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 
- Pteridophyte Phylogeny Group I (2016). "A community-derived classification for extant lycophytes and ferns" (PDF). Journal of Systematics and Evolution. 54 (6): 563–603. doi:10.1111/jse.12229.
- Palmer, Jeffrey (2004). "THE PLANT TREE OF LIFE: AN OVERVIEW AND SOME POINTS OF VIEW". American Journal of Botany. 91 (10): 1437–45. doi:10.3732/ajb.91.10.1437. PMID 21652302.
- Christenhusz, M.J.M.; Chase, M.W. (2014). "Trends and concepts of fern classification". Annals of Botany. 113 (4): 571–594. doi:10.1093/aob/mct299. PMC 3936591. PMID 24532607. Retrieved 17 July 2014.
- Christenhusz, M.J.M.; Zhang, X.C.; Schneider, H. (2011). "A linear sequence of extant families and genera of lycophytes and ferns". Phytotaxa. 19: 5–22.
- Smith, A. R.; Pryer, K. M.; et al. (2006). "A classification for extant ferns". Taxon. 55 (3): 705–731. doi:10.2307/25065646.
- Chase, Mark W.; Reveal, James L. (October 2009), "A phylogenetic classification of the land plants to accompany APG III", Botanical Journal of the Linnean Society, 161 (2): 122–127, doi:10.1111/j.1095-8339.2009.01002.x
- Schuettpelz, Eric. "Fern Phylogeny Inferred from 400 Leptosporangiate Species and Three Plastid Genes," contained in "The Evolution and Diversification of Epiphytic Ferns." Doctoral dissertation, Duke University. 2007. http://dukespace.lib.duke.edu/dspace/bitstream/10161/181/1/D_Schuettpelz_Eric_a_052007.pdf
- Cronquist, Arthur; Takhtajan, Armen; Zimmermann, Walter (April 1966). "On the Higher Taxa of Embryobionta". Taxon. 15 (4): 129–134. JSTOR 1217531.
- Smith et al. 2006.
- "Fern genomes elucidate land plant evolution and cyanobacterial symbioses". Nature Plants. 4 (7): 460–472. July 26, 2018. doi:10.1038/s41477-018-0188-8 – via www.nature.com.
- Chase & Reveal 2009.
- Christenhusz et al. 2011.
- Christenhusz & Chase 2014.
- Pteridophyte Phylogeny Group 2016.
- Samuli Lehtonen (2011). "Towards Resolving the Complete Fern Tree of Life" (PDF). PLoS ONE. 6 (10): e24851. Bibcode:2011PLoSO...624851L. doi:10.1371/journal.pone.0024851. PMC 3192703. PMID 22022365.
- Hardeep S. Rai; Sean W. Graham (2010). "Utility of a large, multigene plastid data set in inferring higher-order relationships in ferns and relatives (Monilophytes)" (PDF). American Journal of Botany. 97 (9): 1444–1456. doi:10.3732/ajb.0900305. PMID 21616899.
- Kathleen M. Pryer; Eric Schuettpelz (2009). "Ferns" (PDF). In S. Blair Hedges; Sudhir Kumar (eds.). The Timetree of Life. Oxford Biology.
- Rothwell, G. W.; Nixon, K. C. (2006). "How does the inclusion of fossil data change our conclusions about the phylogenetic history of euphyllophytes". Int. J. Plant Sci. 167 (3): 737–749. doi:10.1086/503298.
- Kramer, K. U. (1990). Notes on the Higher Level Classification of the Recent Ferns. The Families and Genera of Vascular Plants: Pteridophytes and Gymnosperms. K. Kubitzki, K. U. Kramer and P. S. Green. New York, Springer-Verlag. 1: 49-52
- Chase, Mark W.; Reveal, James L. (2009). "A phylogenetic classification of the land plants to accompany APG III". Botanical Journal of the Linnean Society. 161: 122–127. doi:10.1111/j.1095-8339.2009.01002.x.
- Christenhusz, M. J. M.; Zhang, X. C.; Schneider, H. (18 February 2011). "A linear sequence of extant families and genera of lycophytes and ferns". Phytotaxa. 19 (1): 7. doi:10.11646/phytotaxa.19.1.2.
- Christenhusz, Maarten J.M.; Chase, Mark W. (2014). "Trends and concepts in fern classification". Annals of Botany. 113 (4): 571–594. doi:10.1093/aob/mct299. PMC 3936591. PMID 24532607.
- Pteridophyte Phylogeny Group (November 2016). "A community-derived classification for extant lycophytes and ferns". Journal of Systematics and Evolution. 54 (6): 563–603. doi:10.1111/jse.12229.
- Smith, Alan R.; Kathleen M. Pryer; Eric Schuettpelz; Petra Korall; Harald Schneider; Paul G. Wolf (2006). "A classification for extant ferns" (PDF). Taxon. 55 (3): 705–731. doi:10.2307/25065646. JSTOR 25065646.