Both the complexity of the phenomenon known as extinction
and the vastness of the biosphere, having prompted many scientists to call for a large increase in the number of biologists working both in the field and in laboratories to clarify the relationships among the planet's many endangered life-forms.
(A) and the vastness of the biosphere,
having prompted many scientists to call for a large increase in the number of biologists working both
(B) and the vastness of the biosphere
has prompted many scientists calling for a large increase in the number of biologists both working
(C) and the vastness of the biosphere have prompted many scientists to call for a large increase in the number of biologists working both
(D)
as well as the vastness of the biosphere have prompted many scientists to call for a large increase in the number of biologists who both work
(E)
as well as the vastness of the biosphere has prompted many scientists to call for a large increase in the number of biologists who work both
The idiom is "both X AND Y" not "both x as well as y": out D E. In A having modifies the first part, and in B the subject requires a plural verb.
C is Correct