Shapiro was born in to a Jewish family and was educated in Boston, Massachusetts.

While he was a senior at Harvard he was awarded a graduate fellowship from Yale in 1923 to pursue a genetic study of the descendants of the mutineers of HMS Bounty.

After completing his graduate work in 1926 he went to work at the American Museum of Natural History in New York, and while there conducted a few field trips.

Dr. Shapiro was married in 1938, and he taught at Columbia University from 1938 to 1973.

He was president of the American Eugenics Society from 1956-63.