As heart rate increases, blood pumps faster through your body and you start to have better reflexes. You brain sends out signals to your legs. This can be an example of the flight or fight response. Your leg and arm muscles tighten up, blood is decreasing from lesser needed spots such as your chest, back, and head areas.
This should be an example of genetic drift.
The brown spotted deer would spread their genes more than the white spotted ones which would eventually lead to them completely overpowering genetically the white deer in future generations.