## Abstract

The human brain is unusually large. It has tripled in size from Australopithecines to modern humans^{1} and has become almost six times larger than expected for a placental mammal of human size^{2}. Brains incur high metabolic costs^{3} and accordingly a long-standing question is why the large human brain has evolved^{4}. The leading hypotheses propose benefits of improved cognition for overcoming ecological^{5,6,7}, social^{8,9,10} or cultural^{11,12,13,14} challenges. However, these hypotheses are typically assessed using correlative analyses, and establishing causes for brain-size evolution remains difficult^{15,16}. Here we introduce a metabolic approach that enables causal assessment of social hypotheses for brain-size evolution. Our approach yields quantitative predictions for brain and body size from formalized social hypotheses given empirical estimates of the metabolic costs of the brain. Our model predicts the evolution of adult *Homo sapiens*-sized brains and bodies when individuals face a combination of 60% ecological, 30% cooperative and 10% between-group competitive challenges, and suggests that between-individual competition has been unimportant for driving human brain-size evolution. Moreover, our model indicates that brain expansion in *Homo* was driven by ecological rather than social challenges, and was perhaps strongly promoted by culture. Our metabolic approach thus enables causal assessments that refine, refute and unify hypotheses of brain-size evolution.

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## Acknowledgements

We thank L. Lehmann for advice on the model set-up and for support at the University of Lausanne, where this project was initiated; P. Avila, S. H. Montgomery, S. B. Laughlin, M. Falcone, T. Clutton-Brock, and M. B. Morrissey for discussions; and A. Whiten for feedback. M.G.-F. was funded by a Marie Skłodowska-Curie Individual Fellowship (No 701464) and A.G. was funded by a NERC Independent Research Fellowship (NE/K009524/1). The contents of this paper reflect only the authors’ view and not the views of their funders.

Reviewer information*Nature* thanks A. R. DeCasien and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

### Affiliations

#### School of Biology, University of St Andrews, St Andrews, UK

- Mauricio González-Forero
- & Andy Gardner

### Authors

### Search for Mauricio González-Forero in:

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### Contributions

M.G.-F. conceived and carried out the study. A.G. conceived implementing challenge proportions during small time intervals and how to obtain high fit intervals. M.G.-F. and A.G. wrote the paper.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Mauricio González-Forero.

## Extended data figures and tables

### Extended Data Fig. 1 Shape of EEE versus skill.

**a–c**, Plots of EEE (*e*), its speed and acceleration with respect to skill level under power competence and exponential competence with only ecological challenges (that is,*P*_{1}= 1) for the parameter values used and without maternal provisioning (that is,*φ*= 0, so that*e*=*S*_{1}). For comparison, the curves for power competence are displaced to the left by 1 unit because skill level at birth is 1 for power competence but 0 for exponential competence.**a**,**b**,*e*and its speed at birth and during young ages are smaller for exponential competence than for power competence.**c**, However, the acceleration in*e*at birth and at young ages is larger for exponential competence than for power competence.### Extended Data Fig. 2 Method implementation.

**a**, Typical result with convergence to an uninvadable growth strategy. For the*i*th best-response iteration, the growth strategy shown is the resident (*v*) whose best response $\left({\stackrel{~}{u}}^{\ast}\right)$ is shown next, which is the resident of the*i*+ 1th iteration. Convergence to a best response to itself $\left({u}^{\ast}\right)$ was declared visually, in this case, at iteration 21.**b–f**, Reporting variables across the best-response iterations in**a**.**b–e**, Resulting adult body mass, brain mass, skill level and encephalization quotient across iterations. These values tend to converge more quickly than the growth strategy (**a**).**f**, Rather than visually declaring convergence, convergence should ideally be declared when the difference between mutant and resident is below a chosen threshold. However, numerical jittering prevented the use of this criterion. For example,**f**shows the maximum of $\u2223{\u0169}^{\ast}\left(t\right)-v\left(t\right)\u2223$ across*t*for each iteration in**a**. Without numerical jittering, this maximum should decrease as the growth strategy approaches a best response to itself. However, numerical jittering causes this maximum to be at least equal to the maximum mutation size*δ*= 0.1. The maximum of $\u2223{\u0169}^{\ast}\left(t\right)-v\left(t\right)\u2223$ is occasionally greater than*δ*because ${\u0169}^{\ast}$ and*v*have different partitions over*t*and we use the following approximation: for each*t*in the*t*partitioning of ${\u0169}^{\ast}$, we find the closest*t*in the*t*partitioning ofand calculate the difference $\u2223{\u0169}^{\ast}\left(t\right)-v\left(t\right)\u2223$ at these relatively close times; this may occasionally cause the difference to be the larger than*v**δ*when strategies change suddenly with*t*. Alternative measures of convergence were similarly inadequate (for example, ${\mathrm{\Sigma}}_{t}\u2223{\u0169}^{\ast}\left(t\right)-v\left(t\right)\u2223$).**g**, We implement maternal provisioning differently than before^{24}to incorporate it when there are social challenges. The difference yields no detectable difference in predicted brain and body mass with only ecological challenges after slightly adjusting the EEE from maternal provisioning of a newborn (*φ*_{0}): before^{24},*φ*_{0}= 0.6 for power and*φ*_{0}= 0.8 for exponential competence were used; here,*φ*_{0}= 0.4 for power and*φ*_{0}= 0.6 for exponential competence were used.**h**, Three ways to measure adult fit: (1) at the predicted age of adulthood $\left({x}_{\mathrm{B}}^{\ast}\left({t}_{\mathrm{a}}\right)-{X}_{\mathrm{B}}\left({t}_{\mathrm{a}}\right)\right)$; (2) at the observed age of adulthood $\left({x}_{\mathrm{B}}^{\ast}\left({\tau}_{\mathrm{a}}\right)-{X}_{\mathrm{B}}\left({\tau}_{\mathrm{a}}\right)\right)$; and (3) at the predicted age of adulthood for the prediction and at the observed age of adulthood for the observation $\left({x}_{\mathrm{B}}^{\ast}\left({t}_{\mathrm{a}}\right)-{X}_{\mathrm{B}}\left({\tau}_{\mathrm{a}}\right)\right)$. We use option 2.### Extended Data Fig. 3 Effects of

*Q*and*R*parameters.**a**,**b**, Effects of maintenance costs (*B*_{ i }) on the corresponding tissue mass or skill level. Each*B*_{ i }tends to decrease the value ${x}_{i}^{\ast}\left({\tau}_{\mathrm{a}}\right)$ for the corresponding*i*, but not necessarily for the other*i*(see**c**,**d**).**c**,**d**, Effect of*B*_{ i }on adult brain mass, body mass and encephalization quotient. With power competence (**c**), when*B*_{b}= 310 and 340 MJ kg^{−1}per year (y), the predicted adult brain mass is ${x}_{\mathrm{b}}^{\ast}\left({\tau}_{\mathrm{a}}\right)=1.0298$ and 0.9133 kg, respectively. With exponential competence (**d**), when*B*_{b}= 310, 340 and 370 MJ kg^{−1}y^{−1}, the predicted adult brain mass is ${x}_{\mathrm{b}}^{\ast}\left({\tau}_{\mathrm{a}}\right)=1.542$, 1.3973 and 1.2767 kg, respectively.**e**,**f**, Effects of*B*_{r}when*B*_{r}is small. When*B*_{r}varies between 70 and 2,700 MJ kg^{−1}y^{−1},*B*_{r}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 theparameters (except*R**δ*). The ontogenetic fit is approximately maximized around the benchmark values chosen previously^{24}, which are also used here (except for*φ*_{0}given our improved implementation of*φ*).**i**, Effect of*B*_{r}on the predicted life history with exponential competence. In the left column, from top to bottom, as*B*_{r}decreases, the allocation to the growth of reproductive tissue during adolescence increases (${u}_{\mathrm{r}}^{\ast}$ between*t*_{m}and*t*_{a}) 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*B*_{r}for*B*_{r}≥ 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*B*_{r}≤ 100 MJ kg^{−1}y^{−1}. An exceedingly small*B*_{r}(<70 MJ kg^{−1}y^{−1}) disrupts the predicted life history, which with*B*_{r}= 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*B*_{r}. In**a**–**i**there are only ecological challenges and we use the previous^{24}definition of*φ*.### Extended Data Fig. 4 Effects of challenge types on brain size.

**a**,**b**, Outer rows are for the cooperation cases that were considered; outer columns are for the competence cases.**a**, Around the pure ecological scenario (that is, in a given plot for*P*_{ j }as*P*_{1}decreases, the remaining two*P*_{ j }’s are set to zero).**b**, Around the best fitting scenario for*H. sapiens*(that is, in a given plot for*P*_{ j }as*P*_{1}decreases, the remaining two*P*_{ j }’s are set to the best fitting*P******found in Fig. 3d.**c**, Summary of the qualitative effects of challenge types on brain size. For social challenges, the direction of the arrows is taken from**a**,**b**. For ecological challenges, the direction of the arrow is taken from Extended Data Fig. 3g as the environmental difficulty*α*increases. A dash (−) indicates an approximately invariant relationship and a dot (·) indicates insufficient data points for identifying a relationship. The arrows in Fig. 3c are taken from this summary, in which, for social challenges, the arrows are those of submultiplicative cooperation. AC, additive cooperation; EC: exponential competence; MC, multiplicative cooperation; SC, submultiplicative cooperation.### Extended Data Fig. 5 Typical results when there is convergence to no brain growth or when there is no convergence to an uninvadable growth strategy.

**a**–**e**, Adult values over best-response iterations for cases of no brain growth or no convergence to an uninvadable strategy.**a**, Amplifying cycle leads to no brain growth.**b**, Stable cycle.**c**, Arms race that ends when the solver warns that the optimal control problem (OCP) may be infeasible. This might arise if the best response to the last iteration necessarily involves a substantially different growth strategy, which is not allowed in the optimization as the best response is constrained to be sufficiently similar to that in the previous iteration. It is possible that such substantially different best response involves either no brain growth (for example, as seen under purely ecological challenges when the environmental difficulty is exceedingly high^{24}(Supplementary Information 4.4)) or substantially more allocation to brain growth (which appears unlikely given the energetic constraints).**d**, A short arms race in encephalization quotient that leads to no brain growth.**e**, Amplifying cycle that ends when the solver warns that the OCP may be infeasible.### Extended Data Fig. 6 Identification of best-fitting scenarios across hominins.

Adult fit of predicted adult brain and body mass with those observed in a given species across parameter values for all cases considered. Each dot’s colour gives the adult fit, −

*D*(*τ*_{a}), for the corresponding parameter combination and case.**a**,*H. sapiens*.**b**,*H. neanderthalensis*.**c**,*H. erectus*.### Extended Data Fig. 7 Identification of best-fitting scenarios across hominins, continued.

See legend of Extended Data Fig. 6 for details.

**a**,*H. heidelbergensis*.**b**,*H. ergaster*.**c**,*H. habilis*.### Extended Data Fig. 8 Identification of best-fitting scenarios across hominins, continued.

See legend of Extended Data Fig. 6 for details.

**a**,*H. floresiensis*.**b**,*H. naledi*.**c**,*Australopithecus afarensis*. The best adult fit is −0.24 (**a**), −0.14 (**b**) and −0.23 (**c**).### Extended Data Fig. 9 High fit intervals for best-fitting scenarios across hominins.

Here we show high fit intervals around the best fitting scenarios across hominins having a best adult fit greater than −0.05.

**a**,**c**,**e**,**g, i**,**k**, For the top left plot, as*P*_{1}increases,*P*_{2}decreases, whereas for the remaining plots as*P*_{2},*P*_{3}and*P*_{4}increase,*P*_{1}decreases; for a given plot, the remaining*P*_{ j }are set to the correspondingshown in Fig. 4a (that is, plots are around*P***P******). The dots are the adult fit and the lines are interpolated values using a monotone Hermite spline (splinefun with method monoH.FC in R). The red line is −*D*(*τ*_{a}) = −0.05.**b**,**d**,**f**,**h**,**j**,**l**, The whiskers are the high fit intervals where adult fit is greater than −0.05 and the dots are the estimated ${\stackrel{\u02c6}{\mathbf{P}}}^{\ast}$ giving the best adult fit for the species in the interpolation. The cases of competence and cooperation are as found in Extended Data Figs. 6, 7. Note that for*H. habilis*, the high fit intervals may be wider as the adult fit is increasing at the end of the values of*P*_{2},*P*_{3}and*P*_{4}for which uninvadable growth strategies were obtained.### Extended Data Fig. 10 Detailed life history resulting from the best-fitting scenario for

*H. sapiens*.Plots correspond to Fig. 4b.

**a**, The growth strategy generating the life history.**b**, The resulting growth metabolic rate.**c**,**d**, The mass of all tissues.**e**, The skill level. For comparison with the model’s predicted skill level, ${x}_{\mathrm{k}}^{\ast}$, the black dots in**e**are the observed cumulative distribution of self-reported acquisition ages of food production skills in female Tsimane horticulturalists^{36}.

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