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 while larger early-types are generally assembled later , their luminosity-weighted stellar ages are typically older .
In dense environments , \sim 70 percent of early-type systems are in place by z = 1 and evolve without major interactions thereafter , while in the field the corresponding value is \sim 30 percent .
Averaging across all environments at z \sim 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 \sim 65 percent in clusters due to faster morphological transformations in the such dense environments .
We also 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 \sim 0.5 ) , large ( M _ { B } < -21.5 ) , red ( B - V > 0.7 ) spirals have \sim 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 \sim 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 .