Osteospermum, commonly known as African daisy, is an evergreen subshrub or perennial that grows in sheltered locations in subtropical regions, such as U.S. Department of Agriculture plant hardiness zones 10 and 11.Where summers are cool, osteospermum blooms for a longer period of time.ip. 1  Osteospermum fruticosum, trailing African daisy, is called freeway daisy in parts of California where it is commonly used as a median plant for its ability to withstand stressful conditions and for its frequency of bloom.