b₂ and β₂ as a function of b₁ = β₁ using the second-order spatial estimators. The black dashed line is the b₂(b₁) relation inferred by Lazeyras et al. (2016) from separate-universe simulations. The second-order spatial estimators seem consistent with the literature co-evolution relation down to damping scales of k_d ∼ 0.15 − 0.2 h Mpc⁻¹. It is noteworthy that β₂ < 0 appears to always hold, which means that the width of the galaxy environment distribution p(δ|g) is always smaller than that of the background p(δ). Therefore, the cumulant bias parameter β₂ − β₁ relation appears slightly simpler than the b₂ − b₁ relation.