word-forming element, especially in scientific compounds, meaning "life, life and," or "biology, biology and," or "biological, of or pertaining to living organisms or their constituents," from Greek bios "one's life, course or way of living, lifetime" (as opposed to zoe "animal life, organic life"), from PIE root *gwei- "to live."
The correct usage is that in biography, but since c. 1800 in modern science it has been extended to mean "organic life," as zoo-, the better choice, is restricted in modern use to animal, as opposed to plant, life. Both are from the same PIE root. Compare biology.
1620s, "science of arranging military forces for combat," from Modern Latin tactica (17c.), from Greek taktike techne "art of arrangement," noun use of fem. of taktikos "of or pertaining to arrangement," especially "tactics in war," adjective to taxis "arrangement, an arranging, the order or disposition of an army, battle array; order, regularity," verbal noun of tassein "arrange," from PIE root *tag- "to touch, handle."
<a href="https://www.etymonline.com/word/biotaxy">Etymology of biotaxy by etymonline</a>
Harper, D. (n.d.). Etymology of biotaxy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/biotaxy