| 1 | Leaves alternate |
| 1' | Leaves opposite |
| 2 | Flowers in simple spikes, not glomerulate; tepals more than 4 mm |
| 2' | Flowers in glomerules, these in spikes that may be further branched; tepals less than 4 mm |
| 3 | Herbs; flowers unisexual; top of ovary rounded or thickened, but not with upturned rim; seed exarillate |
| 3' | Lianas (climbing subshrubs); flowers unisexual or bisexual; top of ovary with upturned rim; seed arillate |
| 4 | Plants prostrate, creeping or mat-forming (growing on beaches or in sandy places) |
| 4' | Plants erect or only partly decumbent |
| 5 | Leaves ovate to elliptic or broadly oblanceolate, not succulent; tepals glabrous or pubescent; pseudostaminodia present |
| 5' | Leaves linear to linear-spathulate, succulent; tepals glabrous, except ciliolate at base; pseudostaminodia obscure or absent |
| 6 | Inflorescence of 1-3 slender spikes, each generally several dm long, or spiciform; flowers reflexed early in development |
| 6' | Inflorescence paniculate, capitate, or if spicate, then at most a few cm long; flowers reflexed |
| 7 | Flowers not in glomerules (except A. brasiliensis); bracts white, hyaline; bracteoles rigid, subulate, awned, but not hooked |
| 7' | Flowers in few-flowered, shortly pedunculate glomerules, in glomerules stiff hooked spines present; bracts and bracteoles modified into hooked spines |
| 8 | Inflorescence capitate, immediately subtended by a pair of involucral leaves; filament-tube extending beyond ovary |
| 8' | Inflorescence not capitate or, if so, then the head not immediately subtended by a pair of leaves; filament-tube (and pseudostaminodia if present) forming cup shorter than ovary |
| 9 | Inflorescence paniculate |
| 9' | Inflorescence capitate or short-spicate |
| 10 | Panicle with a diffuse, filigree-like aspect, branches spike-like, flowers not in heads, flowers bisexual or unisexual |
| 10' | Panicle branches not diffuse, usually (e.g., except in P. grandiflora) terminating in a 4-7 mm hemispherical head; flowers bisexual |
| 11 | Tepals glabrous inside; pseudostaminodia present |
| 11' | Tepals with a short or long tuft of hairs inside; pseudostaminodia absent |
