Digitized endocasts and brains: a perspective on measurements and historical analyses of the evolution of 172 fossil and extant amniote specimens

Endocasts and their utility

Cranial endocasts are casts molded by the endocranial cavity of the skull, either naturally through fossilization of interred material, artificially with materials such as plaster or latex, or virtually with computed tomography (CT) scanning and segmentation. Endocasts provide a powerful window into deep time for studying neuroanatomy and brain evolution. Tilly Edinger, the founder of paleoneurology, described endocasts as fossilen Gehirne (Edinger, 1929), or “fossil brains,” and by the time of her death in 1967, had compiled a then-comprehensive annotated bibliography of over a thousand vertebrate fossil genera and their cranial cavity endocasts (Edinger, 1975).

Throughout her career, Edinger noted that bird and mammal endocasts largely mirror brains in size and appearance, although the narrow space around a brain containing meninges, blood vessels, and cerebrospinal fluid add to the surface area and volume of an endocast compared to a brain. Indeed, endocasts are often faithful proxies for brain size, especially in extant, adult vertebrate groups such as mammals (Haight & Nelson, 1987; De Miguel & Henneberg, 2001) and birds (e.g., Iwaniuk & Nelson, 2002; Watanabe et al., 2019).

Neocorticalization and encephalization in mammals

The cerebral cortex (i.e., neopallium, isocortex; Butler & Hodos, 2005) is an outer layer of forebrain consisting of layers of nerve cells. This layered organization of cells is a unique feature of the brain in all living mammals. In this paper, we measured neocorticalization, or the comparative increase in neocortex relative to other brain structures, as the increase in surface area of cerebral cortex dorsal to the rhinal fissure relative to the total cortical surface area (Fig. 1). Encephalization—the evolutionary increase in brain complexity or relative size reflecting environmental adaptations—has been proposed historically as a general phenomenon in many species of mammals and birds that is more or less correlated to natural selection and independent of their phylogenetic details (e.g., Jerison, 1973; Jerison, 1977; Boddy et al., 2012; Ksepka et al., 2020; Smith, 2022 and sources therein; Van Schaik et al., 2023; but for mammals, see Burger et al., 2019; Smaers et al., 2021). For over a century, brain-body allometry, along with the generally concerted evolution of brain regions (study: Finlay & Darlington, 1995; “concerted evolution” term applied: Barton & Harvey, 2000), have explained a large portion of brain size variation across vertebrates (e.g., Snell, 1892; Montgomery, Mundy & Barton, 2016; Moore & De Voogd, 2017; Kotrschal et al., 2017; but see: Smaers & Soligo, 2013; Barton & Montgomery, 2019; Willemet, 2019; Willemet, 2020). Many birds and mammals have evolved a substantially larger brain for a given body size, or larger encephalization, compared to other vertebrates (e.g., Jerison, 1971; Iwaniuk, Dean & Nelson, 2005; Emery, 2006; Franklin et al., 2014; Ksepka et al., 2020; Smaers et al., 2021).

The measurement of neocorticalization evolution is an outstanding example of a quantitative analysis made possible by digitizing data. Surface scanning and software analysis enable direct measurements from virtual models of natural or physical endocasts. This study exploits digitization technology to review 129 three-dimensional (3D) models of fossil endocasts and compare them with the endocasts and brains of 43 extant specimens. Notably, quality comparisons of human-made (e.g., plaster, resin) and natural endocasts are not always possible due to breaks or lack of preservation in natural endocasts. We are unsure exactly of how our late lead author (HJJ) handled these instances—adding yet another caveat to our results. We caution future researchers to be careful in their own comparisons when using our data. For more information on specific endocasts, see Supplemental Information 1A and 1B.

Importance and limitations of this perspective study

Although components of the dataset have been presented in other venues (e.g., Long, Bloch & Silcox, 2015, using data provided by Jerison, 2012), this is the most comprehensive collection to date. Equally importantly, we provide figures for nearly all of the endocasts, many for the first time in the literature. We hope that these illustrations will be a useful resource for future work on endocranial anatomy.

Lastly, we are aware of widespread leaps in the statistical calculation and determination of evolutionary trends collectively known as phylogenetic comparative methods ((PCM); e.g., Harmon, 2019; Adams & Collyer, 2019). We are also aware that many of these methods are more robust and appropriate for application to studies of brain (or brain region) vs. body size in vertebrates (e.g., see review in Striedter & Northcutt, 2019). The use of these methods provides rich and potentially more nuanced and/or more accurate analysis of datasets than the one presented in our paper. However, because this paper serves as the culmination of decades of work by our now-late lead author (HJJ), who passed while this paper was in review, we have elected to present methods consistent with his previous studies for the sake of comparison. We eagerly anticipate that future work will incorporate all or parts of the dataset into more advanced and sophisticated analyses.

Endocast specimens

The first author obtained the majority of the natural and latex endocasts used in this study from the Radinsky Collection at the Field Museum of Natural History (FMNH) in Chicago, most of which were collected and prepared by the late Professor Len Radinsky and catalogued by Collections Manager William Simpson. We also scanned specimens from following collections: University of Adelaide (Adelaide), Victoria, Australia; American Museum of Natural History (AMNH), New York; American Museum of Natural History (AMNH FAM)—Frick Collection at AMNH; The Natural History Museum (NHMUK), London; Carnegie Museum of Natural History (CM), Pittsburgh, Pennsylvania; National Museum of Health and Medicine Defense Health Agency Neuroanatomical Collections Division (NMHM WISC), Silver Spring, Maryland (formerly the University of Wisconsin and Michigan State Comparative Mammalian Brain Collections in Madison, Wisconsin); Falk Collection (Falk), now deposited with Mammals at AMNH; Jura-Museums Eichstaett (JME), Germany; Natural History Museum of Los Angeles County (LACM), California; The Museum of Comparative Zoology (MCZ) at Harvard University, Cambridge, Massachusetts; Muséum National d’Histoire Naturelle (MNHN), Paris; University of California Museum of Paleontology (UCB), California; Museum of the Rockies (MOR), Bozeman, Montana; National Museum of Victoria (NMV), Melbourne, Australia; Canadian Museum of Nature (NMC), Ottawa; Raymond M. Alf Museum of Paleontology at the Webb Schools (RAM), Claremont, California; Senckenberg Natural History Museum (SNHM), Frankfurt, Germany; Texas Memorial Museum (UT) and (TMM), Austin, Texas; United States National Museum (USNM), Washington, DC; University of the Witwatersrand (WITS), Johannesburg, South Africa; and Yale Peabody Museum of Natural History (YPM), New Haven, Connecticut.

Most endocasts in the dataset derive from fossilized mammals, but some endocasts and braincasts (i.e., casted replicas of the actual brain) represent extant species. Four endocasts are from extinct dinosaurs. Prior to our digitization work (see below), and across several decades, collections staff or other researchers prepared non-fossilized endocasts using plaster, latex, thermoplastic, or virtual segmentation. In all cases, the cranial cavity served as a mold for each endocast, with little difference in most cases between endocasts prepared with plaster or latex from a cranial cavity or filled with fossilized matrix preserved when the skull eroded. Idenfication of features on the endocasts best matches the convention put forth by Macrini, Leary & Weisbecker (2022, see their fig 11.3).

Digitization

HJJ digitized endocasts using surface scanning with a Cyberware Model M15 Scanner using Headus 3D Tools software (http://www.headus.com.au), which creates endocast images as complete 360° rotation producing a full scan. After performing a first set of scans, HJJ placed the object in a different orientation to expose areas previously hidden from the laser beam before acquiring a further set of scans. HJJ then merged the final set of 16 scans into a 3D digitized image. Again, we share that there are instances in the dataset of incomplete natural endocasts, and we are unsure of how our late lead author (HJJ) handled these cases while collecting and analyzing data.

Headus outputs the following image measurements: volume in mm³, surface area in mm², and length in mm. HJJ measured endocast lengths from the anterior tip of the forebrain or olfactory bulbs to the posterior hindbrain at the end of the medulla. Surface regions of the endocast, such as olfactory bulbs or neocortex, were virtually measured by HJJ by selecting the region of interest in Cyberware (now Headus 3D) and then measuring the selected region with the CySize tool. HJJ recorded measurements in centimeter-gram-seconds (cgs) unless otherwise noted. Most of the 3D models of endocasts are freely available for viewing and download on MorphoSource at the discretion of collections staff. Table S2 is a list of available endocast and MorphoSource DOIs.

Neocorticolization

Unlike other gyri and sulci, endocast rhinal fissures are a reliable landmark of the ventral boundary of neocortex. It is a superficial landmark that is visible on the brains of living mammals (Welker, 1990). The rhinal fissure differentiates neocortex dorsally from paleocortex ventrally (Kappers, 1909). We define measurements of the surface area of forebrain dorsal to the rhinal fissure as neocortex (see example, Fig. 1).

Brain-body allometry

Brain-body allometry relates endocast volume (representing brain size) to estimated body size. Brain-body allometry was calculated using head+body length as an independent variable and brain size as the dependent variable, as described previously (Jerison, 1973; Jerison, 1991; Jerison, 2001a; Jerison, 2001b; Jerison, 2002). The historical Jerison equation was used here and is consistent with previous analyses of HJJ, but we note the existence of more recent published equations in the literature (e.g., Burger et al., 2019; López-Torres et al., 2024). Briefly, the power function for the regression of body size relative to body length, which reflects a surface area (the skin) for graphing against brain size, was as in Jerison (1973): (1)${\displaystyle P=0.021L^{3.03}}$ where P is body mass or volume, and L is body length in the cgs system. In a few species for which accurate models of the body were prepared, body volume was determined from 3D scans of the model. We then fit brain-body size relationships in different species measured logarithmically by linear regression: (2a)${\displaystyle logE=\alpha logP+logb}$ or the power function: (2b)${\displaystyle E=bP\alpha }$ where E is brain size (from the French, encephale); P is body size (from the French, poids); α is the regression line’s slope, and log b is its y intercept. E and P were in the same units (ml and grams or liters and kilograms) in Eqs. (2a) and (2b) for easy interpretation. For extant species, HJJ either weighed the brains and bodies of them or derived the volumes (HJJ: no correction factor (e.g., Stephan, Frahm & Baron, 1981) applied) from log brain size as a function of log body size graphed. Bivariate statistical regression analysis of the log brain-body relationship for vertebrate classes can estimate α empirically. The empirical encephalization quotient (EQ) in brain size in each species is its residual from the regression, but EQ can be different if the allometric factor is determined by theoretical analysis rather than regression. Therefore, we took EQ as the residual relative to Eqs. (2a) or (2b), with α a theoretical constant of exactly 2/3. In this way, the allometric equation transforms the 3D information of the body into a 2D map created by the brain (Jerison, 2001a; Jerison, 2001b; Jerison, 2002). Extensive discussion of body mass estimation sources and methods is available in File S1A.

Important notes

With the exception of measured values taken directly from 3D surface endocasts, the following results and discussions stem from more traditional methods (e.g., phylogenetically un-informed mathematical regressions of raw data) in that they do not incorporate our field’s most recent understanding of: (1) phylogenetic comparative methods, (2) updated equations and appropriate applications of encephalization quotient (EQ), and (3) methods for estimating brain and brain region sizes from 2D images (e.g., more refined computational models, extrapolation by artificial intelligence) and in extinct non-mammalian amniotes (e.g., correction factors for brains that do not completely fill the endocranial cavity). As such, the calculated values presented here, as well as their bearing on discussions of evolutionary patterns, will require re-analyses outside the scope of this paper to ensure that they are as accurate as possible.

We feel it is important to publish the traditional findings here for two reasons. First, we wish to acknowledge faithfully the scientific contributions of our late lead author. Second, we wish to allow for any direct comparisons between the findings in this paper and those previously published by Jerison (e.g., 1973; 2007; 2012). We encourage those who read and/or may cite this paper to do so with this note’s context in mind. We acknowledge that our dataset is non-comprehensive and that many additional published vertebrate endocasts exist. We encourage other researchers to synthesize and reanalyze all data now available. Some additional published datasets can be found in: Dechaseaux (1958), Silcox, Benham & Bloch (2010), Rowe, Macrini & Luo (2011), Orliac & Gilissen (2012), Long, Bloch & Silcox (2015), Harrington et al. (2016), Bertrand & Silcox (2016), Bertrand et al. (2019), Benoit et al. (2019), Bertrand et al. (2020), and Maugoust & Orliac (2021), Arnaudo & Arnal (2023), and Betrand et al. (2022; 2024b). Additionally, the following recent papers consider relative brain size of vertebrates through time: Tsuboi et al. (2018), Ksepka et al. (2020), Smaers et al. (2021).

Lastly, admittedly, due to the loss of our first author and his insights, we are unable to track down and cite all resources/methods involved in the compilation of body masses reported in Table 1.

Assessing neocorticalization and encephalization over 60 million years using endocasts

Table 1 provides complete summary data on the digitized scans of mammal endocasts and brains. A complete description of endocast provenance, endocast features, and body size determinations are presented in the Supplementary Results. Below, we present the digitized endocast images. Geological Time Scale (v. 6.0), published by the Geological Society of America (Walker & Geissman, 2022), provided dates and correlated time periods listed below.

Edinger’s early horses

To illustrate the use of endocasts in modeling neocorticalization and encephalization, the endocasts of Edinger’s horses (Edinger, 1948), photographs of which have frequently been used to illustrate progressive brain evolution (e.g., MacFadden, 1994; Simpson, 1951; subsequent sources that cite them), are first presented. Figure 2 shows scans of endocasts of five of Edinger’s species and adds Hyracotherium (FMNH PM 59207=AMNH 55268). Edinger’s “Eohippus” (YPM 11694, listed as “Tillyhorse” in Table 1) is from Radinsky (1976). The digitized models of the bodies presented in Figs. 3 and 4 are scans of careful sculptures by Gidley (1927), from which the length, surface area, and volume were determined. The endocast of Mesohippus (Fig. 4A) was larger, more encephalized, and much more convoluted than that of Hyracotherium (Fig. 3A). Figure 5 shows the remainder of the endocasts of Edinger’s equoid genera: three fossil genera and three recent genera, including a zebra and two domesticated horses (a pony and a draft horse, reflecting body size variations within the domesticated species).

Paleocene fossils

The earliest digitized mammalian endocasts presented here are of the very large and heavy late Paleocene Titanoides and Barylambda, and the smaller Arctocyon, with the Paleocene sampled, here defined as about 66 Ma to 56 Ma. The Paleocene-Eocene boundary in our sample is somewhat artificial; the Phenacodus specimen is an individual that had survived into the early Eocene, but it should be representative of Paleocene members of the genus. These species are shown in Fig. 6.

Early eocene fossils

The Early Eocene dates used here are from 56 Ma to 42 Ma, and the endocasts of Coryphodon, Palaeosyops, Heptodon, and Isectolophus are shown in Fig. 7; Edinger’s Eocene “Eohippus” and Hyracotherium are shown in Figs. 2 and 3; Hyrachyus, Orthocynodon (“Amynodon”), Amynodon, and Eomoropus are shown in Fig. 8; Mesatirhinus junius, Mesatirhinus petersoni, Pachyaena, and Mesonyx are shown in Fig. 9; and Smilodectes and Notharctus are shown in Figs. 10A and 10B.

Later Eocene fossils

Here, “Later Eocene” is 42 Ma to 34 Ma. The endocast images of Necrolemur and Adapis are shown in Fig. 10; Uintatherium, Menodus (Titanotherium), Moeritherium, and Arsinotherium in Fig. 11; Pterodon, Cynodictis, Cynohyaenodon, and Procynodictis in Fig. 12; Cebochoerus, Hylomeryx, Mixtotherium, and Chadronia in Fig. 13; and Anoplotherium, Patriomanis, Poebrotherium, and Bathygenys in Fig. 14.

Oligocene fossils

The “Oligocene” samples date from 34 Ma to 23 Ma. These dates anchor the analysis of neocorticalization as changes with the passage of time. Daphoenus, Dinictis, Eusmilus, and Hoplophoneus are shown in Fig. 15; Merycoidodon, Mesohippus, Promerycochoerus, and Hesperocyon in Fig. 16; Leptictis (Ictops), Leptauchenia, Halitherium, and Hapalops in Fig. 17; Leontinia, Rhynchippus, Archaeotherium, and Promartes in Fig. 18; and Mesocyon in Fig. 19A.

Mio-Pliocene fossils

This group dates from 23 Ma to mid-Pliocene, about 3 Ma. Mustelictis, Leptocyon, and Eporeodon are shown in Fig. 19; Enaliarctos, Potamotherium, Plesiogale, and Zodiolestes in Fig. 20; Desmathyus (Hesperhyus), Oxydactylus, Homalodotherium, and Borhyaena in Fig. 21; Protypotherium, Proterotherium, Nesodon, and Merycochoerus in Fig. 22; Adinotherium, Merychippus (Atavahippus), Plionictis, and Pseudaelurus in Fig. 23; Paracynarctus, Ustatochoerus (note: endocast volume is large due to expanded cerebellum, but relative telencephalon size is comparable that of modern species), Carpocyon (“Osteoborus”), and Pseudhipparion in Fig. 24; Paratomarctus, Hemicyon, Pseudotypotherium, and Tyopotheriopsis in Fig. 25; and Cormohipparion, Procamelus, Homotherium, and Mylodon in Fig. 26.

Plio-pleistocene and recent fossils

Glossotherium, Arctodus, Aenocyon dirus, and Megalonyx are shown in Fig. 27; Nothrotheriops, Panthera, Smilodon, and Urocyon are shown in Fig. 28; Platygonus, Sthenurus, Thylacoleo, and Archaeolemur are shown in Fig. 29; Pachylemur (Lemur) insignis, and Palaeopropithecus, Australopithecus robustus, and Australopithecus africanus in Fig. 30.

Cetacean fossils

As in the living cetacean brain, no rhinal fissure exists in these fossils and thus no indication of an olfactory bulb or tract; therefore, we could not assess neocorticalization. See scans of the three fossil whales in the left panel of Fig. 31.

Extant non-primate mammals

Aonyx, Ursus (Black Bear), Canis latrans, and Felis catus are shown in Fig. 32; Cerdocyon, Odocoileus, Ursus (Kodiak), and Lama are shown in Fig. 33; Lutra lutra, Lutra canadensis, Procyon endocast and braincast, and Nasua are shown in Fig. 34; and Phascolarctos, Macropus, Vombatus, and Taxidea in Fig. 35.

Extant primates

Chiropotes, Mandrill, Homo-Falk A, and Homo-Falk B are shown in Fig. 36, and primate endocasts and braincasts (16 left hemisphere endocasts) are shown in Fig. 37.

Brain size—uses and limitations

For closely-related extant mammal species, brain size, and especially relative brain size, has been put forth as a generally effective tool for estimating many traits such as information processing capacity (i.e., “intelligence”; e.g., Roth & Dicke, 2005) and sources therein, but also note the authors’ emphasis on number of cortical neurons rather than brain size; (Striedter & Northcutt, 2019) and sources therein, (Smaers et al., 2021); but see Van Schaik et al., 2021), the size of certain gross brain regions (e.g., O’Keefe & Nadel, 1978; Stephan, Frahm & Baron, 1981; Stephan, Baron & Frahm, 1991; Jerison, 1991; Barton & Harvey, 2000; Baddeley, 2007; Brown et al., 2016), brain and cortex surface areas (Jerison, 1982; Ridgway & Brownson, 1984; Haug, 1987; this study), and neuronal density (Herculano-Houzel, 2010; Herculano-Houzel, 2017; Dicke & Roth, 2016). Yet, lack of functional demand for, or gradual disuse of, brain regions can result in reorganization of the cortical projections with important changes in the details of the brain maps (e.g., Qi, Stepniewska & Kaas, 2000). Importantly, changes in cortical organization are rarely if ever observable on endocasts and thus represent a limitation to how much can be extrapolated from comparative analyses of extant taxa. Indeed, uniquely specialized behavioral capacities and related brain structures+functions evolved, and it remains unclear if endocasts consistently and fully capture the frequency and/or nuances of these instances of reorganization through deep time. We note that some studies have been successful at showing evolutionary impact of functional demands on the evolution of brain size and shape (e.g., Bertrand et al., 2021; Bertrand et al., 2024a; Bertrand et al., 2024b; Schwartz et al., 2023).

Yet, endocasts remain a rich source of information about brain size, shape, and composition in extinct taxa, especially if the uniformitarian hypothesis (Simpson, 1970) holds for the neurobiology and physiology of vertebrates. Further, especially in mammals and birds, fidelity between brain and endocast produces highly detailed endocasts (e.g., Jerison, 1969; Jerison, 1973; Jerison, 1977; De Miguel & Henneberg, 1998; Iwaniuk & Nelson, 2002; Macrini et al., 2007; Watanabe et al., 2019; Early et al., 2020), and these close brain:endocast relationships appears to extend far into the fossil record (e.g., Rowe, Macrini & Luo, 2011; Balanoff, Smaers & Turner, 2016 and sources therein). There are rare but specific cases where evidence from fossils sometimes contests the uniformitarian hypothesis. For example, the endocast volume of the Eocene Hyracotherium in this study is 24 ml, and given endocast shape, we roughly estimate the approximate volume of its cerebellum as at least five ml—about twice as large as expected given comparative data. Although these cases inject complexity in the interpretation of quantitative trends, there are nevertheless present interesting demonstrations of difference that have potential to shape our understanding of how, when, and, perhaps why, brain regions evolve.

Mammalian olfactory bulbs

Evolutionary studies of amniote olfactory bulbs are a challenge, especially for non-mammals, because olfactory bulbs may be broken, distorted, or not visible on natural endocasts. Because of the uncertainties, our analyses of neocorticalization exclude the olfactory bulbs from the measurement of the endocast. However, all digitized endocast files and associated figures in this paper include the olfactory bulb for potential future study. For additional information on specific cases, see Supplemental Information 1B.

Midbrain exposure in mammals

Dorsal midbrain (tectal) exposure is striking in the koala (Phascolarctos cinereus) brain (Haight & Nelson, 1987) but is obscured on the endocast by the overlying confluence of sinuses (Fig. 35A). The morphological and/or functional underpinnings(s) of this prominent tectum is/are not yet well understood. Interestingly, some, but not all, extant bats have visible tecta on their endocasts (Maugoust & Orliac, 2023), and the colliculi in at least some extinct bats are visible in endocasts (Maugoust & Orliac, 2021 and sources therein). Thus, we find no predictable pattern for when or how to model an exposed dorsal midbrain in extinct mammalian taxa unless there is direct evidence for an exposed tectum on the endocast (e.g., four separate bumps for the corpora quadrigemina).

Increased neocorticalization in mammals

We graph increase in neocortical surface ratio (forebrain surface area/total surface area of the brain or endocast) over geologic time in Fig. 38. In Fig. 38, extant species line up as the vertical column of points at 0 Ma. At 60 Ma (X =  − 60), the average neocorticolization for mammals sampled is 15%. Indeed, we reasonably approximate the earliest sampled extinct species, Arctocyon and Titanoides, as neocorticalized at 22.5% (compare to 10.3% with olfactory bulbs included in Bertrand et al., 2022) and 14.1%, respectively. Today (0 Ma, X = 0), average neocorticaliation is 58%. These results are similar to the preliminary study of Jerison (2012) that reported an increase of 5% neocorticalization per 10 million years. For further useful comparisons and updates to these findings, see Bertrand et al., 2022 and Bertrand et al., 2024a.

Briefly, we note here that the euprimates included in our analysis and that of Jerison (2012) come out to be “above average” with respect to neocortical size. However, we defer to the results and discussion of Long, Bloch & Silcox (2015) for more in-depth consideration and analyses of stem primates.

Neocorticalization and encephalization in mammals

As similarly reported in Jerison (2012), graphing mammalian neocortical surface area against EQ (Fig. 39) demonstrates that neocortal expansion plateaus at about 80% once EQ reaches ∼2.0. That this plateau exists suggests that neocorticalization is constrained by factors unrelated to brain size, which itself shows no upper-limit fall-off. Certainly, topics of neural packing constraints (e.g., Assaf et al., 2020) and the phylogenetic conservation of mammalian order connectomes (Suarez et al., 2022), scaling of brain matter composition (Ardesch et al., 2022), and neuronal wiring costs in mammals (Huang & Yu, 2023) are hot topics in the literature. We look forward to future illuminating discoveries in these fields.

Mammalian encephalization

As a between-species trait, brain size is determined primarily by body size, and that is its “allometric” factor. Further, mammalian relative brain size enlarged beyond expectations set by the trend of non-mammalian vertebrates (Fig. 40). (Notably, independent variations in body size impact changes in relative brain size, too.) Importantly, we remind readers that this result should not be taken at face-value or as a novel finding because our analysis does not include data or results from recent studies on the evolution of relative brain size in mammals (e.g., Bertrand et al., 2022). About 80% of the variance in brain size in extant mammals is attributable to body size differences (Fig. 40B; r = 0.81). The residual from the allometric regression of log brain size on log body size is the statistic that defines an encephalization quotient (EQ). Thus, across species, EQ presumably describes at least some of the remaining 20% variance, which is evidenced by the variability of EQ in our sample.

Mammal-reptile boundary

Brain-body relationships in large numbers of living amniotes (mammals, N = 647; birds, N = 219; and reptiles, N = 59) have been described historically using convex polygons to better understand inter-class allometric relationships (Jerison, 2007; Fig. 40A). Extant birds and mammals show similar encephalization, with the bird polygon overlapping a portion of the larger mammalian polygon. Results for extant reptiles show them to be less encephalized (see also Van Dongen, 1998 for larger sample size), and their polygon rests below those for birds and mammals. Non-amniote vertebrates (not graphed in Fig. 40) fall within or below the reptile polygon (further evidence: Van Dongen, 1998, Jerison, 2001b). Electric fish, however, are within the mammalian range, cartilaginous fish overlap the reptilian and mammalian ranges, and “agnathans” form a small polygon at the lower margin of the main fish polygon (for details, see Jerison, 2000).

Re-examining these historical polygons in light of this perspective study, we added all digitized data and their regression line in Fig. 40B; only the fossil data and their regression line were added to Fig. 40C. Unsurprisingly, only a few of the extinct mammals fell below the lower boundary of the extant mammalian polygon, representing a potential “starting point” for the encephalization that took place as mammals evolved to reach the present lower limit.

However, the datum contributed by Arctocyon primaevus is surprising and represents a mammalian point falling within the (extinct) dinosaur polygon. This requires reconsideration of previous conclusions about the allometric border between mammals and reptiles (Jerison, 1973), as dinosaurs have hitherto been considered a natural extension of the polygon of extant reptiles. The datum on Arctocyon is robust, with the endocast prepared by Russell & Sigogneau-Russell (1965) quite brain-like (Fig. 6), and the measurements accurate. Although the body size was originally uncertain, a reanalysis of the skeletal material by Argot (2013) is definitive, making the body size estimate as good as it can be. Interestingly, and relevant to this finding for Arctocyon, Bertrand et al. (2022) found a temporary lag in relative brain size for placental mammals in the Paleocene as compared to the Mezozoic due to body size increasing prior to brain size.

Therefore, the area of the polygon drawn for dinosaurs requires reconsideration. Fig. 40D summarizes a new view of mammal-dinosaur allometric relationships. HJJ redrew the upper boundary of the reptile-dinosaur convex polygon, and instead of connecting foci of the extant reptile polygon to a convex polygon that included speculations about dinosaur brain sizes, in Fig. 40D, HJJ extended the reptile polygon (dotted line) to include larger body sizes. The earlier drawing assumed that dinosaur brains were half the volume of their endocasts and bounded their assumed brain sizes. The new extended boundary of the reptile polygon is a brain boundary (not a brain-endocast boundary) assumes that living reptile brain sizes would best estimate dinosaur brain sizes, with a parallel lower boundary drawn through the smallest reptile brain sizes to complete the new convex polygon. This finding is generally corroborated by the findings of Morhardt (2016, chapter 3), which incorporate modern phylogenetic methods.

The newly drawn boundaries do not depend on prior estimates of brain-endocast relationships in dinosaurs. Rather, they assume that dinosaur brains would follow similar size rules as living reptile brains (again, see Morhardt, 2016, chapter 3; but see Caspar et al., 2024 for updates and further details on patterns for specific dinosaur groups and their impact on the findings of this study). In Fig. 40D, fifty-nine data points from extant reptiles (Platel, 1979) were overlain on the reptile polygon to help visualize how the polygon was drawn, as well as to show that the original polygon, established from far fewer data points (Jerison, 2007), remains useful. The maxima of the extant reptile polygon are a 134 kg crocodile (Crocodylus acutus) and a 205 kg alligator (Alligator mississippiensis), with their brains measuring 15.6 g and 14.08 g, respectively. Using these new boundaries, the lowest mammalian point, Arctocyon primaevus, now lies above the reptile polygon (Fig. 40D), still supporting the hypothesis that there is a distinct mammal-reptile boundary.

Exponential increases in mammalian cortical surface area

Surface-area-to-volume relationships for extant and extinct mammal taxa are presented in Fig. 41, with endocast surfaces of all sampled taxa (extinct and extant) regressed against their respective endocast volumes in Fig. 41A, and cortical surface areas of all sampled extant taxa regressed against brain size (volume) in Fig. 41B. The regression equation in Fig. 41B is a power function with the exponent 0.91. That this exponent is much greater than 2/3 (i.e., consistent scaling of a 3D object and its surface area; see exponent in Fig. 41A) shows that as brain size increases, the rate at which surface area increases accelerates in a highly predictable (r = 0.996) fashion. We attribute this rate change to exponential increases in convolutedness. To clarify, although convolutedness appears here to be almost entirely a function of brain size, there is further evidence that species do differ in convolutedness, at least at the ordinal level (e.g., see manatees and beavers in this study). The difference is small (Pillay & Manger, 2007), and it reflects the patterning of convolutions in orders of mammals (Welker, 1990; Van Essen, 1997), in particular of ungulates compared to other orders. Another caveat to consider here is the possibility for interspecific variation in convolution patterns on endocasts (Welker, 1990).

Proper mass

As stated earlier, despite general consistency in mammalian brain:brain region scaling, instances have been identified in which brain regions undergo statistically significant size change relative to other closely related species and in response to evolutionary changes in function and/or behaviors (i.e., “principle of proper mass” (PPM); e.g., Jerison, 1973; Jerison, 2001a; Jerison, 2001b; Butler & Hodos, 2005). The most dramatic of these features in mammals is the evolutionary enlargement of forebrain and neocortex. One caveat to PPM captured in this paper is the lack of difference in cortical convolutions between raccoons (Procyon lotor) and coatimundi (Nasua narica) despite validated differences in their foraging styles and how those styles map electrophysiologically in the brain (Welker & Campos, 1963; Johnson, 1990; Welker, 1990; but see Boch et al. (2024)) for a potential unifying hypothesis related to the expansion of the postcruciate gyrus). Thus, although the principle of proper mass is intuitive and often demonstrated, it is not always a foolproof assumption in the analysis of endocasts.

Within-species variation

A previous analog analysis of twenty natural endocasts—collected at the Reeves Fossil Bed in the Big Bend area of Texas, Chadronian, end of the Eocene (Wilson, 1971) and regarded as variants of a single species, Bathygenys reevesi—revealed that endocast volumes were between 10 and 12 ml and normally distributed, with a coefficient of variation (CV) of about 10% (Jerison, 1979). The same analysis showed that a CV of ∼10% was also a good fit for the data of other extant and fossil brains and endocasts including house cats, chimpanzees, living and fossil equoids, and living and fossil hominins (Jerison, 1979). Here, we calculated CVs here using data from eight Bathygenys endocast specimens lacking olfactory bulbs for comparison with the general sample (Table 2). Using digitized endocast data, the CVs for endocast volume, surface area, neocortical area, and neocortical:surface area ratio were 10.6%, 9.9%, 7.8%, and 6.5%, respectively. This compares to a previous analysis of digitized CT images of 157 Bathygenys samples, which showed higher CVs for the length of olfactory bulbs (CV = 15.8%), width of the hypophyseal endocast (CV = 16.3%), and cerebellum (13%) (Macrini, 2009). Although higher, we conclude that these CV values are similar enough to the current results to raise no important questions about the adequacy of measurements on a single specimen of a single species to represent its brain as the information-processing organ. Certainly, the issue of within-species variation is question-specific, with high variability at the species level being more relevant to finer (e.g., intra-Family) versus broader (e.g., inter-Order) comparisons.