Young animals are dependent on their parents for food and shelter. The preposition "for" is often used to indicate purpose. In this example, food and shelter are the purpose of the young animals' dependence. "For" is also used in many other situations and has many meanings. I think it's best to look at some common meanings and examples. https://dictionary.cambridge.org/dictionary/english/for

зависеть from кого-то in чём-то это попытка прилепить родную лексику в английский язык правильно ... on... for...

for

I would use "for".... Young animals are dependent on their parents for food and shelter.

Probably “giving” I think. If you put “giving” on the blank, it means that young animals ask for food and shelter from their parents. Therefore preposition is not needed in this sentence.