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Keyed in multiple places:

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Key to Asteraceae, Key M: Herbaceous composites with the leaves alternate or basal and the heads radiate, the rays white, pink, purple, and with a pappus of bristles only

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1 Head 1 per plant (individual rosette); stems 0.1-0.3 dm tall; [TX and OK westwards]
1 Heads 5-300+ per (well-developed) plant; stems 0.3-35 dm tall; [collectively widespread].
  2 Stems with numerous thorns (1-2 cm long, modified axillary branches), and few or no leaves
  2 Stems leafy, not armed with thorns.
    3 Leaves unlobed; plant perennial from caudices, crowns, or rhizomes.
      4 Annuals from taproots; ray florets 0.3-7 mm long.
        5 Ray laminae 0.3-1.0 mm long; cypselas 1.0-1.5 mm long, compressed, 1-nerved on each face
        5 Ray laminae 1.3-7 mm long; cypselas (1.2-) 1.5-2.7 (-3) mm long, compressed or not, 5-18-nerved.
          6 Disc flowers 25-35 per head; ray flowers in 1 series
      4 Perennials from caudices, crowns, or rhizomes; ray florets > 3 mm long.
             7 Basal and lower stem leaves petiolate, with blades cordate to rounded at the base
               8 Heads borne in corymbiform arrays, the branches often subtended by large and leaf-like bracts; phyllaries < 2.5 (-3)× as long as wide, often > 1 mm wide; plants (in most species) colonial by rhizomes; rays (in most species) white; phyllaries (in many species) glandular
               8 Heads borne in paniculiform arrays, the branches bearing small and narrow bracts; phyllaries > 3× as long as wide, often < 1 mm wide; plants (in most species) solitary; rays (in most species) blue, violet, or pink; phyllaries eglandular
             7 Basal and lower stem leaves sessile (sometimes cordate-clasping), or if petiolate then with cuneate to attenuate bases.
                 9 Rays pink, purple, lavender, blue, or pale pink [plants with pale pink rays may need to be keyed both ways].
                   10 Heads borne either in flat-topped or rounded, corymbose arrays, or in narrow racemiform or spiciform panicles, or solitary.
                     11 Leaves 1.2-4.0 cm long, 1-4 mm wide, stiff, scabrous margined and weakly spine-tipped; plants 1-7 dm tall; pappus in 2 series, the inner much longer than the outer (ca. 1 mm long) bristles
                     11 Leaves either longer or broader or both, herbaceous; Leaves (5-) 13-45 mm wide, herbaceous, neither scabrous-margined nor spine-tipped; plants 4-30 dm tall; pappus not divided into distinct inner and outer series.
                       12 Plants 10-35 dm tall; larger leaves (basal or low on the stem) with cuneate or attenuate bases, the blades 30-50 cm long; [non-native, rarely persistent or spreading from horticultural use]
                       12 Plants 1-12 dm tall; larger leaves with blades 2-20 cm long; [natives, collectively widespread and common in our region]
                 9 Rays white (or very slightly pink-flushed).
                          13 Heads borne either in flat-topped or rounded, corymbose arrays, or in narrow racemiform/spiciform panicles, or solitary.
                            14 Heads borne in either narrow racemiform/spiciform panicles, or in corymbose arrays.
                                16 Disc flowers yellow (and often fading to pink or purplish).
                                  17 Rays 2-7, the ray ligules 2-11 mm long, often twisted or contorted; phyllaries whitish with a distinct green tip, the green area about as wide as long
                                  17 Rays (8-) 9-40, the ray ligules 4-20 mm long, generally planar (or neatly coiling at post-maturity); phyllaries various.
                                    18 Pappus not divided into distinctively different outer and inner series; leaves toothed or entire.

Key to Asteraceae, old Key J: Herbaceous composites with the leaves alternate or basal and the heads radiate, the rays white, pink, purple

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1 Receptacles chaffy (paleate).
  2 Phyllaries dry, scarious-margined.
    3 Ray florets 1-5 mm long; heads small in corymbiform arrays
    3 Ray florets > 5 mm long; heads large, terminating the branches
      4 Ray florets < 2.5 mm long; disk florets sterile, with an undivided style
      4 Ray florets > 5 mm long; disk florets fertile, with a divided style.
        5 Ray florets pink or light purple, > 15 mm long; heads single
        5 Ray florets white, 5-10 mm long; heads 20-100 in a compound corymb
1 Receptacles naked (epaleate).
             7 Achene faces minutely glandular-glochidiate (bearing small gland-like bristles)
               8 Leaves basal; cypselae marginally 2-ribbed; mature plants < 2 dm tall
               8 Leaves cauline (and sometimes also basal); cypselae with ± 10 ribs; mature plants > 2 dm tall
          6 Pappus present, of bristles or scales.
                   10 Heads primarily discoid with reduced ray florets
                   10 Heads radiate with conspicuous ray florets.
                     11 Taprooted annuals; ray florets 1-7 mm long.
                       12 Leaves and stems not fleshy, rarely glabrous; cypselas < 1.4 mm long
                       12 Leaves and stems fleshy, mostly glabrous; cypselas > 1.4 mm long
                     11 Not taprooted and mostly perennials; ray florets > 3 mm long.
                          13 Ray florets usually > 60; blooming Apr-Oct
                          13 Ray florets usually < 60; blooming late May-Nov.
                            14 Receptacles hemispheric to conic; pappus often with 2-4 awns (Boltonia) or lacking awns and coroniform (Astranthium).
                              15 Achenes not narrowly winged, the surfaces minutely glandular-glochidiate (bearing small gland-like bristles)
                            14 Receptacles flat to slightly convex; pappus lacking awns.
                                           21 Pappus double, with inner bristles distinctly longer than outer bristles.
                                               23 Ray florets white to pink or blue or purple, more numerous (usually 8-30); cypselas glabrous to pubescent but not densely silky.
                                                 24 Ray florets white or pink to blue or purple; involucres 7-12 mm long; phyllaries usually > 1 mm wide.
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