of [@Gao:2007], who found that the halo assembly bias signal does not depend on redshift when the halo samples are selected using a fixed cut in peak height ($\nu = \delta_c/\sigma(M_h)$, where $\sigma(M_h)$ is the root mean square linear overdensity within a sphere with mean mass $M_h$, and $\delta_c(z)$ is the linear overdensity threshold for collapse at redshift z). For an increase in the peak height from $\nu = 0.5$ to $\nu = 1.55$ (the peak height values of the minimum halo mass of our simulation at $z=0$ and $z=3$, respectively), [@Gao:2007] found that the difference in the clustering signal between early and late-forming haloes decreases (with early formed haloes being more clustered at low $\nu$). For haloes selected by their concentration, they showed that at low peak height, high concentration haloes are more correlated than late forming, low concentration haloes, and for high peak height, low concentration haloes are more correlated than high concentration haloes. These results are equivalent to the redshift evolution trend found for a fixed halo mass cut. The same can be concluded if a fixed cut in the nonlinear mass for collapse is used [@Wechsler:2006].

![image](Fig2a.pdf){width="47.00000%"} ![image](Fig2b.pdf){width="47.00000%"} ![image](Fig2c.pdf){width="47.00000%"} ![image](Fig2d.pdf){width="47.00000%"}

To better understand how the age 