There aren't going to be a study on there because the most relevant feature is evolutionary adaptation. Going deep on a single topic works great when that topic is in vogue, but leaves you open to disastrous results if that topic loses its sheen (or becomes over-subscribed with competition). Think, for example, of those poor engineers who invested their lives in BlackBerry systems. Conversely, seeking to build a wide range of skills necessarily reduces your ability to go deep on any one topic, but gives you the ability to more quickly react to shifts in the industry.

Thus, anecdotally at least, my company (and I) advise our staff to become 'T-shaped' - have one area of deep competence, but familiarize yourself with other areas at least to the extent that you can have an intelligent conversation on the topic. This leaves you desirable for your knowledge but not forever tied to that one area.

I know you wanted a study, and the above is anecdotal, but it's based my experience recruiting and many discussions with candidates.