^{Disclaimer - Even though my personal views are well-established, I'd like to point out that I am not out to make a point with this question, and I am absolutely not out to establish whether any specific perspective is true. I am simply curious about this. I know the atheistic views, I know the day-age theory, the gap theory, etc, but I've never heard an answer to this, good or bad. I'd like to know what the answer is from those who genuinely hold this view.}

Theistic Evolution defined from Wikipedia:

Theistic evolution or evolutionary creation is a concept that asserts that classical religious teachings about God are compatible with the modern scientific understanding about biological evolution. In short, theistic evolutionists believe that there is a God, that God is the creator of the material universe and (by consequence) all life within, and that biological evolution is simply a natural process within that creation. Evolution, according to this view, is simply a tool that God employed to develop human life. According to the American Scientific Affiliation:

In general, most Christian teachings assert that the relationship between God and Man is unique, and different than the relationship between God and other animals.

Assuming that theistic evolution is a valid point of view (and I'm not arguing that it's not), are there any established teachings from any denomination or proponents that explain at what point we evolved enough to have a unique relationship with God?

Barring that, what characteristics had to be present in order to have said relationship. The ability to speak? Cognitive reasoning?

The Wikipeda article lists several denominations that hold a theistic evolutionary view. I'd like answers/reasoning from any of those perspectives, or from any established organization that holds/defends this view.