- Inference of ecological and social drivers of human brain-size evolution

Effects of Q and R parameters a, b, Effects of maintenance costs (Bi) on the corresponding tissue mass or skill level. Each Bi tends to decrease the value xi∗(τa)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{i}^{\ast }({\tau }_{{\rm{a}}})$$\end{document} for the corresponding i, but not necessarily for the other i (see c, d). c, d, Effect of Bi on adult brain mass, body mass and encephalization quotient. With power competence (c), when Bb = 310 and 340 MJ kg⁻¹ per year (y), the predicted adult brain mass is xb∗(τa)=1.0298\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{{\rm{b}}}^{\ast }({\tau }_{{\rm{a}}})=1.0298$$\end{document} and 0.9133 kg, respectively. With exponential competence (d), when Bb = 310, 340 and 370 MJ kg⁻¹ y⁻¹, the predicted adult brain mass is xb∗(τa)=1.542\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{{\rm{b}}}^{\ast }({\tau }_{{\rm{a}}})=1.542$$\end{document}, 1.3973 and 1.2767 kg, respectively. e, f, Effects of Br when Br is small. When Br varies between 70 and 2,700 MJ kg⁻¹ y⁻¹, Br has no detectable effect on adult brain mass and encephalization quotient. g, h, Ontogenetic fit with H. sapiens around the used values for each of the R parameters (except δ). The ontogenetic fit is approximately maximized around the benchmark values chosen previously²⁴, which are also used here (except for φ0 given our improved implementation of φ). i, Effect of Br on the predicted life history with exponential competence. In the left column, from top to bottom, as Br decreases, the allocation to the growth of reproductive tissue during adolescence increases (ur∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${u}_{{\rm{r}}}^{\ast }$$\end{document} between tm and ta) and adolescence shortens. In the central column, the increased allocation to the growth of reproductive tissue increases the mass of reproductive tissue, but brain mass does not change with Br for Br ≥ 70 MJ kg⁻¹ y⁻¹. In the right column, as the mass of reproductive tissue increases, body mass increases slightly, which is more noticeable for Br ≤ 100 MJ kg⁻¹ y⁻¹. An exceedingly small Br (<70 MJ kg⁻¹ y⁻¹) disrupts the predicted life history, which with Br = 60 MJ kg⁻¹ y⁻¹ is severely different from that of H. sapiens (for example, there is brain growth late in life and reproductive growth from birth). Similar results arise for even smaller Br. In a–i there are only ecological challenges and we use the previous²⁴ definition of φ.