1. Futuyma, D. J. Evolutionary constraint and ecological consequences. Evolution 64, 1865–1884 (2010).

2. Gould, S. J. The Structure of Evolutionary Theory (Harvard Univ. Press, Cambridge, 2002).

3. Amundson, R. The Changing Role of the Embryo in Evolutionary Thought: Roots of Evo-Devo (Cambridge Univ. Press, Cambridge, 2005).

4. Jerison, H. J. Evolution of the Brain and Intelligence (Academic Press, New York, 1973).

5. Striedter, G. F. Principles of Brain Evolution (Sinauer Associates, Sunderland, 2005).

6. Gould, S. J. Allometry in primates, with emphasis on scaling and the evolution of the brain. Contrib. Primatol. 5, 244–292 (1975).

7. Huxley, J. S. Problems of Relative Growth (Methuen & Co., London, 1932).

8. Lande, R. Quantitative genetic-analysis of multivariate evolution, applied to brain–body size allometry. Evolution 33, 402–416 (1979).

9. Grabowski, M. Bigger brains led to bigger bodies?: The correlated evolution of human brain and body size. Curr. Anthropol. 57, 174–196 (2016).

10. Riska, B. & Atchley, W. R. Genetics of growth predict patterns of brain-size evolution. Science 229, 668–671 (1985).

11. Tsuboi, M. et al. Evolution of brain–body allometry in Lake Tanganyika cichlids. Evolution 70, 1559–1568 (2016).

12. Voje, K. L., Hansen, T. F., Egset, C. K., Bolstad, G. H. & Pelabon, C. Allometric constraints and the evolution of allometry. Evolution 68, 866–885 (2014).

13. Pelabon, C. et al. On the relationship between ontogenetic and static allometry. Am. Nat. 181, 195–212 (2013).

14. Snell, O. Die abhängigkeit des hirngewichtes von dem körpergewicht und den geistigen fähigkeiten. Eur. Arch. Psychiatry Clin. Neurosci. 23, 436–446 (1892).

15. Yopak, K. E. Neuroecology of cartilaginous fishes: the functional implications of brain scaling. J. Fish. Biol. 80, 1968–2023 (2012).

16. Martin, R. Relative brain size and basal metabolic-rate in terrestrial vertebrates. Nature 293, 57–60 (1981).

17. Kleiber, M. The Fire of Life: An Introduction to Animal Energetics (John Wiley & Sons, New York, 1961).

18. Benson-Amram, S., Dantzer, B., Stricker, G., Swanson, E. M. & Holekamp, K. E. Brain size predicts problem-solving ability in mammalian carnivores. Proc. Natl Acad. Sci. USA 113, 2532–2537 (2016).

19. MacLean, E. L. et al. The evolution of self-control. Proc. Natl Acad. Sci. USA 111, E2140–E2148 (2014).

20. Roth, G. & Dicke, U. Evolution of the brain and intelligence. Trends Cogn. Sci. 9, 250–257 (2005).

21. Finarelli, J. A. & Flynn, J. J. Brain-size evolution and sociality in Carnivora. Proc. Natl Acad. Sci. USA 106, 9345–9349 (2009).

22. Boddy, A. M. et al. Comparative analysis of encephalization in mammals reveals relaxed constraints on anthropoid primate and cetacean brain scaling. J. Evol. Biol. 25, 981–994 (2012).

23. Holekamp, K. E., Swanson, E. M. & Van Meter, P. E. Developmental constraints on behavioural flexibility. Phil. Trans. R. Soc. B 368, 20120350 (2013).

24. Montgomery, S. H. et al. The evolutionary history of cetacean brain and body size. Evolution 67, 3339–3353 (2013).

25. Felsenstein, J. Phylogenies and the comparative method. Am. Nat. 125, 1–15 (1985).

26. Lynch, M. Methods for the analysis of comparative data in evolutionary biology. Evolution 45, 1065–1080 (1991).

27. Riska, B. Regression-models in evolutionary allometry. Am. Nat. 138, 283–299 (1991).

28. Hansen, T. F. & Bartoszek, K. Interpreting the evolutionary regression: the interplay between observational and biological errors in phylogenetic comparative studies. Syst. Biol. 61, 413–425 (2012).

29. Pagel, M. D. & Harvey, P. H. The taxon-level problem in the evolution of mammalian brain size—facts and artifacts. Am. Nat. 132, 344–359 (1988).

30. Hansen, T. F. & Houle, D. Measuring and comparing evolvability and constraint in multivariate characters. J. Evol. Biol. 21, 1201–1219 (2008).

31. Noreikiene, K. et al. Quantitative genetic analysis of brain size variation in sticklebacks: support for the mosaic model of brain evolution. Proc. R. Soc. B 282, 20151008 (2015).

32. Rogers, J. et al. Heritability of brain volume, surface area and shape: an MRI study in an extended pedigree of baboons. Hum. Brain Mapp. 28, 576–583 (2007).

33. Kotrschal, A. et al. Artificial selection on relative brain size in the guppy reveals costs and benefits of evolving a larger brain. Curr. Biol. 23, 168–171 (2013).

34. Peper, J. S., Brouwer, R. M., Boomsma, D. I., Kahn, R. S. & Poll, H. E. H. Genetic influences on human brain structure: a review of brain imaging studies in twins. Hum. Brain Mapp. 28, 464–473 (2007).

35. Cheverud, J. M. et al. Heritability of brain size and surface-features in rhesus macaques (Macaca-Mulatta). J. Hered. 81, 51–57 (1990).

36. Airey, D. C., Castillo-Juarez, H., Casella, G., Pollak, E. J. & DeVoogd, T. J. Variation in the volume of zebra finch song control nuclei is heritable: developmental and evolutionary implications. Proc. R. Soc. B 267, 2099–2104 (2000).

37. Hansen, T. F., Pelabon, C. & Houle, D. Heritability is not evolvability. Evol. Biol. 38, 258–277 (2011).

38. Hansen, T. F., Pienaar, J. & Orzack, S. H. A comparative method for studying adaptation to a randomly evolving environment. Evolution 62, 1965–1977 (2008).

39. Grabowski, M., Voje, K. L. & Hansen, T. F. Evolutionary modeling and correcting for observation error support a 3/5 brain–body allometry for primates. J. Hum. Evol. 94, 106–116 (2016).

40. Mink, J. W., Blumenschine, R. J. & Adams, D. B. Ratio of central nervous-system to body metabolism in vertebrates—its constancy and functional basis. Am. J. Physiol. 241, R203–R212 (1981).

41. Barton, R. A. & Capellini, I. Maternal investment, life histories, and the costs of brain growth in mammals. Proc. Natl Acad. Sci. USA 108, 6169–6174 (2011).

42. Isler, K. & van Schaik, C. P. The expensive brain: a framework for explaining evolutionary changes in brain size. J. Hum. Evol. 57, 392–400 (2009).

43. Iwaniuk, A. N. & Nelson, J. E. Developmental differences are correlated with relative brain size in birds: a comparative analysis. Can. J. Zool. 81, 1913–1928 (2003).

44. Martin, R. D. & Harvey, P. H. in Size and Scaling in Primate Biology (ed. Jungers, W. L.) Ch. 8 (Springer, New York, 1985).

45. Nealen, P. M. & Ricklefs, R. E. Early diversification of the avian brain: body relationship. J. Zool. 253, 391–404 (2001).

46. Pagel, M. Inferring the historical patterns of biological evolution. Nature 401, 877–884 (1999).

47. Halley, A. C. Minimal variation in eutherian brain growth rates during fetal neurogenesis. Proc. R. Soc. B 284, 20170219 (2017).

48. Halley, A. C. Prenatal brain–body allometry in mammals. Brain Behav. Evol. 88, 14–24 (2016).

49. Raff, R. A. The Shape of Life: Genes, Development, and the Evolution of Animal Form (Univ. Chicago Press, Chicago, 1996).

50. Bolstad, G. H. et al. Genetic constraints predict evolutionary divergence in Dalechampia blossoms. Phil. Trans. R. Soc. B 369, 20130255 (2014).

51. Svensson, E. & Calsbeek, R. (eds) The Adaptive Landscape in Evolutionary Biology (Oxford Univ. Press, Oxford, 2012).

52. Walsh, B. & Blows, M. W. Abundant genetic variation plus strong selection = multivariate genetic constraints: a geometric view of adaptation. Annu. Rev. Ecol. Evol. Syst. 40, 41–59 (2009).

53. Arnold, S. J., Pfrender, M. E. & Jones, A. G. The adaptive landscape as a conceptual bridge between micro- and macroevolution. Genetica 112, 9–32 (2001).

54. Arnold, S. J., Burger, R., Hohenlohe, P. A., Ajie, B. C. & Jones, A. G. Understanding the evolution and stability of the G-matrix. Evolution 62, 2451–2461 (2008).

55. Jones, A. G., Arnold, S. J. & Burger, R. Evolution and stability of the G-matrix on a landscape with a moving optimum. Evolution 58, 1639–1654 (2004).

56. Pavlicev, M., & Cheverud, J. M. Constraints evolve: context dependency of gene effects allows evolution of pleiotropy. Annu. Rev. Ecol. Evol. Syst. 46, 413–434 (2015).

57. Jones, A. G., Burger, R. & Arnold, S. J. Epistasis and natural selection shape the mutational architecture of complex traits. Nat. Commun. 5, 3709 (2014).

58. Willis, J. H., Coyne, J. A. & Kirkpatrick, M. Can one predict the evolution of quantitative characters without genetics? Evolution 45, 441–444 (1991).

59. Houle, D., Bolstad, G. H., van der Linde, K. & Hansen, T. F. Mutation predicts 40 million years of fly wing evolution. Nature 548, 447–450 (2017).

60. Williams, G. C. Natural Selection: Domains, Levels, and Challenges (Oxford Univ. Press, New York, 1992).

61. Finlay, B. L. & Darlington, R. B. Linked regularities in the development and evolution of mammalian brains. Science 268, 1578–1584 (1995).

62. Striedter, G. F. & Charvet, C. J. Developmental origins of species differences in telencephalon and tectum size: morphometric comparisons between a parakeet (Melopsittacus undulatus) and a quail (Colinus virgianus). J. Comp. Neurol. 507, 1663–1675 (2008).

63. Koyabu, D. et al. Mammalian skull heterochrony reveals modular evolution and a link between cranial development and brain size. Nat. Commun. 5, 3625 (2014).

64. Iwaniuk, A. N. & Nelson, J. E. Can endocranial volume be used as an estimate of brain size in birds? Can. J. Zool. 80, 16–23 (2002).

66. Crile, G. & Quiring, D. P. A record of the body weight and certain organ and gland weights of 3690 animals. Ohio J. Sci. 40, 219–260 (1940).

67. Hrdlička, A. Brain Weight in Vertebrates Vol. 3 (Smithsonian Institution, 1905).

68. Mangold-Wirz, K. Cerebralisation und ontogenesemodus bei eutherien. Acta Anat. 63, 449–508 (1966).

69. Isler, K. et al. Endocranial volumes of primate species: scaling analyses using a comprehensive and reliable data set. J. Hum. Evol. 55, 967–978 (2008).

70. Hrdlička, A. Weight of the brain and of the internal organs in American monkeys with data on brain weight in other apes. Am. J. Phys. Anthropol. 8, 201–211 (1925).

71. Gittleman, J. L. Carnivore brain size, behavioral ecology, and phylogeny. J. Mammal. 67, 23–36 (1986).

72. Matějů, J. et al. Absolute, not relative brain size correlates with sociality in ground squirrels. Proc. R. Soc. B 283, 20152725 (2016).

73. Blinkov, S. M. & Glezer, I. A. I. The Human Brain in Figures and Tables: A Quantitative Handbook (Basic Books, New York, 1968).

74. Starck, J. M. Zeitmuster der Ontogenesen bei nestflüchtenden und-nesthockenden Vögeln. Cour. Forsch. Inst. Senckenb. 114, 1–319 (1989).

75. R Core Team R: A Language and Environment for Statistical Computing v.3.4.0 (R Foundation for Statistical Computing, Vienna, 2017).

76. Jetz, W. et al. Global distribution and conservation of evolutionary distinctness in birds. Curr. Biol. 24, 919–930 (2014).

77. Bininda-Emonds, O. R. P. et al. The delayed rise of present-day mammals. Nature 446, 507–512 (2007).

78. Rabosky, D. L. et al. Rates of speciation and morphological evolution are correlated across the largest vertebrate radiation. Nat. Commun. 4, 1958 (2013).

79. Pyron, R. A. & Wiens, J. J. A large-scale phylogeny of Amphibia including over 2800 species, and a revised classification of extant frogs, salamanders, and caecilians. Mol. Phylogenet. Evol. 61, 543–583 (2011).

80. Velez-Zuazo, X. & Agnarsson, I. Shark tales: a molecular species-level phylogeny of sharks (Selachimorpha, Chondrichthyes). Mol. Phylogenet. Evol. 58, 207–217 (2011).

81. Zheng, Y. C. & Wiens, J. J. Combining phylogenomic and supermatrix approaches, and a time-calibrated phylogeny for squamate reptiles (lizards and snakes) based on 52 genes and 4162 species. Mol. Phylogenet. Evol. 94, 537–547 (2016).

82. Bouckaert, R. et al. BEAST 2: a software platform for Bayesian evolutionary analysis. PLoS Comput. Biol. 10, e1003537 (2014).

83. Benton, M. J. et al. Constraints on the timescale of animal evolutionary history. Palaeontol. Electron. 18, 1–106 (2015).

84. Sanderson, M. J. Estimating absolute rates of molecular evolution and divergence times: a penalized likelihood approach. Mol. Biol. Evol. 19, 101–109 (2002).

85. Chamberlain, S. A. & Szöcs, E. taxize: taxonomic search and retrieval in R. F1000Res. 2, 191 (2013).

86. Cook, R. D. & Weisberg, S. Residuals and Influence in Regression (Chapman and Hall, New York, 1982).

87. Pinheiro, J. B. D., DebRoy, S., Sarkar, D. and R Core Team nlme: Linear and Nonlinear Mixed Effects Models v.3.1.131 (2017).

88. Harmon, L. J., Weir, J. T., Brock, C. D., Glor, R. E. & Challenger, W. GEIGER: investigating evolutionary radiations. Bioinformatics 24, 129–131 (2008).

89. Hansen, T. F. Stabilizing selection and the comparative analysis of adaptation. Evolution 51, 1341–1351 (1997).

90. Martins, E. Estimating the rate of phenotypic evolution from comparative data. Am. Nat. 144, 193–209 (1994).

91. Boettiger, C., Coop, G. & Ralph, P. Is your phylogeny informative? Measuring the power of comparative methods. Evolution 66, 2240–2251 (2012).

92. Oikawa, S. & Itazawa, Y. Relative growth of organs and parts of the carp, Cyprinus carpio, with special reference to the metabolism–size relationship. Copeia 1984, 800–803 (1984).

93. Kawabe, S., Matsuda, S., Tsunekawa, N. & Endo, H. Ontogenetic shape change in the chicken brain: implications for paleontology. PLoS ONE 10, e0129939 (2015).

94. Oikawa, S., Takemori, M. & Itazawa, Y. Relative growth of organs and parts of a marine teleost, the porgy, Pagrus-Major, with special reference to metabolism–size relationships. Jpn. J. Ichthyol. 39, 243–249 (1992).

95. Muggeo, V. M. Segmented: an R package to fit regression models with broken-line relationships. R News 8, 20–25 (2008).