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Agastache are wonderful herbs, in the Mint Family (Lamiaceae), with fragrant foliage and beautiful flowers. Most species are native to North America, but there is one mesic species, Agastache rugosa, native to eastern Asia, Taiwan and Japan.
All Agastache benefit form good drainage, but species from more mesic areas such as northern & eastern North America and Asia are much more tolerant of frequent watering and wetter conditions. These are primarily bee-pollinated plants with blue-purple or white flowers. Anise-hyssop (Agastache foeniculum) is probably the best known species.
The species and hybrids from the southwestern U.S. and Mexico, such as Agastache rupestris, benefit more from sharp drainage and somewhat drier conditions. Interestingly, many of these species are adapted for hummingbird pollination.
These are just generalizations to consider. Preferred cultural conditions are a blurry line, especially now that there are many hybrids of mixed parentage.
Note: Agastache is pronounced with four syllables. The 'ch' is a hard K sound, and the final 'e' is pronounced.