Although one can obviously think of counter-examples, we would generally expect that the more specific term dog can only be used in contexts where animal can be used and that the more general term animal might be used in all of the contexts where dog is used and possibly others.
we might expect that distributional generality is correlated with semantic generality -a word has high recall/low precision retrieval of its hyponyms' co-occurrences and high precision/low recall retrieval of its hypernyms' co-occurrences.