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Flora of New York/Clade ferns

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Class Polypodiopsida contains the ferns, including the eusporangiate ferns (horsetails, scouring rushes, moonworts, and grape ferns) and the leptosporangiate ferns of subclass Polypodiidae.[1][2]

Cladogram of ferns showing outgroups and the four subclasses down to orders:

tracheoophytes
lycophytes
Lycopodiopsida

Lycopodiales

Isoetales

Selaginellales

euphyllophytes
Polypodiopsida (ferns)
Equisetidae

Equisetales

Ophioglossidae

Psilotales

Ophioglossales

Marattiidae

Marattiales

Polypodiidae

Osmundales

Hymenophyllales

Gleicheniales

Schizaeales

Salviniales

Cyatheales

Polypodiales

spermatophytes

gymnosperms ↓

angiosperms ↓↓

eusporangiate
ferns
leptosporangiate
ferns

A more detailed cladogram of New York State ferns down to subgenera or single species:

ferns
Equisetales : Equisetaceae : Equisetum

subg. Equisetum (6 horse tails)

subg. Hippochaete (7 scouring rushes)

Psilotales : Psilotaceae (0 whisk ferns in NY)

Ophioglossales : Ophioglossaceae

OphioglossoideaeOphioglossum pusillum (northern adder's-tongue) 

Botrychioideae

Botrypus virginianum (rattlesnake fern)

Sceptridium (4 evergreen grapeferns)

Botrychium (7 moonworts, grape ferns)

Marattiales : Marattiaceae (0 marattid ferns in NY)

Osmundales : Osmundaceae

Osmundastrum cinnamomeum (cinnamon fern)

Claytosmunda claytoniana (interrupted fern)

Osmunda regalis (royal fern)

Hymenophyllales : Hymenophyllaceae

Hymenophylloideae (0 filmy ferns)

TrichomanoideaeCrepidomanes intricatum (Appalachian bristle fern) 

Gleicheniales

Gleicheniaceae (0 forked ferns)

Matoniaceae (0 fan ferns)

Dipteridaceae (0 umbrella ferns)

Schizaeales

LygodiaceaeLygodium palmatum (American climbing fern)

SchizaeaceaeSchizaea pusilla (curlygrass)

Salviniales

SalviniaceaeAzolla cristata (mosquitofern)

MarsileaceaeMarsilea quadrifolia (water clover)

Cyatheales (0)

Polypodiales (continued below)

eusporangiate
ferns
leptosporangiate
ferns

Continuation of Polypodiales part of above cladogram of New York State ferns, including the six suborders employed by PPG I (2016):

Polypodiales

Saccolomatineae (1 genus, 0 in NY)

Lindsaeineae (3 families, 0 in NY)

Pteridineae : Pteridaceae

CryptogrammoideaeCryptogramma stelleri (fragile rockbrake}

PteridoideaePteris multifida (brake fern - excluded!)

Cheilanthoideae

Pellaea atropurpurea (purple cliffbrake)

Pellaea glabella (smooth cliffbrake)

Myriopteris lanosa (hairy lip-fern)

Vittarioideae

Adiantum pedatum (northern maidenhair fern)

Vittaria appalachiana (Appalachian shoestring fern)

Dennstaedtiineae : Dennstaedtiaceae

Dennstaedtia punctilobula (hay-scented fern)

Pteridium aquilinum (brackenfern)

Aspleniineae
Cystopteridaceae

Cystopteris (4 bladderferns)

Gymnocarpium dryopteris (northern oak fern)

DiplaziopsidaceaeHomalosorus pycnocarpos (narrow-leaved glade fern)

AspleniaceaeAsplenium (11 spleenworts)

Thelypteridaceae

PhegopteridoideaePhegopteris (2 beech ferns)

ThelypteridoideaeThelypteris (3 marsh ferns)

WoodsiaceaeWoodsia (5 cliff ferns)

Athyriaceae

Athyrium (2 lady ferns)

Deparia acrostichoides (silvery spleenwort)

Onocleaceae

Onoclea sensibilis (sensitive fern)

Matteuccia struthiopteris (ostrich fern)

Blechnaceae : Woodwardioideae

Anchistea virginica (Virginia chainfern)

Lorinseria areolata (netted chainfern)

Polypodiineae
Dryopteridaceae : Dryopteridoideae

Dryopteris (28 woodferns)

Polystichum (4 holly ferns)

Cyrtomium falcatum (netvein hollyfern - excluded)

Polypodiaceae : Polypodioideae

Polypodium (3 rock-cap ferns)

Pleopeltis polypodioides (resurrection fern excluded)