Expected MCB Student Activity by Department

Assumptions

Example: Biochemistry

Expectation value for the number of students in the department = (10/83)(95) = 11.4
Expectation value for the number of MCB students in the department = 11.4 - 10 = 1.4
Since basic-science faculty are obliged to take departmental students first, MCB students fill only those slots not occupied by departmental students.  On the basis of faculty representation alone, Biochemistry would expect to have six [(10/83)(52) = 6] MCB students.  However, that analysis does not take into account the facts that a lab can support only a finite number of students and that labs in non-basic-science departments have more vacancies available only to MCB students.
My informal poll finds that Biochemistry trained 5 PhD students from the MCB Program during the period 1993-1999, and there was an average of three (3) MCB students in the department at any one time.
After reducing expectations to account for occupancy of departmental slots, Biochemistry has recruited more than twice the expected number of MCB students.
Expectation value for the number of MCB student rotations per year = (1.4/52)(30) = 0.8

My informal poll finds that Biochemistry trained 13 rotation students from the MCB Program during the period 1993-1999, that is, an average of 2.2 students per year.

Biochemistry has trained more than twice the expected number of rotation students.
 

Why doesn't a basic-science department recruit MCB students to the level of its faculty representation in the MCB program?

Each lab would have to support more students.  Departmental fellowships might be expected to support higher occupancy of basic-science labs.  However, like MCB fellowships, they typically support only the first couple of years of training.  Thus, the number of students per lab may be limited by extramural funding.  Other factors that potentially limit occupancy include the number of available projects, faculty contact time, and laboratory resources.

Will unification of recruitment and 1st-year training of graduate students reduce the number of students in the Biochemistry department?

Yes.  The number of students in the department should drop to the total expected [(10/83)(95) = 11.4], as opposed to the current level (10 departmental + 3 MCB), a loss of two (1.6) students.