Question: Are Alloxylon and Schoenoplectus both types of tree?

Context paragraphs:
Bicycle tree: A bicycle tree or "cycle tree" or "bike tree" is a bicycle parking system that resembles a tree in shape.  There are a few types that have been developed.

Alloxylon pinnatum: Alloxylon pinnatum, commonly known as Dorrigo waratah, is a tree of the family Proteaceae found in warm-temperate rainforest of south-east Queensland and northern New South Wales in eastern Australia.  It has shiny green leaves that are either pinnate (lobed) and up to 30 cm long, or lanceolate (spear-shaped) and up to 15 cm long.  The prominent pinkish-red flower heads, known as inflorescences, appear in spring and summer; these are made up of 50 to 140 individual flowers arranged in corymb or raceme.  These are followed by rectangular woody seed pods, which bear two rows of winged seeds.

Computational phylogenetics: Computational phylogenetics is the application of computational algorithms, methods, and programs to phylogenetic analyses.  The goal is to assemble a phylogenetic tree representing a hypothesis about the evolutionary ancestry of a set of genes, species, or other taxa.  For example, these techniques have been used to explore the family tree of hominid species and the relationships between specific genes shared by many types of organisms.  Traditional phylogenetics relies on morphological data obtained by measuring and quantifying the phenotypic properties of representative organisms, while the more recent field of molecular phylogenetics uses nucleotide sequences encoding genes or amino acid sequences encoding proteins as the basis for classification.  Many forms of molecular phylogenetics are closely related to and make extensive use of sequence alignment in constructing and refining phylogenetic trees, which are used to classify the evolutionary relationships between homologous genes represented in the genomes of divergent species.  The phylogenetic trees constructed by computational methods are unlikely to perfectly reproduce the evolutionary tree that represents the historical relationships between the species being analyzed.  The historical species tree may also differ from the historical tree of an individual homologous gene shared by those species.

Thespesia populnea: Thespesia populnea, commonly known as the Indian tulip tree, Pacific rosewood, or Portia tree , is species of flowering plant in the mallow family, Malvaceae.  It is a small tree or arborescent shrub that has a pantropical distribution, found on coasts around the world.  However, the Portia tree is probably native only to the Old World, and may have originated in India.  Nowadays, its wood is mainly used in making furniture because of its good ability to undergo carving.  The wood from the tree was used by early Tamil people to make instruments in ancient Tamilakam.  It is possibly indigenous to the Hawaiian Islands and elsewhere in the Pacific, but may have been spread by early Polynesians for its useful wood and bast fibres.  The Portia tree reaches a height of 6 - tall and a trunk diameter of 20 - .  It grows at elevations from sea level to 275 m in areas that receive 500 - of annual rainfall.  The Portia tree is able to grow in the wide range of soil types that may be present in coastal environments, including soils derived from quartz (sand), limestone, and basalt; it favours neutral soils (pH of 6–7.4).

Schoenoplectus: Schoenoplectus (club-rush [Old World species], bulrush or tule [New World species]) is a genus of plants in the sedges with a cosmopolitan distribution.  Note that the name bulrush is also applied to species in the unrelated genus "Typha" as well as to other sedges.  The genus "Schoenoplectus" was formerly considered part of "Scirpus", but recent phylogenetic data shows that they are not closely related.

Schoenoplectus americanus: Schoenoplectus americanus (syn.  "Scirpus americanus") is a species of flowering plant in the sedge family known by the common names chairmaker's bulrush and Olney's three-square bulrush.  It is native to the Americas, where it is known from Alaska to Nova Scotia and all the way into southern South America; it is most common along the East and Gulf Coasts of the United States and in parts of the western states.  It grows in many types of coastal and inland wetland habitat, as well as sagebrush, desert scrub, chaparral, and plains.  This rhizomatous perennial herb easily exceeds two meters in height.  The stiff stems are sharply three-angled and usually very concave between the edges.  Each plant has three or fewer leaves which are short and narrow.  The inflorescence is a small head of several spikelets which may be brown to bright orange, red, purplish, or pale and translucent.  They have hairy edges.  The fruit is a brown achene.  The plant reproduces sexually by seed and colonies spread via vegetative reproduction, sprouting from the rhizomes.

Alloxylon wickhamii: Alloxylon wickhamii is a rainforest tree to 30 m tall in the family Proteaceae.  It has been found only (endemic) in the Wet Tropics of Queensland.

Alloxylon flammeum: Alloxylon flammeum, commonly known as the Queensland tree waratah or red silky oak, is a medium-sized tree of the family Proteaceae found in the Queensland tropical rain forests of northeastern Australia.  It has shiny green elliptical leaves up to 18 cm (7.2 in) long, and prominent orange-red inflorescences that appear from August to October, followed by rectangular woody seed pods that ripen in February and March.  Juvenile plants have large (up to 25 cm (10 in) long) deeply lobed pinnate leaves.  Previously known as "Oreocallis wickhamii", the initial specimen turned out to be a different species to the one cultivated and hence a new scientific name was required.  Described formally by Peter Weston and Mike Crisp in 1991, "A. flammeum" was designated the type species of the genus "Alloxylon".  This genus contains the four species previously classified in "Oreocallis" that are found in Australasia.

Celtic sacred trees: Many types of trees found in the Celtic nations are considered to be sacred, whether as symbols, or due to medicinal properties, or because they are seen as the abode of particular nature spirits.  Historically and in folklore, the respect given to trees varies in different parts of the Celtic world.  On the Isle of Man, the phrase ‘fairy tree’ often refers to the elder tree.  The medieval Welsh poem "Cad Goddeu (The Battle of the Trees)" is believed to contain Celtic tree lore, possibly relating to the "crann ogham", the branch of the ogham alphabet where tree names are used as mnemonic devices.

Alloxylon: Alloxylon is a genus of four species in the family Proteaceae of mainly small to medium-sized trees.  They are native to the eastern coast of Australia, with one species, "A. brachycarpum" found in New Guinea and the Aru Islands.  The genus is a relatively new creation, being split off from "Oreocallis".  The name is derived from Ancient Greek "allo-" "other" or "strange" and "xylon" or "wood" due to their unusual cell architecture compared with the related genera "Telopea" and "Oreocallis".  In Australia, they are known as tree waratahs due to similarities in the inflorescences between them and the closely related "Telopea".

Supporting paragraphs: Alloxylon Schoenoplectus
Answer: no