their descendants at $z=0$ but with a higher amplitude. The behaviour of the tracking sample cannot be easily related to the [@Wechsler:2006] or [@Gao:2007] results, since there is no fixed mass cut (or peak height or nonlinear mass for collapse) in the tracking sample. We interpret this non-evolution in the halo clustering as a negligible change in the comoving position and abundance of the haloes in this redshift range. This means that the evolution of halo assembly bias is not caused by a change in the clustering of haloes with extreme values of formation time or concentration. Instead we attribute the evolution of the assembly bias signal at a fixed halo number density to a shift in the ranking of haloes according to their mass and secondary property. This means that, for example, haloes with the highest concentrations at $z=0$ are not necessarily the ones with the highest concentrations at $z=3$.

We demonstrate this shift in the ranking of the haloes in Table \[Table:SampleEv\]. Here we show that fewer than $40$ per cent of the progenitors of $z=0$ haloes were part of the original sample at $z=1$. At $z=3$ this number decreases to $\sim 20$ per cent. This shift also 