Secondary halo bias: mean halo effective bias ${⟨b_h|\overline{n}⟩}_q^{\theta }$ measured in bins of the halo (log) number density using a number of halo properties as secondary properties, θ, namely, logV_max, ℰ_h, ℳ₅, Δ₅, 𝒟₅, 𝒯_A. In each number density-bin, the sample has been divided in quartiles, q, of the property θ. We show results from the lower (first) quartile (circles) and the upper (third) quartile (squares), for two modified gravity models F5₁ (light blue) and F6₁ (light green) alongside results from the ΛCDM reference (black), all of them at the same redshift, z = 0.5.