"When challenged on this issue most anthropologists argue that for questions about animals per se one had better turn to sciences such as biology or ethology. To point out to them that in addition to a human-animal relationship there also exists something like an animal-human relationship, and that totally ignoring the latter will lead to a one-sided subject-object approach is a waste of time. As present the anthropocentrism in anthropology goes virtually unchallenged."
http://www.upc-online.org/thinking/anthro.htm
In your context you may also say "human-animal"

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Note added at 54 min (2007-11-11 12:57:15 GMT)
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I think "interaction" could be a good option for "relationship"
"La Zooantropologia ha come obbiettivo lo studio del rapporto uomo-animale negli eventi di interazione e relazionali e la valutazione per la prima volta dei contributi apportati all’uomo in questa relazione."
http://www.aoc-animals.it/zooantropologia.htm

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Note added at 59 min (2007-11-11 13:02:39 GMT)
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Some occurrences in Native English for zoo-anthropology or anthropo-zoology (but they seem used like neologisms or linguistic inventions:
"A new science one might call anthropo-zoology or zoo-anthropology. This science is a deep study of human beings, of animals, of their mutual relations, present and potential. In this discipline, researchers encourage close relations with the animal, and study the developing relation between human and so-called "beast"."
http://www.interspecies.com/pages/book4.html

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Note added at 1 ora (2007-11-11 13:04:57 GMT)
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Anthropozoology of Equids
http://www.arch.cam.ac.uk/~ml12/download/chap_15_Levine.pdf