[Wikipedia] Mediterranean Basin & Macaronesia region native: Distribution This plant is native to the Mediterranean Basin and the Macaronesia region: (Canary Islands, Madeira, Cape Verde). It is widely naturalized elsewhere in the temperate world, including the United States. There is an endemic subspecies in the local flora of the Columbretes Islands of the western Mediterranean. (link added by Mary Ann Machi)

[Cal-IPC] Invasiveness: Lobularia maritima (sweet Alyssum) is a perennial (family Brassicaceae) found along the coast of California and in the San Francisco Bay area. Sweet Alyssum is a common ornamental plant that has escaped cultivation and invaded disturbed coastal dunes, scrub, bluffs, prairies and riparian areas. It has a long flowering season, and appears to have the ability to rapidly colonize suitable habitats. This Mediterranean native may crowd out native plants in some habitats. (link added by Mary Ann Machi)