Question: Are both Polypodium and Mukdenia considered genus species of ferns?

Context articles: Tree fern
Frond dimorphism
Polypodium
Leptosporangiate fern
Mukdenia
Polypodium appalachianum
Clostridium tetani
Tatrasuchus
Phlebodium
Lophosoria quadripinnata

The tree ferns are the ferns that grow with a trunk elevating the fronds above ground level.
 Most tree ferns are members of the "core tree ferns", belonging to the families Dicksoniaceae, Metaxyaceae, and Cibotiaceae in the order Cyatheales.
 In addition to those families, many ferns in other groups may be considered tree ferns, such as several ferns in the family Osmundaceae, which can achieve short trunks under a metre tall, and particularly ferns in the genus "Cibotium", which can grow ten metres tall.
 Fern species with short trunks in the genera "Blechnum, Calochleana, Cnemedaria, Culcita" (Europe's only tree fern), "Cystodium, Leptopteris, Lophosoria, Sadleria, Thyrsopteris" and "Todea" could also be considered tree ferns in a liberal interpretation of the term.
Frond dimorphism refers to a difference in ferns between the fertile and sterile fronds.
 Since ferns, unlike flowering plants, bear spores on the leaf blade itself, this may affect the form of the frond itself.
 In some species of ferns, there is virtually no difference between the fertile and sterile fronds, such as in the genus "Dryopteris", other than the mere presence of the sori, or fruit-dots, on the back of the fronds.
 Some other species, such as "Polystichum acrostichoides" (Christmas fern), or some ferns of the genus "Osmunda", feature dimorphism on a portion of the frond only.
 Others, such as some species of "Blechnum" and "Woodwardia", have fertile fronds that are markedly taller than the sterile.
 Still others, such as "Osmunda cinnamomea" (Cinnamon fern), or plants of the family Onocleaceae, have fertile fronds that are completely different from the sterile.
Polypodium is a genus of 75–100 species of true ferns, widely distributed throughout the world, with the highest species diversity in the tropics.
 The name is derived from Ancient Greek "poly" (πολύ) "many" + "podion" (πόδιον) "little foot", on account of the foot-like appearance of the rhizome and its branches.
 They are commonly called polypody or rockcap fern, but for many species unique vernacular names exist.
Leptosporangiate ferns are 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.
Mukdenia is a genus of plants in the saxifrage family, Saxifragaceae, consisting of 2 species.
 They are native to woodland areas of east Asia and Japan.
Polypodium appalachianum is a fern species native to eastern North America.
 Sometimes called the Appalachian polypody or Appalachian rockcap fern, it is very similar in appearance to "Polypodium virginianum".
 For years, "P. virginianum" -- long considered a variety of the British "Polypodium vulgare" -- was recognized as having cryptic races, with diploid, triploid, and tetraploid representatives.
 Since the triploid specimens bore abortive spores, it was apparently the hybrid between the diploid and tetraploid groups.
 In 1991, it was resolved that the type of "P. virginianum" was the tetraploid series, and that it is an allotetraploid species of hybrid origin, with the diploid species as one parent.
 The diploid species was then named "P. appalachianum".
 The other parent of "P. virginianum" was found to be "Polypodium sibiricum".
 The tetraploid of hybrid derivation tolerates warmer climates than either parent.
Clostridium tetani is a rod-shaped, anaerobic species of pathogenic bacteria, of the genus "Clostridium".
 Like other "Clostridium" genus species, it is Gram-positive, and its appearance on a gram stain resembles tennis rackets or drumsticks.
 "C. tetani" is found as spores in soil or in the gastrointestinal tract of animals.
 "C. tetani" produces a potent biological toxin, tetanospasmin, and is the causative agent of tetanus, a disease characterized by painful muscular spasms that can lead to respiratory failure and, in up to 10% of cases, death.
Tatrasuchus is an extinct genus of temnospondyl amphibian from the Middle Triassic of Poland.
 It is classified as a member of the family Cyclotosauridae or Mastodonsauridae.
 It is closely related to the genus "Cyclotosaurus".
 The type species, "Tatrasuchus kulczyckii", was named in 1996.
 Damiani (2001) considered genus "Kupferzellia" Schoch (1997) from Middle Triassic of Germany to be a junior synonym of "Tatrasuchus", and recombined its type species, "K. wildi" as the second species of "Tatrasuchus".
 This classification was followed by some authors, e.g. Fortuny "et al." (2011); other authors, e.g. Schoch (2008), maintain "Tatrasuchus" and "Kupferzellia" as distinct genera.
Phlebodium is a small genus of two to four species of ferns, native to tropical and subtropical regions of the Americas.
 The genus is closely related to "Polypodium", and the species were formerly included in that genus.
Lophosoria quadripinnata is a species of fern that, according to DNA molecular analysis, belongs to the Dicksoniaceae family, where it is placed in the genus "Lophosoria".
 It is found in the Americas spanning from Cuba and Mexico to Chile.
 In Chile it is present in the area between Talca and Aysén including Juan Fernández Islands.
 In Argentina it grows only in the humid valleys of western Neuquén and Río Negro Province.
 Diamondleaf fern is a common name.
 In Spanish it is known as 'ampe' (from the Mapudungun añpe) or palmilla, but one has to remember that there are several species of ferns called "palmillas" that have larger or smaller fronds, and which grow in colder climates.
 It is a medium-sized plant, growing to about 4–5 feet (though 10–12 feet in a sheltered place at Arduaine Garden in Argyll, Scotland) and even though the rhizome does not grow a trunk, it is clearly related to the other tree ferns due to features that were apparently already present in their common ancestor, like 'pneumathodes', and the rhizome which changed from the dorsiventral symmetry typical of the other ferns, to a radial symmetry typical of tree ferns.
 Their large and multiple pinnate fronds, with the petiole raised adaxially, and the hairs on the rhizome and lower part of the petioles, also resemble those of tree ferns.
 To identify the species, use the position and characteristics of the spores found on the fertile fronds.
 The genus already existed in the Cretaceous Period in southern Gondwana according to fossil remains found in Antarctica.
 The species is well known as an ornamental plant.