0.5 cm in diameter, or an elongated capsule, 8-10 cm long and ca. 0.7 cm in diameter.
                   10 Leaflets < 3× as long as wide, broadly rounded at the tip; fruit an elongated capsule, 8-10 cm long and ca. 0.7 cm in diameter [peninsular FL]
                   10 Leaflets > 4× as long as wide, acute at the tip; fruit a 4-seeded drupe, < 0.5 cm in diameter; [widespread in our region]
                       12 Leaves pinnately compound, with 7-15 coarsely serrate leaflets; perianth biseriate, with a green synsepalous calyx and an orange sympetalous corolla; fruit an elongate capsule, with many winged seeds; stems to 20 cm in diameter, with tan bark
                       12 Leaves either pinnately compound, the leaflets 3-7 and coarsely serrate, or more complexly compound, the leaflets 5-many, not serrate though often lobed; perianth uniseriate, with a white, pink, or purplish aposepalous calyx and no corolla; fruit an aggregate of plumose achenes; stems to 1 cm in diameter, brown or green
                     11 Plant a tree or shrub, with stiff branches.
                          13 Leaves 3-7-foliolate and strictly 1-pinnate; leaflets with a few very coarse teeth; 1st year stems green; fruit a pair of winged, asymmetrical samaroid mericarps
                          13 Leaves 3-15-foliolate, 1-pinnate or partially 2-pinnate; leaflets evenly serrate with many teeth or entire; 1st year stems tan to brown (very new growth may be green); fruit either a symmetrical (winged) samara (Fraxinus) or a purplish-black, many-seeded berry (Sambucus).
                            14 Fruit a purplish-black or red, 4-seeded berry (Sambucus); plant a shrub or small tree; stems hollow or pithy; petiole prominently grooved on the upper side; fresh leaves somewhat fleshy in texture
                            14 Fruit either a green or tan, symmetrical (winged) samara or a blackish 5-seeded dryish drupe; plant a small to large tree; stems solid and woody; petiole nearly round in ×-section (not grooved); fresh leaves membranaceous or coriaceous in texture.
                              15 Fruit a symmetrical samara; axillary buds suprapetiolar (though sometimes almost hidden within the strongly U-shaped petiolar attachment; [common native (also planted)]

Key J1: woody plants with opposite, simple, palmately or pinnately lobed leaves

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  2 Leaves harshly scabrous on the upper surface; leaves typically a mix of alternate, opposite, and whorled
  2 Leaves glabrous or glabrescent on the upper surface; leaves strictly opposite
    3 Plants climbing by twining; stems with retrorse prickles; foliage scabrous
    3 Plants erect trees or shrubs; stems not prickly; foliage smooth or pubescent, but not scabrous.
      4 Leaves 3-9-lobed, the margins generally serrate or sublobed; fruit either a drupe or a schizocarp of 2 samaroid mericarps (maple “keys”).
        5 Fruit a schizocarp of 2 samaroid mericarps (maple “keys”); stamens (4-) 8 (-12); small to large trees; petioles >1× as long as the leaf blade
        5 Fruit a drupe; stamens 5; shrubs; petioles < ¾× as long as the leaf blade
      4 Leaves 3-lobed, the margins entire; fruit a capsule.
          6 Flowers white to yellow; capsules linear, >10× as long as wide; leaf undersurface with curly simple hairs; nectar glands present in the main vein axils on the undersurface of the leaf (visible from the underside or the upperside in fresh leaves and herbarium specimens)
          6 Flowers lavender; pods ellipsoid, < 2× as long as wide; leaf undersurface with branched (dendritic) stellate hairs; nectar glands absent
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