The progenitor set of present-day early-type galaxies
  We present a comprehensive theoretical study, within a fully realistic semi-analytical framework, of the photometric properties of early-type progenitors in the redshift range 0<z<1, as a function of the luminosity and local environment of the early-type remnant at present-day. We find that, averaging across all environments at z~1, less than 50 percent of the stellar mass which ends up in early-types today is actually in early-type progenitors at this redshift. The corresponding value is ~65 percent in clusters due to faster morphological transformations in the such dense environments. We develop probabilistic prescriptions which provide a means of including spiral (i.e. non early-type) progenitors at intermediate and high redshifts, based on their luminosity and optical (BVK) colours. For example, at intermediate redshifts (z~0.5), large (M_B<-21.5), red (B-V>0.7) spirals have ~75-95 percent chance of being a progenitor, while the corresponding probability for large blue spirals (M_B<-21.5, B-V<0.7) is ~50-75 percent. Finally, we explore the correspondence between the true progenitor set of present-day early-types and the commonly used `red-sequence', defined as the set of galaxies within the part of the colour-magnitude space which is dominated by early-type objects. While large members (M_V<-22) of the `red sequence' trace the progenitor set accurately in terms of numbers and mass, the relationship breaks down severely at fainter luminosities (M_V>-21). Hence the red sequence is generally not a good proxy for the progenitor set of early-type galaxies. 
S. Kaviraj, J. E. G. Devriendt, I. Ferreras, S. K. Yi and J. Silk