Etymology
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symbiosis (n.)
1876, as a biological term, "union for life of two different organisms based on mutually benefit," from Greek symbiosis "a living together," from symbioun "live together," from symbios "(one) living together (with another), partner, companion, husband or wife," from assimilated form of syn- "together" (see syn-) + bios "life" (from PIE root *gwei- "to live"). Given a wider (non-biological) sense by 1921. An earlier sense of "communal or social life" is found in 1620s. A back-formed verb symbiose is recorded from 1960.
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symbiotic (adj.)
1882, in biology, from stem of symbiosis + -ic. Of human activities from 1951. Related: Symbiotical; symbiotically.
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Symbionese (adj.)
in Symbionese Liberation Army (SLA), name adopted by a socialist revolutionary group active in U.S. 1972-76, coined from simbion "an organism living in symbiosis, from symbioun (see symbiosis) + people-name ending -ese.
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*gwei- 
also *gweie-, Proto-Indo-European root meaning "to live."

It forms all or part of: abiogenesis; aerobic; amphibian; anaerobic; azo-; azoic; azotemia; bio-; biography; biology; biome; bionics; biopsy; biota; biotic; cenobite; Cenozoic; convivial; couch-grass; epizoic; epizoon; epizootic; macrobiotic; Mesozoic; microbe; Protozoa; protozoic; quick; quicken; quicksand; quicksilver; quiver (v.) "to tremble;" revive; survive; symbiosis; viable; viand; viper; vita; vital; vitamin; victuals; viva; vivace; vivacious; vivarium; vivid; vivify; viviparous; vivisection; whiskey; wyvern; zodiac; Zoe; zoetrope; zoic; zoo-; zoolatry; zoology; zoon; zoophilia; zoophobia; zooplankton.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit jivah "alive, living;" Old Persian *jivaka- "alive," Middle Persian zhiwak "alive;" Greek bios "one's life, course or way of living, lifetime," zoe "animal life, organic life;" Old English cwic, cwicu "living, alive;" Latin vivus "living, alive," vita "life;" Old Church Slavonic zivo "to live;" Lithuanian gyvas "living, alive," gyvata "(eternal) life;" Old Irish bethu "life," bith "age;" Welsh byd "world."
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mutualism (n.)

1845, in reference to the doctrine of French anarchist/socialist Pierre-Joseph Proudhon (1809-1865) that individual and collective well-being is attainable only by mutual dependence, from French mutuellisme. In biology, "a symbiosis in which two organisms living together mutually and permanently help and support one another," from 1876, from mutual + -ism.

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