A new chemo-evolutionary population synthesis model for early-type   galaxies. I: Theoretical basis
  We have developed a new stellar population synthesis model designed to study early-type galaxies. It provides optical and near-infrared colors, and line indices for 25 absorption lines. It can synthesize single age, single metallicity stellar populations or follow the galaxy through its evolution from an initial gas cloud to the present time. The model incorporates the new isochrones of the Padova group and the latest stellar spectral libraries. The model has been extensively compared with previous ones in the literature to establish its accuracy as well as the accuracy of this kind of models in general.   Using the evolutionary version of the model we find that we cannot fit the most metal-rich elliptical galaxies if we keep the IMF constant and do not allow infall of gas. We do however reproduce the results of Arimoto \& Yoshii (1986) for the evolution of the gas, and produce colors, and, for the first time with this type of models, absorption line-strengths. It is in fact possible to fit the data for the elliptical galaxies by varying the IMF with time. Our numerical model is in good broad agreement with the analytical 'simple model'. In the present paper we describe the model, and compare a few key observables with new data for three early-type {\em standard} galaxies. However the data, as well as our fits, will be discussed in much more detail in a second paper (Vazdekis {\it et al.} 1996), where some conclusions will be drawn about elliptical galaxies on the basis of this model. 
A. Vazdekis (IAC), E. Casuso (IAC), R.F. Peletier (Groningen, IAC) and   J.E. Beckman (IAC)