This is a blind guess but I wonder if it is similar to the Nederlandse structuring of "[...] in de natuur." --> "[...] in nature."
Your guess is correct. The short answer for this is that articles in English are weird (for a Germanic / European language).
The slightly longer answer is that in the Middle Ages Britain got repeatedly invaded by Scandinavian peoples (these days also known as "Vikings"), by some speaking Norse or German dialects, but a bit later and most notably by the French-speaking "Normans". In the process English changed quite a bit and became increasingly creolised. One effect of this was that gender as a grammatical category lost a lot of its markers (and vanished more and more over time). Of the former three different articles of Old English, "se" (formerly masculine) survived and later changed to "the", while "þæt" (formerly neuter) became "that" and "sēo" (formerly feminine) might have turned into "she". Since this also meant that articles had essentially lost one of their core functions, namely that of marking gender, they somehow also changed in other regards in the process.
with my smartphone i can't see the helpful links like yours. You have an idea what i can do?
I think "The bear lives out in the WILD" is a more natural translation to English.
I don't know how wild nature has to be to be counted as the WILD/the WILDERNESS, but in norwegian there is definitely a difference between naturen og villmarken (though they overlap).
A bear might live "i naturen", but also "i villmarken". But "villmarken" is farther from civilization.
Wild is short for wilderness and has a overlapping but slightly different meaning than nature. It means untouched nature. You only get that deeper out. Villmarken sounds much closer to wilderness based on what kim-gab said. Translating naturen as th wild is just wrong. I don't understand why so many native English speakers especially Americans don't know what words mean.
I have never heard any English speaker, Amerikaner or otherwise say that something lives out in nature. Type "the bear lives out in nature" into Google and see if you find that construction used by anyone.