Large-scale effective bias as a function of virial mass, assigned as described in Sect. 3. The main panels (a,b,c,d) show the effective bias measured from the reference and the results from the property assignment at ɀ = 0 (left), ɀ = 0.5 (center), and ɀ = 1 (right column), with (labeled Assignment+MS) and without (labeled Assignment) the MS approach. Panel a shows the results of using only dark matter properties Θ_dm in the assignment of maximum circular velocity and virial mass. Panel b shows the results of adding the information from the individual bias. Panel c shows the results after including halo environment properties Θ_H, and panel d shows the result of including both bias and environment properties. The bottom panels show, in each case, the ratio to the primary bias obtained from the mock catalog using its original properties (the latter shown as black points in all main panels). The gray region in these bottom panels depicts 10% deviation with respect to unity. The error bars denote the error on the mean bias-property relation.