What is a biological approach to determining when a mother and her conceptus become separate individuals?

Electroencephalography.

Explanation:

Electroencephalography is used to measure brain activity in terms of electrical activity. It is done by attaching electrodes on the scalp, or sometimes by placing electrodes directly in the brain. Using electroencephalography can help determine when the fetus starts having its own brain activities, which means that it is now a separate entity distinguishable from its mother. Using electroencephalography to see brain waves can give us a deeper insight into the age old complicated issue of when a mother and her conceptus become separate individuals.