A supposition is different from an assumption. A supposition is an unproven hypothesis, which may be more or less supported by evidence or purely speculative. Assumptions are a set of facts or circumstances that are assumed (rather than established by direct evidence) on which conclusions or suppositions have been based.
A supposition that is presented with no supporting evidence should go in the Research Notes section. However, a supposition that is supported by reasonable evidence/argument can, and probably should, go in the bio, so long as the basis for that supposition is presented/discussed and the discussion indicates that it is a supposition (eg uses "may") rather than a proven conclusion.
Any assumptions on which statements, conclusions, hypotheses discussed a bio are based, belong in the discussion in the bio rather than in the Research Notes section.