N(m|M) dm \, .$$

The upper pannel of figure \[fig:fdest\] shows the destroyed mass fraction as a function of halo mass for our base mass-luminosity relation, given by equation (\[mlfit\]), while the bottom pannel shows the effect on the total luminosity. As can be seen, this is most pronounced at the lower end of the mass scale shown, and becomes small enough to have little effect at high mass.

![Upper pannel: total mass in subhaloes which have been completely disrupted, as a fraction of the total halo mass. Bottom pannel: total luminosity as a function of halo mass with or without using the fraction of mass in destroyed subhaloes shown in the upper pannel. Results are for the K-band, using the base mass-luminosity relation of equation (\[mlfit\]).[]{data-label="fig:fdest"}](fig2a.ps "fig:"){width="84mm"} ![Upper pannel: total mass in subhaloes which have been completely disrupted, as a fraction of the total halo mass. Bottom pannel: total luminosity as a function of halo mass with or without using the fraction of mass in destroyed subhaloes shown in the upper pannel. Results are for the K-band, using the base mass-luminosity relation of equation (\[mlfit\]).[]{data-label="fig:fdest"}](fig2b.ps "fig:"){width="84mm"}

There are two additional factors that need to be noted. First, the introduction 