Supplementary information Primate brain size data were taken from (Stephan et al. 1981), while data on group size are from Dunbar (1992) and Smuts et al (1987); we classified species’ social systems ourselves, with reference to the primary literature and guidance from Smuts et al. (1987) and van Schaik & Kappeler (2003). Carnivore brain sizes were taken from (Dunbar & Bever 1998; Kruska 1988), and social system and group size from (Gittleman 1989), except for missing species which were based on (Nowak 1999). Ungulate brain size data were taken from several different sources (Jerison 1973; Oboussier 1966); (Haarmann 1975; Mangold-Wirz 1966). Information on sociality, group size, diet and habitat use were taken from additional published sources (Brashares et al. 2000; Jarman 1974; Kingdon 1997; Nowak 1999). Ungulate phylogeny was a composite based on several recently published trees (Flagstad et al. 2001), (Gatesy et al. 1997) (Murphy et al. 2001); carnivore phylogeny on (BinindaEmonds et al. 1999)et al18, and primate phylogeny was based on (Purvis 1995). For primate total brain size, the best model retained log group size (F1,38 = 13.37, p <0.001) and diet (F1,38 = 76.43, p < 0.001). For carnivores, the best model retained social system (F3,81 = 5.29, p = 0.002) and strata use (F1,81= 16.30, p < 0.001, model adjusted r2 = 0.22), whereas for ungulates, the best model retained social system (F3,61 = 4.52, p = 0.006) and diet (F4,61 = 4.12, p = 0.005, model adjusted r2 = 0.22). Primate activity budget data were collected from the following sources: Cercopithecus lhoesti (Kaplin & Moermond 2000); Cercopithecus mitis (Pazol & Cords 2005); Lagothrix lagothricha (Defler 1995); Ateles belzebuth, A. geoffroyi, A. paniscus (Korstjens et al. in press); P. ruformitratus, P. temminckii, P. tephrosceles, P. badius (Korstjens & Dunbar in press); Aotus trivirgatus, Callecebus moloch, Cebus apella, Allouatta palliata, Saguinus fusicollis, Saguinus imperator, Siamiri sciurus, Papio anubis (Leonard & Robertson 1997); Presbytis entellus (Fashing 2001); Pan paniscus, P.troglodytes (Lehmann et al. in press); Gorilla gorilla (Lehmann et al. unpub. manuscript); Hylobates agillis, H. concolor, H. hoolock, H. klossii, H. lar, H. muelleri, H. pileatus, H.syndactylus (Lan and Dunbar). Ungulate activity budgets were collected from the following sources: Damaslicus dorcas, Redunca fulvorufula (Klein & Fairall 1986), Kobus ellipsiprymnus (Wirtz & Oldekop 1991); Theropithecus gelada (Dunbar unpub. Data), Ourebia ourebia (Adamczak 1999), Aepyceros melampus, Raphicerus campestris, Tragelaphus strepsiceros (du Toit & Yetman 2005); Oreotragus oreotragus (R.Dunbar, unpublished); Syncerus caffer (Turner et al. 2005); Capra hircus (R.Dunbar, unpublished). References Adamczak, V. G. 1999 Variation in the mating system of oribi, Ourebia ourebi, vol. Ph.D. Liverpool: University of Liverpool. Bininda-Emonds, O. R. P., Gittleman, J. L. & Purvis, A. 1999 Building large trees by combining phylogenetic information: a complete phylogeny of the extant Carnivora (Mammalia). Biological Reviews 74, 143-175. Brashares, J. S., Garland, T. & Arcese, P. 2000 Phylogenetic analysis of coadaptation in behavior, diet, and body size in the African antelope. Behavioral Ecology 11, 452-463. 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Proceedings Of The Royal Society Of London Series B-Biological Sciences 268, 667-677. Gatesy, J., Amato, G., Vrba, E., Schaller, G. & DeSalle, R. 1997 A cladistic analysis of mitochondrial ribosomal DNA from the bovidae. Molecular Phylogenetics And Evolution 7, 303-319. Gittleman, J. L. 1989 Carnivore group living: comparative trends. In Carnivore behavior, ecology and evolution, vol. 1 (ed. J. L. Gittleman), pp. 183-208. Ithaca: Cornell University. Haarmann, K. 1975 Morphologische und histologische Untersuchungen am Neocortex von Boviden (Antiplopinae, Cephalopinae) und Traguliden mit bemerkungen zur Evolutionshöhe. J. Hirnfirsch 16, 91-116. Jarman, P. J. 1974 Social organization of antelope in relation to their ecology. Behaviour 48, 215-&. Jerison, H. J. 1973 Evolution of the brain and intelligence. London: Academic Press. Kaplin, B. A. & Moermond, T. C. 2000 Foraging ecology of the mountain monkey (Cercopithecus l'hoesti): Implications for its evolutionary history and use of disturbed forest. American Journal Of Primatology 50, 227-246. Kingdon, J. 1997 The Kingdon field guide to mammals. London.: Academic Press. Klein, D. R. & Fairall, N. 1986 Comparative foraging behavior and associated energetics of impala and blesbok. Journal Of Applied Ecology 23, 489-502. Korstjens, A. H. & Dunbar, R. I. M. in press Time constraints limit group sizes and distribution in red and black-and-white colobus monkeys. International Journal Of Primatology. Korstjens, A. H., Verhoeckx, I. L. & Dunbar, R. I. M. in press Time as a constraint on group size in spider monkeys. Behavioural Ecology and Sociobiology. Kruska, D. 1988 Mammalian domestication and its effectof brain structure and behavior. In Intelligence and Evolutionary Biology (ed. H. J. Jerison & I. Jerison), pp. 211-249. Berlin: Springer-Verlag. Lehmann, J., Korstjens, A. H. & Dunbar, R. I. 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Pazol, K. & Cords, M. 2005 Seasonal variation in feeding behavior, competition and female social relationships in a forest dwelling guenon, the blue monkey (Cercopithecus mitis stuhlmanni), in the Kakamega Forest, Kenya. Behavioral Ecology And Sociobiology 58, 566-577. Purvis, A. 1995 A composite estimate of primate phylogeny. Philosophical Transactions Of The Royal Society Of London Series B-Biological Sciences 348, 405-421. van Schaik, C.P. & Kappeler, P.M. 2003. The evolution of social monogamy in primates. In: U.R.Reichard & C.Boesch (eds) Monogam: Mating Strategies and Partnerships in Birds, Humans and Other Mammals, pp. 81-92. Smuts, B. B., Cheney, D. L., Seyfarth, R. M., Wrangham, R. W. & Struhsaker, T. T. 1987 Primate Societies. Chicago: Univ Chicago Press. Stephan, H., Frahm, H. & Baron, G. 1981 New and revised data on volumes of brain structures in insectivores and primates. Folia Primatologica 35, 1-29. Turner, W. C., Jolles, A. E. & Owen-Smith, N. 2005 Alternating sexual segregation during the mating season by male African buffalo (Syncerus caffer). Journal Of Zoology 267, 291-299. Wirtz, P. & Oldekop, G. 1991 Time budgets of waterbuck (Kobus ellipsiprymnus) of different age, sex and social status. Zeitschrift Fur SaugetierkundeInternational Journal Of Mammalian Biology 56, 48-58. Table S1. Definitions of the ecological and social criteria used in all analyses across the three focal taxa. Factor Diet Habitat Primates >75% leaves Vegetarian >75% leaves and fruit Grazer >75% Grasses and annuals Frugivore >75% Fruit Mixed-invertebrates Primarily insects, molluscs, worms plus other material Browser >75% leaves, bark FolivoreFruigivore >75% fruit Mixed- vertebrates Primarily small vertebrates, Some fruit, plus some invertebrates. Frugivore >75% leaves and fruit Browser-Frugivore >75% fruit and browse Mixed diet- fruit, gum, insects, vertebrates Grazer-Browser >75% grasses and browse Omnivore Omnivore Mixed including tubers and some animal matter Large vertebrates Diet primarily composed of large vertebrates and some carrion Open Species found in open grassland and savanna habitats Mixed Species found in either both open and forested habitats or in habitat matrices (e.g. woodland-savanna) Closed Species found in closed/forested habitats Semiarboreal Arboreal Activity Ungulates Folivore Terrestrial Strata Carnivores Primarily moves and forages on the group Generally moves on the ground, can forage and sleep in the trees Spends the most time including resting, moving and sleeping in trees Terrestrial Primarily moves and forages on the group Semiarboreal/Arboreal Can move on the ground, often forages and sleeps in trees Diurnal Active during daylight hours Cathemeral/ All hours Active either at dawn and dusk or at any hour Nocturnal Primarily active at night Figure S1. Primate phylogeny and phylogenetic residuals Latin Lemur fulvus Varecia variegatus Lepilemur rufiventor Avahi laniger Avahi occidentalis Propithecus verreauxi Indri indri Microcebus murinus Cheirogaleus medius Cheirogaleus major Galagoides demidovii Galago senegalensis Otolemur crassicaudatus Loris tardigradus Nycticebus coucang Perodictus potto Tarsius spectrum Callithrix jacchus Cebuella pygmea Saguinus oedipus Saguinus fuscollis Callimico geoldii Cebus sp. Saimiri sciureus Aotus trivirgatus Callicebus moloch Pithecia monarchus Alouatta sp. Ateles geoffroyi Lagothrix lagotricha Macaca mulatta Cercocebus albigena Papio anubis Cercopithecus ascanius Cercopithecus mitis Erythrocebus Miopithecus talapoin Procolobus badius Nasalis larvatus Hylobates lar Gorilla gorilla Pan troglodytes Homo sapiens Social multi-male multi-male solitary monogamous monogamous multi-male monogamous solitary solitary solitary harem harem solitary harem solitary solitary monogamous monogamous monogamous monogamous monogamous harem multi-male multi-male monogamous monogamous multi-male harem multi-male multi-male multi-male multi-male multi-male harem harem harem multi-male multi-male harem monogamous harem multi-male monogamous PGLS brain 0.02 -0.09 -0.34 -0.31 -0.21 -0.21 -0.23 -0.09 -0.17 -0.21 0.06 -0.05 -0.19 -0.07 -0.08 -0.14 -0.05 0.03 0.02 0.06 0.09 0.03 0.25 0.26 0.05 0.06 0.17 -0.11 0.14 0.25 0.09 0.13 0.06 0.25 0.01 0.16 0.30 0.04 -0.07 0.23 0.01 0.18 0.58 PGLS neocortex brain residuals -0.02 -0.06 -0.07 -0.05 -0.05 -0.05 -0.03 -0.05 -0.07 -0.09 -0.02 -0.04 -0.05 0.02 -0.03 -0.05 0.00 0.05 0.05 0.05 0.05 0.05 0.05 0.07 0.03 0.04 0.03 0.02 0.04 0.03 0.06 0.04 0.04 0.05 0.06 0.07 0.07 0.04 0.03 0.02 0.01 0.04 0.03 Figure S2. Ungulate phylogeny and social data Species Bos grunniens Syncerus caffer Tragelaphus scriptus Tragelaphus spekii Tragelaphus imberbis Tragelaphus strepsiceros Taurotragus oryx Oreotragus oreotragus Madoqua kirki Neotragus moschatus Raphicerus camptestris Raphicerus melanotis Ourebia ourebia Gazella dorcas Gazella granti Gazella thomsoni Antidorcas marsupialis Antilope cervicapra Litocranius walleri Kobus leche Kobus defassa Kobus kob Redunca fulvorufula Redunca arundinum Redunca redunca Cephalophus natalensis Cephalophus nigrifrons Sylvicapra grimmia Cephalophus monticola Cephalophus zebra Cephalophus leucogaster Cephalophus sylvicultor Oryx gazella Oryx beisa Hippotragus niger Hippotragus equinus Damaliscus lunatus Alcelaphus buselaphus Sigmoceros lichtensteini Connochaetes taurinus Hemitragus jemlahicus Ammotragus lervia Rupicapra rupicapra Aepyceros melampus Hydropotes Capreolus Alces Odocoileus Mazama Rangifer tarandus Cervus nippon Cervus elaphus Dama dama Muntiacus Giraffa camelopardalis Okapia Antilocapra Hyemoschus aquaticus Tragulus javanicus Tragulus meminna Choeropsis Hippopotamus Camelus bactrianus Babyrousa babyrousa Hylochoerus Potomochoerus porcus Phacochoerus aethiopicus Sus scrofa Tayassuidae Social PGLS brain residuals harem multi-male solitary harem harem harem multi-male monogamous monogamous monogamous solitary solitary harem harem harem harem multi-male harem harem harem harem harem harem harem harem monogamous monogamous monogamous monogamous monogamous monogamous monogamous harem multi-male harem harem harem harem harem harem harem monogamous harem harem solitary harem solitary multi-male solitary multi-male monogamous harem harem solitary harem monogamous harem solitary solitary solitary solitary multi-male harem multi-male multi-male harem harem multi-male harem 0.04 0.06 0.03 0.07 -0.02 0.13 0.05 -0.05 -0.07 -0.02 -0.11 -0.04 -0.11 -0.05 0.04 0.02 0.07 0.03 0.01 0.02 0.03 0.02 0.01 -0.03 -0.03 0.09 0.08 0.07 0.03 0.14 0.13 0.12 0.10 0.04 0.06 0.12 0.12 0.09 0.16 0.17 0.02 0.10 0.10 0.09 -0.08 0.11 0.20 0.07 0.20 0.16 0.19 0.23 0.18 0.22 0.18 0.23 0.25 -0.39 -0.35 -0.20 0.10 -0.18 0.18 -0.12 -0.29 -0.08 -0.08 0.06 0.05 Figure S3. Carnivore tree and social data. Species Martes foina Martes martes Martes pennanti Eira barbara Galictis vittata Galictis cuja Mustela nigripes Mustela putorius Mustela nivalis Mustela erminea Mustela vison Meles meles Melogale personata Lutra canadensis Lutra lutra Pteronura brasiliensis Conepatus humboldti Conepatus chinga Mephitis mephitis Taxidea taxus Procyon cancrivorus Procyon lotor Nasua rufa (narica?) Nasua nasua Bassariscus astutus Potos flavus Ailurus fulgens Thalarctos maritimus Ursus horribilis Ursus arctos Ursus americanus Ursus torquatus Melursus ursinus Helarctos malayanus Ailuropoda melanoleuca Canis latrans Canis lupus Canis mesomelas Canis aureus Canis adustus Lycaon pictus Acinonyx jubatus Cynictis penicillata Nyctereutes procyonoides Cerdocyon thous Chrysocyon brachyurus Cuon alpinus Pseudalopex griseus Pseudalopex culpaeus Pseudalopex gymnocercus Urocyon cinereoargenteus Vulpes zerda Vulpes velox Alopex lagopus Vulpes ruppelli Vulpes vulpes Otocyon megalotis Genetta tigrina Genetta servalina Genetta genetta Viverra tangalunga Viverra civetta Paradoxurus hermaphroditus Cryptoprocta ferox Crossarchus obscura Crossarchus "zebra" Mungos mungo Ichneumia albicauda Suricata suricata Herpestes javanicus Herpestes smithi Hyaena brunnea Hyaena hyaena Crocuta crocuta Proteles cristatus Panthera tigris Panthera pardus Panthera leo Panthera onca Lynx rufus Lynx canadensis Leopardus pardalis Caracal caracal Felis silvestris Leptailurus serval Herpailurus yagouaroundi Social PGLS brain residuals solitary solitary solitary monogamous harem harem solitary solitary solitary solitary solitary multi-male solitary solitary solitary monogamous solitary solitary solitary solitary solitary solitary harem harem solitary harem monogamous solitary solitary solitary solitary solitary solitary solitary solitary monogamous multi-male monogamous monogamous monogamous multi-male solitary multi-male monogamous monogamous monogamous multi-male monogamous monogamous monogamous monogamous monogamous monogamous monogamous monogamous monogamous monogamous solitary solitary solitary solitary solitary solitary solitary multi-male multi-male multi-male solitary multi-male harem harem multi-male solitary multi-male solitary solitary solitary multi-male solitary solitary solitary solitary solitary solitary solitary monogamous 0.06 0.10 -0.01 0.22 0.00 0.05 -0.06 -0.16 -0.06 -0.03 -0.33 -0.07 -0.06 0.01 0.24 0.08 -0.14 -0.03 -0.46 0.01 0.25 0.02 0.04 0.06 0.06 0.10 0.11 0.00 -0.08 -0.03 -0.07 0.08 -0.10 0.43 -0.01 0.11 0.05 0.01 0.03 0.03 0.09 -0.08 0.04 -0.18 0.04 0.03 0.22 0.05 0.08 0.11 0.13 0.14 0.07 0.13 0.01 0.05 -0.04 -0.05 -0.04 -0.05 -0.01 -0.15 -0.14 -0.03 -0.13 -0.12 -0.25 -0.06 0.03 -0.01 -0.06 -0.14 -0.12 -0.05 -0.03 -0.10 0.06 -0.11 0.13 0.13 -0.09 0.03 -0.02 0.06 -0.01 0.18