In our SCUBA survey of Perseus, we find that the fraction of protostellar cores increases towards higher masses and the most massive cores are all protostellar. In this paper we consider the possible explanations of this apparent mass dependence in the evolutionary status of these cores, and the implications for protostellar evolution and the mapping of the embedded core mass function (CMF) onto the stellar IMF. We consider the following potential causes: dust temperature; selection effects in the submillimetre and in the mid-infrared observations used for pre/protostellar classification; confusion and multiplicity; transient cores; and varying evolutionary timescales. We develop Core Mass Evolution Diagrams (CMEDs) to investigate how the mass evolution of individual cores maps onto the observed CMF. Two physical mechanisms -- short timescales for the evolution of massive cores, and continuing accumulation of mass onto protostellar cores -- best explain the relative excess of protostars in high mass cores and the rarity of massive starless cores. In addition, confusion both increases the likelihood that a protostar is identified within a core, and increases mass assigned to a core. The observed pre/protostellar mass distributions are consistent with faster evolution and a shorter lifetime for higher-mass prestellar cores. We rule out longer timescales for higher-mass prestellar cores. The differences in the prestellar and protostellar mass distributions imply that the prestellar CMF (and possibly the combined pre+protostellar CMF) should be steeper than the IMF. A steeper prestellar CMF can be reconciled with the observed similarity of the CMF and the IMF in some regions if a second opposing effect is present, such as the fragmentation of massive cores into multiple systems.
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