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Key S1: herbaceous dicots with opposite, simple, and unlobed leaves on the stem

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1 Inflorescence an involucrate head subtended by phyllaries, the heads solitary or many and variously arrayed in secondary inflorescences, the ovary inferior, the corolla connate and tubular at least basally, the calyx absent, the stamens 5, the fruit a cypsela
1 Inflorescence, flower, and fruit structure various, but not with the combination of features as above (sometimes the flowers in a head, e.g. Pycnanthemum in LAMIACEAE, but then with other features differing, such as stamens 4, or green calyx present, or fruit a schizocarp of mericarps, etc.).
  2 Leaves scale-like, stems fleshy; flowers embedded in the fleshy stem, no perianth present; [saline environments (coastal or rarely inland)].
  2 Leaves small to large; stems not fleshy; flowers sessile or on pedicels; [collectively of many habitats, saline and not].
      4 Perianth of a single whorl (petals absent) (note that in Mirabilis in NYCTAGINACEAE the petaloid calyx is subtended by a 5-lobed fused set of involucral bracts).
        5 Leaves herbaceous, suborbicular, about as long as wide or wider than long; calyx 3- or 4-merous; stamens 4, 8, or 12.
          6 Plant ascending, with a single node (2 leaves); leaves > 6 cm long and wide; calyx 3-merous, brown to yellowish; stamens 12
          6 Plant creeping, with many nodes; leaves 3-15 mm long and wide; calyx 4-merous, yellow to greenish; stamens 4 or 8
        5 Leaves fleshy, linear, lanceolate, to broadly ovate, at least slightly longer than broad; calyx 5-merous; stamens 3, 5, or 10.
             7 Flowers axillary, sessile or nearly so, solitary or a few; petaloid sepals widely spreading, separate; leaves linear to oblanceolate; stamens 5 or 30-50
             7 Flowers in terminal cymose panicles; petaloid sepals connate into a narrow tube (reminiscent of the corolla of Ipomoea); leaves lanceolate, elliptic, ovate, or broadly ovate; stamens 3 or 5
      4 Perianth in 2 whorls (sepals and petals both present).
                 9 Leaves distinctly 3-veined from the base, the 3 veins converging again at the leaf apex
               8 Petals connate into a tube (at least basally); inflorescence often a head or dense terminal cyme (also axillary, or solitary on long peduncles).
                   10 Petals 5; stamens 3, 4, or 5
                     11 Upright herb; flowers in axils or terminal corymbs
                       12 Flowers in terminal corymbs; fruit dry
                   10 Petals 4 (or 6 or 8 in Richardia in RUBIACEAE); stamens 4, 6, or 8.
                          13 Inflorescence a head or more diffuse (see below), sometimes subtended by green bracts.
                            14 Leaves serrate; corolla bilaterally symmetrical (especially the flowers near the outer edge of the head); inflorescence a head
                            14 Leaves entire; corolla radially symmetrical; inflorescence a head or more diffuse (see below).
                              15 Petals acute; flowers in terminal panicles, cymes, or panicles, or axillary; plant habit various, not simultaneously with all the characters below
                              15 Petals broadly rounded; flowers axillary, solitary; plant a diffusely branched herb with linear leaves
                                16 Perianth of a single whorl (petals absent) or missing entirely (petals and sepals both absent). {key lead number needs adjusting}
                                  17 Inflorescence a cyathium, consisting of a single pistillate flower (reduced to a single 3-carpellate pistil) and 2 or more staminate flowers (each reduced to 1 stamen), borne in a cup-like involucre, the involucre bearing pointed or rounded glands, these sometimes brightly colored and petaloid, mimicking an individual flower (the cyathia then secondarily arranged in terminal cymes, or solitary and axillary, etc.); fresh plants with milky juice; fruit a 3-lobed, 3-locular capsule
                                  17 Inflorescence not a cyathium (and staminate or bisexual flowers with > 1 stamen, except Callitriche in PLANTAGINACEAE); fresh plants lacking milky juice; fruit various, not as above.
                                    18 Flowers many, in axillary spikes, cymes, or glomerules, or in terminal spikes, heads, cymes, or panicles; leaves entire or serrate.
                                             22 Leaves entire, or with a few very obscure crenations (Iresine) or basally disposed rounded lobe-like teeth (Atriplex); plants without stinging hairs.
                                                 24 Style 1; leaves generally either longer than 30 mm, or wider than 8 mm (if linear and smaller than those dimensions, then fleshy).
                                16 Perianth in 2 whorls (sepals and petals both present).
                                                        27 Pistils 4-5, in a single whorl; stamens 4, 5, 8, or 10; fruit an aggregate of follicles
                                                      26 Gynoecium either of 1 pistil (with 1 or more carpels), or of 2 pistils, united only by the style and stigma (APOCYNACEAE).
                                                            29 Leaves with pellucid punctate glands (most easily visible with transmitted light); stamens often fascicled into 3, 4, or 5 fascicles; petals yellow or pinkish
                                                                 31 Petals 3; sepals 5, dimorphic, the 2 outer sepals narrower than the 3 inner and concave sepals; stamens (3-) 5-15 (-25)
                                                                 31 Petals 4-7; sepals 4-7, normally monomorphic; stamens 4, 5, 6, 8, 10, or 12 (or sometimes rarely 2 or 3).
                                                                     33 Capsule 1-locular, dehiscent apically by teeth or valves; sepals connate into a tube or separate; styles 2-5; perianth 4-5-merous; stamens 4, 5, 8, or 10 (or rarely 2 or 3)
                                                                       34 Corolla radially symmetrical (or so slightly bilaterally symmetrical as to be mistakable as radially symmetrical); stamens as many as the corolla lobes (or 1 less in Ruellia in ACANTHACEAE, Buchnera in OROBANCHACEAE, Trichostema in LAMIACEAE, and Verbena in VERBENACEAE); carpels 2 or 3.
                                                                         35 Pistils 2, united only by the style and stigma; fruit a schizocarp of 2 1-carpellate follicles (often single by abortion); plant with milky juice when fresh (except Catharanthus); leaves entire
                                                                         35 Pistil 1 (of 2-5 fused carpels); fruit either a 2-5-carpellate capsule or of 2 or 4 1-seeded nutlets derived from 2 carpels; plant lacking milky juice; leaves entire or serrate.
                                                                                  39 Stamens either 4, 1 fewer than the 5 corolla lobes, or 2 (with 2 staminodes); corolla usually slightly bilaterally symmetrical (the flower as a whole made bilaterally symmetrical by the 2 or 4 stamens).
                                                                       34 Corolla bilaterally symmetrical (or the corolla 2-lipped but the corolla lobes twisted so as to make the flower asymmetrical); fertile stamens fewer than the corolla lobes (except Plantago in PLANTAGINACEAE, which is equal, with 4 each; a few genera have a 5th, sterile, stamen which is obviously different in form than the 4 fertile stamens) (note that many corollas are bilabiate and the number of corolla lobes, 4 or 5, may be difficult to interpret); carpels 2.
                                                                                             44 Carpels 2, each carpel slightly to deeply lobed, separating at maturity into 4 half-carpellate units (not separating in Phyla in VERBENACEAE); fruit a schizocarp of 4 mericarps (or 2 nutlets in Phyla in VERBENACEAE).
                                                                                               45 Inflorescence a thyrse, verticillaster, or terminal cyme, the flowers borne in cymose lateral branches; corolla strongly bilaterally symmetrical (rarely nearly radially symmetrical); stems square in ×-section (or sometimes rounded, especially on older growth); fresh plants often (but not always) aromatic
                                                                                               45 Inflorescence of spikes, racemes, or heads, the flowers or fruits single at nodes; corolla often nearly radially symmetrical; stems rounded in X-section (rarely square); fresh plants usually not aromatic
                                                                                                                     55 Inflorescence of 1 or more terminal (and sometimes upper axillary) spikes or racemes; corolla 10-50 mm long (6-8 mm long in Phryma in PHRYMACEAE), white, pink, blue, purple, or yellow; fruit either a loculicidal capsule (OROBANCHACEAE) or a single seeded achene (Phryma in PHRYMACEAE).
                                                                                                                53 Flowers axillary and solitary, borne in the axils of normally-sized leaves or somewhat reduced but still large and leaf-like bracts [some taxa keyed here and below].
                                                                                                                                      63 Corolla red or orange, with a very narrow, cylindrical tube, the lobes then flaring into a limb about 1 cm across; plants blackening on drying; [rare exotic, in crop fields, a noxious hemiparasitic weed under quarantine]
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