  We derive an analytic model for the redshift evolution of linear-bias,
allowing for interactions and merging of the mass-tracers, by solving a second
order differential equation based on linear perturbation theory and the
Friedmann-Lemaitre solutions of the cosmological field equations. We then study
the halo-mass dependence of the bias evolution, using the dark matter halo
distribution in a $\Lambda$CDM simulation in order to calibrate the free
parameters of the model. Finally, we compare our theoretical predictions with
available observational data and find a good agreement. In particular, we find
that the bias of optical QSO's evolve differently than those selected in X-rays
and that their corresponding typical dark matter halo mass is $\sim 10^{13}
h^{-1} M_{\odot}$ and $\magcir 5 \times 10^{13} h^{-1} M_{\odot}$,
respectively.
