Bur-buttercup (Ceratocephala testiculata (Crantz) Besser, also in floras as Ranunculus testiculatus Crantz, has been collected in dry compacted, sunny soils like roadsides, campgrounds, and fairgrounds in Indiana, Ohio, and southwestern Ontario and will doubtless be found in Michigan at some point. It is a small ephemeral stemless annual with beaked achenes forming a distinctive cylindrical bur. Paun et al. (2005) and Emadzade et al. (2010) clarify the phylogeny of Ranunculus and allies, and we recognize the small genera Coptidium, Ficaria, and Halerpestes.

1. Leaves dissected into very narrow, almost hair-like, segments, submersed.

2. Petals white; achenes transversely ridged; leaf segments not over 0.3 mm in diameter, rounded in cross-section.

3. Styles (at least the longest) and achene beaks 0.6–1.1 mm long, more than 1/3 the length of the achene body.

R. longirostris

3. Styles and achene beaks ca. 0.2–0.5 mm long, less than about 1/3 the length of the body.

R. trichophyllus

2. Petals yellow; achenes smooth or warty but not transversely wrinkled; leaf segments (at least the broader ones) over 0.3 mm wide, definitely flattened.

4. Body of achene ca. 1.7–2.2 mm long, with a conspicuous corky keel; beak of achene ca. 1–1.5 (–2) mm long; petals (5–) 7–14 (–16) mm long.

R. flabellaris (in part)

4. Body of achene ca. 1.1–1.5 mm long, the sides ± thickened but without a corky keel; beak of achene ca. 0.5 mm long; petals 3.5–5 (–6.5) mm long.

R. gmelinii (in part)

1. Leaves simple, lobed, or compound but not finely dissected and usually not normally submersed.

5. Leaves all unlobed, linear to lance-elliptic, entire or at most denticulate.

6. Largest leaves at least (5–) 7 mm wide and (5–) 7 cm long (including petiole), clearly to obscurely denticulate with ± remote callus-like teeth; achenes with a distinct beak at least 0.5 mm long; petals usually at least 5 mm long.

R. ambigens

6. Largest leaves less than 4 mm wide (usually 1 mm or less, often filiform), usually less than 7 cm long, entire; achenes with beak less than 0.3 mm long; petals ca. 2–4 (–5) mm long.

R. reptans

5. Leaves (at least the cauline ones) with blades deeply cleft or lobed more than halfway to the base.

7. Plants with a very lax or creeping stem (growing in wet muddy or mossy places); leaf blades palmately lobed, the lobes crenate or with rounded teeth.

8. Body of achene ca. 1.7–2.2 mm long, with a conspicuous corky keel; beak of achene ca. 1–1.5 (–2) mm long; petals (5–) 7–14 (–16) mm long.

R. flabellaris (in part)

8. Body of achene ca. 1.1–1.5 mm long, the sides ± thickened but without a corky keel; beak of achene ca. 0.5 mm long; petals 3.5–5 (–7) mm long.

R. gmelinii (in part)

7. Plants with an erect leafy stem, or if trailing shoots or stolons present, the leaves clearly compound and sharply toothed; leaf blades various.

9. Petals less than 5 mm long, shorter than the sepals; achenes either plump, or flattened with a recurved beak; basal leaves often much less deeply lobed than cauline leaves.

10. Stem and petioles with spreading hairs; achenes strongly flattened, with a prominent beak recurved (hooked) at the tip (evident on carpels at anthesis).

R. recurvatus

10. Stem and petioles glabrous or with a few delicate mostly curly hairs; achenes plump (with convex sides), the minute beak less than 0.3 mm long.

11. Basal leaves (at least some of them) cordate to reniform, not at all lobed; fruiting heads less than 1.5 times as long as thick; achenes shiny, ca. 1.5–2 mm long with subterminal beak, the margins not corky, and the sides at most minutely dotted; deciduous or mixed forests (often disturbed areas).

R. abortivus

11. Basal leaves ± lobed; fruiting heads usually cylindrical, 1.5–3 times as long as thick; achenes rather dull, ca. 1 mm long with terminal beak, ± corky margin, and slightly wrinkled or pebbled sides; wet shores, ditches, etc.

R. sceleratus

9. Petals usually longer and exceeding the sepals (shorter only in R. macounii and R. pensylvanicus); achenes flattened (except in R. rhomboideus), the beak straight or curved (or sometimes minutely hooked in species with large petals); basal leaves, if any, deeply lobed, cleft, or compound (unlobed only in R. rhomboideus).

12. Basal leaves simple, the blades crenate, unlobed; achenes plump (convex on sides), ca. 1.6–2.2 mm long.

R. rhomboideus

12. Basal leaves deeply cleft, lobed, or compound (or absent); achenes flattened, the body at least 2 mm long and the beak at maturity at least 0.4 mm long.

13. Petals scarcely if at all longer than the sepals; anthers less than 1 mm long; achenes in a cylindrical or ovoid head; stems and petioles with spreading hairs.

14. Petals 4.5–6.5 mm long, about equaling the sepals (often slightly longer); beak of achene ca. 0.7–1.5 mm long; fruiting head ovoid; a rare northern species at Lake Superior.

R. macounii

14. Petals 2.5–4 (–4.5) mm long, distinctly shorter than the sepals; beak of achene ca. 0.4–1 mm long; fruiting head ± cylindrical; frequent throughout Michigan.

R. pensylvanicus

13. Petals much exceeding the sepals; anthers mostly (0.9–) 1.1–2.8 mm long; achenes in a spherical or nearly spherical head; stems often glabrous or with hairs mostly ± appressed (especially on upper portion) but sometimes spreading.

15. Leaves simple, very deeply cleft but the terminal lobe not stalked; receptacle glabrous; common weed of fields and disturbed places (spread into moist ground everywhere).

R. acris

15. Leaves compound, at least the terminal primary lobe (leaflet) definitely stalked; receptacle ± bristly or hairy; a rare introduction (R. repens, R. bulbosus) or native (R. fascicularis, R. hispidus).

16. Style slender and elongate (rarely deltoid), soon becoming (1–) 1.5–3 mm long, stigmatic only at the tip; native, widespread in wet or dry places.

17. Ultimate major lobes of upper leaves linear-oblanceolate, frequently less than 4 mm wide; teeth or lobes of leaflets obtuse to rounded; the roots often tuberous-thickened; petals linear-oblong, usually widest near or below the middle; rhizomes not surviving from year to year; plants erect, not stoloniferous, of dry sandy or rocky habitats.

R. fascicularis

17. Ultimate leaf lobes broad (mostly over 5 mm); teeth or lobes of leaflets (at least upper ones) ± acute; the roots long and fibrous (sometimes thick but not tuberous); petals rounded-obovate, widest above the middle; rhizome only partly dying back each year; plants often elongating and becoming decumbent and ± stoloniferous as anthesis progresses, often of swampy habitats (one scarce variety in uplands).

R. hispidus

16. Style ± deltoid, short (less than 1 mm), stigmatic more than half its length; usually in disturbed places, uncommon.

18. Plants usually strongly stoloniferous, without bulbous base; sepals spreading; beak of achenes ca. 0.8–1 mm long.

R. repens

18. Plants erect, solitary, not colonial from stolons, bulbous-based or not; sepals becoming reflexed; beak of achenes ca. 0.3–0.8 mm long.

19. Plants with a conspicuous, bulbous base; petals 8–14 mm long.

R. bulbosus

19. Plants lacking a bulbous-thickened base; petals 5–10 mm long.

R. sardous