Question: Are both Carludovica and Beech native to the same continents?

Context paragraphs:
Carludovica: Carludovica is a genus in the family Cyclanthaceae.  It is native to tropical America, from southern Mexico and Guatemala to Ecuador and Bolivia.  "Carludovica" is named in honor of Charles IV of Spain and his wife Maria Luisa of Parma.

Beech: Beech ("Fagus") is a genus of deciduous trees in the family Fagaceae, native to temperate Europe, Asia and North America.  Recent classification systems of the genus recognize ten to thirteen species in two distinct subgenera, "Engleriana" and "Fagus".  The "Engleriana" subgenus is found only in East Asia, and is notably distinct from the "Fagus" subgenus in that these beeches are low-branching trees, often made up of several major trunks with yellowish bark.  Further differentiating characteristics include the whitish bloom on the underside of the leaves, the visible tertiary leaf veins, and a long, smooth cupule-peduncle. " Fagus japonica", "Fagus engleriana", and the species "F. okamotoi", proposed by the botanist Chung-Fu Shen in 1992, comprise this subgenus.  The better known "Fagus" subgenus beeches are high-branching with tall, stout trunks and smooth silver-grey bark.  This group includes "Fagus sylvatica", "Fagus grandifolia", "Fagus crenata", "Fagus lucida", "Fagus longipetiolata", and "Fagus hayatae".  The classification of the European beech, "Fagus sylvatica" is complex, with a variety of different names proposed for different species and subspecies within this region (for example "Fagus taurica", "Fagus orientalis", and "Fagus moesica").  Research suggests that beeches in Eurasia differentiated fairly late in evolutionary history, during the Miocene.  The populations in this area represent a range of often overlapping morphotypes, though genetic analysis does not clearly support separate species.

Fagus crenata: Fagus crenata, known as the Japanese beech, Siebold's beech, or buna, is a deciduous tree of the beech genus, "Fagus", of the family Fagaceae.  It is native to Japan, where it is widespread and often one of the dominant trees of Japan's deciduous forests.  It is found from the Oshima Peninsula in Hokkaidō south to the Ōsumi Peninsula in Kyūshū.  In north-east Honshū it grows in large stands from sea level up to 1400 metres but in the south-west of its range it is restricted to mountainous areas and occurs in small, isolated populations.  It grows in well-drained, loamy or sandy soils.

Fagus engleriana: Fagus engleriana, also known as Chinese beech, is a species of beech native to central and eastern China (Anhui, Guangxi, Guizhou, Henan, Hubei, Hunan, Shaanxi, Sichuan, Yunnan, and Zhejiang provinces) where it grows in broad-leaved and mixed forests.  It can reach 25 m in height.

Hainich National Park: Hainich National Park (German: "Nationalpark Hainich" ), founded on December 31, 1997, is the 13th national park in Germany and the only one in Thuringia.  One of the main objectives of the park is the protection of native beech forest.  In 2011, the park was added to the Primeval Beech Forests of the Carpathians and the Ancient Beech Forests of Germany World Heritage Site.

Fagus orientalis: Fagus orientalis, commonly known as the Oriental beech, is a deciduous tree in the beech family Fagaceae.  It is native to Eurasia, in Eastern Europe and Western Asia.

Fagus grandifolia: Fagus grandifolia (American beech or North American beech) is the species of beech tree native to the eastern United States and extreme southeast Canada.  The genus name "Fagus" is Latin for "beech", and the species name "grandifolia" comes from "grandis" "large" and "folium" "leaf".

Hypsizygus tessellatus: Hypsizygus tessellatus or buna shimeji is an edible mushroom native to East Asia.  It is cultivated locally in temperate climates in Europe, North America and Australia and sold fresh in super markets.  In nature, shimeji are gilled mushrooms that grow on wood.  Most often the mushroom is found on beech trees, hence the common name, Beech Mushroom.  They are often small and thin in appearance and popular in many nations across the world.

Cyttaria gunnii: Cyttaria gunnii, commonly known as the myrtle orange or beech orange, is an orange-white coloured and edible ascomycete fungus native to Australasia.  It is a specific parasite of myrtle beech ("Nothofagus cunninghamii") trees.

Fagus japonica: Fagus japonica, known as the Japanese Blue Beech or in Japanese as inubuna ("dog buna") or kurobuna ("black buna"), is a deciduous tree of the beech family Fagaceae.  It is native to Japan, where it is one of the main tree species in natural deciduous forests particularly on the Pacific side of the country.

Supporting paragraphs: Carludovica Beech
Answer: no