Applying to EEB PhDs at Princeton

Does anyone have any idea how competitive this specific program is? I know that the overall acceptance rate for the Natural Sciences is about 14%.

I have a professor who considers me a good candidate for his lab and would take me on. But the difficulty of actually being accepted to such a competitive school is very daunting.

General advice would be appreciated. EEB-specific and/or Princeton-specific advice would be very appreciated.

Thank you!