This is a notoriously difficult genus native to North America, with hybridization obscuring the differences between a number of species. Some specimens will not work in this (or any other) key. Incomplete specimens (e.g., lacking basal parts or adequate notes on the label) are often not satisfactory for identification.

Many characters used in this genus (at least in the key) are difficult to apply in the absence of both options before the user. Experience with the genus will help to interpret such non-quantitative terms as “densely” pubescent or “nearly” glabrous stems. It is usually best to judge stem pubescence at the middle of the stem. Some species or individuals with hairy stems may have them glabrous toward the base (or even merely harsh, from persistent bases of worn-off hairs, at the middle); and some with stems glabrous at the middle may have short, usually antrorse, hairs toward the summit and on branches of the inflorescence. Even defining (and thus measuring) a petiole can be puzzling, as it is usual for at least a narrow strip of green leaf tissue to border the petiole on each side, making it “winged.” We have considered the distal end of the petiole to be where the blade ± abruptly expands and the sides of the winged petiole are therefore no longer nearly parallel.

In several species some of the upper leaves are usually or consistently alternate, perhaps 2 leaves or perhaps all but the lowermost 2 or 3 pairs. Depauperate plants (e.g., in H. annuus) tend to have more opposite leaves as well as appearing quite different from plants grown under optimal conditions. Leaves in some species (e.g., H. giganteus, H. strumosus, H. tuberosus) may have scattered to dense glandular dots beneath. Some species thrive in moist ground and others on dry sites, but most at least tolerate a wide range of habitat and readily spread into disturbed sites.

1. Plants annual, from a taproot; disk (i.e., lobes of disk corollas) brown to purple (very rarely yellow); leaves with blades ± broadly ovate on definite petioles, usually mostly alternate (except at lowest nodes).

2. Leaf blades distinctly deltoid, less than 1.3 times as long as broad, sharply and regularly toothed (resembling leaves of Populus deltoides); receptacular chaff glabrate to merely ciliate at tip; phyllaries glabrous to sparsely hispidulous on back.

H. debilis

2. Leaf blades longer and/or irregularly (if at all) toothed; receptacular chaff with tuft of long white hairs at tip or phyllaries with long stiff hairs on back.

3. Receptacular chaff at most all uniformly ciliate; phyllary margins and backs with longer stiff hairs.

H. annuus

3. Receptacular chaff at center of disk tipped with fringe of prominent long white hairs; phyllary margins and back scabrous or with stiff bristles less than 0.3 mm long.

H. petiolaris

1. Plants perennial; disk (i.e., lobes of disk corollas) yellow (except in H. pauciflorus); leaves with blades variable, in many species sessile or nearly so and/or narrowly elliptic, in some species all opposite.

4. Phyllaries all rounded to obtuse (or nearly so) at the apex; disk corollas red-purple (yellow in the hybrid H. ×laetiflorus, often with less obtuse phyllaries).

H. pauciflorus

4. Phyllaries (except sometimes a few outer ones) acute to acuminate at the apex; disk corollas yellow.

5. Leaves mostly crowded at the base of the plant (only 1 or 2 pairs of reduced leaves or bracts on upper half of stem); phyllaries ± imbricate (of different lengths) and appressed in the involucre.

H. occidentalis

5. Leaves present along full length of stem; phyllaries looser, not overlapping much on apical half, often with prolonged spreading tips.

6. Principal mid-cauline leaves (if not all) sessile or subsessile (with petioles, if any, less than 4 mm long).

7. Leaves clasping at the base and (like the stem and phyllaries) ± densely soft-pubescent.

H. mollis

7. Leaves with blades tapered or rounded at base but not clasping.

8. Widest part of leaf near or shortly below the middle, the base ± tapered and often including a short, indistinct, winged petiole.

9. Leaves as scabrous beneath as they are above, linear to narrowly elliptic-lanceolate, usually ± folded lengthwise, arcuate, and entire (rarely toothed); stem with ± appressed hairs, the upper part (or peduncles) usually with evident dense white antrorse pubescence; phyllaries with margins very rarely bearing cilia as long as 1 mm and at least some with tip prolonged into a soft, non-green bristle.

H. maximiliani

9. Leaves less densely scabrous or smooth beneath (although softer pubescence may be present), narrowly elliptic to ovate-lanceolate, flat, ± distinctly though shallowly toothed; stem with spreading hairs, the upper part (or peduncles) seldom with appressed white pubescence; phyllaries with marginal cilia mostly 1 mm or more long and with tip acute or attenuate but hardly bristle-like.

H. giganteus (in part)

8. Widest part of leaf at base of blade, which is broadly obtuse or rounded or even subcordate, with at most a tiny petiole.

10. Stem glabrous and smooth, even glaucous, at least below the inflorescence (except at nodes); lowest lateral veins of leaf usually joining midrib at base of blade (i.e., at summit of the extremely short “petiole”).

H. divaricatus

10. Stem at least sparsely hairy (or scabrous from persistent bases of worn hairs); lowest lateral veins of leaf joining midrib slightly above base of blade (i.e., green tissue present below junction of the veins).

H. hirsutus

6. Principal mid-cauline leaves with petioles (± winged) over 5 mm long.

11. Stems with ± spreading, sometimes scattered, hairs or at least scabrous from bases of worn hairs.

12. Phyllaries with many or most cilia 1 mm or more long; leaf blades lance-elliptic, less than 3 cm (very rarely 4.5 cm) broad, petioles less than 1.5 cm long.

H. giganteus (in part)

12. Phyllaries with marginal cilia all or mostly less than 0.8 mm long; leaf blades ovate-elliptic, the largest at least (3–) 3.5 cm broad, on conspicuously winged petioles ca. 1.5 cm or longer.

H. tuberosus

11. Stems glabrous or essentially so, even glaucous, especially toward the base (not always near the heads).

13. Heads (including rays) ca. 3 cm broad or smaller, the disk less than 1 cm broad and the rays ca. 0.8–1.6 cm long.

H. microcephalus

13. Heads at least 4 cm broad, the disk ca. 1.5–2.3 cm broad and the rays ca. 1.8–4.3 cm long.

14. Leaves only slightly scabrous to the touch above (the tiny pustulate-based projections appressed), usually not over 3 (rarely to 5.5) cm broad, the blades ca. 4–8 times as long as broad, alternate on upper part of stem.

H. grosseserratus

14. Leaves very scabrous to the touch above (the tiny sharp projections more erect or spreading), usually over 3 cm broad, the blades ca. (2.2–) 2.5–3.8 times as long as broad, opposite throughout (or sometimes 1–2 pairs alternate below heads).

15. Leaf blades often coarsely and evidently toothed, glabrate or at most sparsely pubescent beneath; phyllaries with prolonged and loose tips distinctly longer than the disk (though some often reflexed).

H. decapetalus

15. Leaf blades shallowly toothed to entire, ± densely pubescent beneath; phyllaries usually only slightly if at all exceeding the disk.

H. strumosus