Melaluca (Melaleuca quinquenervia) comes from Australia. However, non-native can also mean plants from another region (within the same country). Smooth cordgrass (Spartina alterniflora), a desirable native plant on the U.S. Atlantic coast, is invasive on the Pacific coast, covering oyster beds and other vital habitat.pproximately 1,400 of Floridaâs plants are non-native plants. Many non-natives are not invasive and support human health and economic interests such as crop production and landscaping.