(Initiated by a response from Amy Edgell)
Dogtooth operates like a fairy tale or a parable, it is not a direct representation of reality, it is more designed to get us to reflect on social issues/problems/practices that are generally hard for us to understand because they are such part of our naturalized everyday lives.
While we could consider Dogtooth to be about "isolated" communities, we don't have to necessarily directly relate it to such an absolute environment. It should also give us pause in thinking about how we, in our mainstream social realities, attempt to isolate, manipulate, ignore and distort the realities about the world out of a fear for the results of hidden truths. In fact we could even apply it to many broader social institutions/groups/practices (religion, schools, universities, governments, sex education, corporations, official histories, etc... ) that practice what the father does in this tale. Likewise, not so different from the children in Dogtooth, what kind of stunted, illusionary, or, even dangerous, people are produced by institutions/groups/practices based on deception, ignorance and manipulation?