Cronquist, Takht. & W.Zimm.
Polypodiidae, commonly called leptosporangiate ferns, is a subclass of ferns. It is the largest group of living ferns, including some 11000 species worldwide. They constitute the subclass Polypodiidae, but are often considered to be the class Pteridopsida or Polypodiopsida, although other classifications assign them a different rank. The leptosporangiate ferns are one of the four major groups of ferns, with the other three being the Eusporangiate ferns comprising the marattioid ferns (Marattiidae, Marattiaceae), the horsetails (Equisetiidae, Equisetaceae), and whisk ferns and moonworts.
There are approximately 8465 species of living leptosporangiate ferns, compared with about 2070 for all other ferns, totalling 10535 species of ferns. Almost a third of leptosporangiate fern species are epiphytes.
These ferns are called leptosporangiate because their sporangia arise from a single epidermal cell and not from a group of cells as in eusporangiate ferns (a polyphyletic lineage). The sporangia are typically covered with a scale called the indusium, which can cover the whole sorus, forming a ring or cup around the sorus, or can also be strongly reduced to completely absent. Many leptosporangiate ferns have an annulus around the sporangium, which ejects the spores.
The leptosporangiate ferns were first recognized as a group, the "Leptosporangiateen", by Karl Ritter von Goebel in 1881, who placed the eusporangiate ferns with seed plants and vascular plants into a coeval "Eusporangiateen". As this classification artificially split the ferns, Christian Luerssen subdivided the homosporous ferns only into Eusporangiatae and Leptosporangiatae in 1884–9. The latter group was treated at a variety of ranks in subsequent systems of classification. The subclass "Polypodiidae" was first published and used for the homosporous leptosporangiate ferns by Cronquist, Takhtajan and Zimmermann in 1966, typified on Polypodium L.. Other contemporary classifications used the name Filicidae for this subclass.
Smith et al. (2006) carried out the first higher-level classification of ferns based on molecular phylogenetics. They included heterosporous water ferns (Salviniales) (placed in a separate subclass by Cronquist et al. due to their highly modified morphology) within the leptosporangiate ferns, which they elevated to the rank of class as the Polypodiopsida (published by Cronquist et al. to include all ferns).
Later classifications renamed the group Polypodiidae, initially as a subclass of Equisetopsida sensu lato. This subclass comprises leptosporangiate ferns as opposed to the remaining three subclasses which are informally referred to as eusporangiate ferns. The following diagram shows a likely phylogenic relationship between subclass Polypodiidae and the other Equisetopsida subclasses in that system
In 2014, Christenhusz and Chase grouped all the fern subclasses together as Polypodiophyta and in 2016 the Pteridophyte Phylogeny Group (PPG) adopted the class Polypodiopsida sensu lato for the four fern subclasses. The following cladogram shows the phylogenic relationship between the subclasses according to the PPG. The first three small subclasses being informally grouped as eusporangiate ferns, in contrast to the Polypodiidae or leptosporangiate ferns. Polypodiidae is shown as a sister group of Marattiidae.
In the PPG classification the Polypodiidae are divided into seven orders (Osmundales, Hymenophyllales, Gleicheniales, Schizaeales, Salviniales, Cyatheales, and Polypodiales), 44 families, 300 genera, and an estimated 10,323 species.
These seven orders are phylogenetically related as follows:
The following phylogram shows a likely relationship between the other vascular plant classes and the leptosporangiate ferns. It was formerly unclear about the relationship between Equisetopsida, Psilotopsida, and Marattiopsida, but recent studies have shown that Equisetopsida is most likely sister to Psilotopsida.
Discussion of molecular classification
There has been some challenge to recent molecular studies, claiming that these provide a skewed view of the phylogenetic order because they do not take into account fossil representatives. However, the molecular studies have clarified relations among families that had already been thought to be polyphyletic before the advent of molecular information but that were left in their polyphyletic ranks because there was not enough information to do otherwise. The classification of ferns using these molecular studies, which have generally supported one another, reflects the best information available at present, because traditional morphological characters are not always informative in elucidating evolutionary relationships among ferns 
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