Question: Are both Dodecatheon and Bloomeria native to North America?

Context paragraphs:
Emerald ash borer: Agrilus planipennis, commonly known as the emerald ash borer, is a green buprestid or jewel beetle native to northeastern Asia that feeds on ash species.  Females lay eggs in bark crevices on ash trees, and larvae feed underneath the bark of ash trees to emerge as adults in one to two years.  In its native range, it is typically found at low densities and does not cause significant damage to trees native to the area.  Outside its native range, it is an invasive species and is highly destructive to ash trees native to northwest Europe and North America.  Prior to being found in North America, very little was known about emerald ash borer in its native range; this has resulted in much of the research on its biology being focused in North America.  Local governments in North America are attempting to control it by monitoring its spread, diversifying tree species, insecticides, and biological control.

Dodecatheon poeticum: Dodecatheon poeticum is commonly known as the poet's shooting star or the Narcissus shooting star.  "D. poeticum" is a species of the genus "Dodecatheon" which is native to the states of Oregon and Washington in western North America.  The genus "Dodecatheon" contains herbaceous flowering plants and is also a part of the primrose family Primulaceae.  This plant has basal clumps of leaves and drooping flowers that occur at the apex of tall stems that rise from where the leaves join.

Dodecatheon jeffreyi: Dodecatheon jeffreyi is a species of flowering plant in the primrose family known by the common names Sierra shooting star, Jeffrey's shooting star, and tall mountain shooting star.  This wildflower is native to western North America from California to Alaska to Montana, where it grows in mountain meadows and streambanks.  This is a thick-rooted perennial with long, slightly wrinkled leaves around the base.  It erects slim, tall, hairy stems which are dark in color and are topped with inflorescences of 3 to 18 showy flowers.  Each flower nods, with its pointed center aimed at the ground when fresh, and becomes more erect with age.  It has four or five reflexed sepals in shades of pink, lavender, or white which lie back against the body of the flower.  Each sepal base has a blotch of bright yellow.  From the corolla mouth protrude large dark anthers surrounding a threadlike stigma.  The flowers of this species were considered good luck by the Nlaka'pamux people, who used them as amulets and love charms.  Dodecatheon jeffreyi is named in honor of John Jeffrey.

Native Tour: The Native Tour (also known as the Native Summer Tour in North America or Native Fall Tour in Europe) is the third headlining concert tour by American pop-rock band, OneRepublic in support of their third studio album, "Native" (2013).  OneRepublic were joined on the Native Summer leg of the tour by, The Script and American Authors, and on the European "Native Fall Tour" leg by Kongos.  The tour has traveled across five continents; Asia, Europe, Oceania, North America, and Africa.  The tour began on April 2, 2013, in Milan, Italy and finished on September 20, 2015, in São Paulo, Brazil.

Bloomeria: Bloomeria, a geophyte in the family Asparagaceae, subfamily Brodiaeoideae, was named for Hiram Green Bloomer (1819–1874) an early San Francisco botanist.  It consists of three species native to California and Baja California:

Dodecatheon: Dodecatheon is a genus of herbaceous flowering plants in the family Primulaceae.  The species have basal clumps of leaves and nodding flowers that are produced at the top of tall stems rising from where the leaves join the crown.  The genus is largely confined to North America and part of northeastern Siberia.  Common names include shooting star, American cowslip, mosquito bills, mad violets, and sailor caps.  A few species are grown in gardens for their showy and unique flower display.

Dodecatheon hendersonii: Dodecatheon hendersonii is a species of flowering plant in the family Primulaceae, native to western North America, from California north to southern British Columbia and Idaho.  In California, it occurs in the northwest (except the north coast), the Cascade Range, the Sierra Nevada foothills, the Central Valley, the San Francisco Bay Area, the north Inner South Coast Ranges, and the San Bernardino Mountains.  It is generally found in open woodlands, from sea level in British Columbia, up to 1900 m altitude in California.  Common names include broad-leaved shooting star, Henderson's shooting star, mosquito bills, and sailor caps.

Cakile: Cakile is a genus within the flowering plant family Brassicaceae.  Species in this genus are commonly known as searockets, though this name on its own is applied particularly to whatever member of the species is native or most common in the region concerned, the European searocket "Cakile maritima" in Europe, and the American searocket "C. edentula" in North America.  The genus is native to Europe, Asia and North America, but the European searocket has been introduced into North America and has spread widely on both east and west coasts; in many places it is replacing the native "C. edentula", and is regarded as an undesirable invasive species.

Dodecatheon frigidum: Dodecatheon frigidum, commonly called the western arctic shootingstar, is a plant species found in arctic and subarctic regions in the northwestern part of North America and in Asiatic Russia.  It is common across much of Alaska, and has also been reported from Yukon, Northwest Territories, British Columbia, northern Saskatchewan, and on the Chukotsk Peninsula in the Russian Far East (often erroneously regarded as part of Siberia).  It is usually found in moist areas such as bogs, lakeshores, riverbanks, moist meadows, and heathcliff tundras.  It can found on melting snow on or near permafrost.

Dodecatheon meadia: Dodecatheon meadia is a species of flowering plant in the family Primulaceae, native to North America.  It is found in the American South, as well as the Upper Midwest, Kansas, New York, Pennsylvania and the Canadian province of Manitoba.  It grows in woods and prairies and tolerates partial shade.

Supporting paragraphs: Dodecatheon Bloomeria
Answer: yes