Time evolution of MFs (top to bottom) for all the fields at three specific threshold values spanning the full range, for the Fiducial model (solid line) and for the NoAGN model (dashed line). Threshold values (blue, green, red in increasing order): log(T[K]) = {4, 5, 6}; log(P/k_B[cm⁻³K]) = {3, 3.9, 4.8}; log(n[cm⁻³]) = { − 3, −2, −1}; log(n_HI[cm⁻³]) = {−4,−3,−2}; log(n_H2[cm⁻³]) = { − 4, −2.5, −1}; log(Z[Z_⊙]) = { − 2, −1, 0}. The shaded band indicates the redshift range 1.5 < z < 2.5 around the peak of star formation rate density, which approximately coincides with the maximum of AGN luminosity function for AGN with bolometric luminosity 10⁴⁵ < L_bol/(erg s⁻¹) < 10⁴⁶; vertical lines mark the maximum of the AGN luminosity function for AGN with 10⁴⁴ < L_bol/(erg s⁻¹) < 10⁴⁵ (z ≃ 1) and 10⁴⁶ < L_bol/(erg s⁻¹) < 10⁴⁸ (z ≃ 2). As discussed in Sect. 4.2, these curves display many distinct features depending on the captured feedback processes, supporting the informative value of the cosmic evolution of morphology (each feature likely encodes a specific signature of the underlying process).