Canadian Journal of Psychology, 1991. 45(4), 507 522
Sex Differences in Human Brain Size and the General Meaning of Differences in Brain Size Michael Peters University of Guelph ABSTRACT Contrary to commonly held convictions, there is no clear association between brain size and body parameters in humans. Within sexes, once age and health status are controlled for, there is no significant association between brain size and body height for females. For males, body height accounts for no more than .04% of the variance in brain size. The relation between brain weight and body weight is even less clearly defined. Nevertheless, there are large and significant differences in brain size between the sexes. If no adequate body parameters can be found that scale to brain size within the sexes, the marked dimorphism between males and females makes it even more difficult to find a common set of parameters that allow evaluation of brain size differences between sexes. Within and across sexes, there is no convincing link between a limited measure of behavioural capacity (1Q) and brain size. This leads to the more general question: Why would one expect such a link, and, if it is not found, what docs this mean in the context of general theories of cortical function? RKSUMK Contraircment aux croyances populaires, il n'y a pas chcz l'humain de relations claircs entre la taille du cerveaux et les paramctrcs corporcls. Dans le meme sexe, unc fois l'age et I'etat de sante controles, il n'y a pas de relation significative cntrc la taille du cerveau et la grandeur en cc qui concerne les femelles. Chez les males, la grandeur tient compte pour environ .04% dc la variance dans la taille du cerveau. La relation poids du cerveau ct poids du corps est encore moins bien definie. Neanmoins, des differences significatives existent entre les sexes en cc qui concerne la taille du ccrvcau. S'il s'avfere difficile de trouvcr des paramctres corporels adcquals qui eorrelent la taille du ccrvcau avee le sexe, le dimorphisme marque entre les males ct les femelles rend encore plus difficile la mise en evidence d'un ensemble commun de paramelres qui permet 1'evaluation dc differences entre les sexes dans la taille du cerveau. Unc analyse intra et intersexes indique qu'il n'y a pas dc lien convaincant entre une mesure limitec dc capacitc comportementale (i.e., QI) el la taille du cerveau. Ce qui nous mine a une question plus generale: pourquoi devrions-nous nous attendre a un tel lien, et, s'il n'est pas trouve, qu'estce que cela pourrait significr dans 1c contexte des theories generates du fonctionncment cerebral. Those who study brain/body size relations in modern and extinct mammals (cf. Jerison & Jerison, 1988) state specifically that within-spedes brain/body size comparisons do not have the same meaning as between-species comparisons. Unfortunately, psychologists who make claims about the relation between brain size and intelligence (cf. Rushton, 1988) and those who attack such claims do not take this distinction into consideration. Because of this, there is a general assumption that brain and body size are related within
This work was supported by Natural Science and Engineering Research Council of Canada Grant No. A 7054. Please address correspondence to Michael Peters, Phd, Dcpt. Psychology. University of Guelph, Guelph, Ontario, Canada NIG 2W1. E-mail: [email protected] 507
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species just as they are between species. In addition, there is a belief, based on evolutionary trends in mammals, and particularly hominids, that larger brains stand for greater behavioural capacity1. Again, the assumption is that trends valid for between-specics comparisons are valid for within-specics comparisons. Are these assumptions justified, and, if not, what are the implications, especially in terms of the large sex differences in brain size? These questions will be considered below. In Part 1, the nature of the available evidence that relates brain size to body size will be discussed. In Part 2, the scant evidence on the relation between brain size and intelligence will be reviewed, followed in Part 3 by a consideration of the significance of brain size in the context of current theories of cortical function. It should be noted that the entire discussion will be limited strictly to brain size as such. No consideration will be given to the possibility of different organizational patterns in male and female brains (Kimura, 1987) because this docs not relate to brain size in any obvious way. 1. BRAIN/BODY SIZE RELATIONS Gould (1981) illustrated how anatomical information on differences in brain size between races and sexes was used in a pernicious way to confirm existing prejudices in terms of mental capacity. Although brain size differences between races are not at all firmly established (Tobias, 1970), the differences in brain size between the sexes are sizable and confirmed across various samples. They do have to be accounted for. An obvious possibility is that the sex differences in brain size are related to differences in body size. After all, one would expect that brain size is scaled in some way to body size so that females, being some 12-15% smaller in body si/.c than males, would be expected to have smaller brains than males. Similarly, it is assumed that within the sexes, brain size is scaled to body size. What is the evidence for such scaling? In order to answer this question, the allometry of brain/body relations has to be considered in some detail. The term allometry refers here to the evaluation of changes in the size of the brain relative to body size. The Expected Brain Size for a Mammal of a Given Size Empirical work such as described in Jcrison's (1973) path-breaking book on the evolution of brain and intelligence shows that when the brains of large numbers of individuals of different modern mammalian orders are measured, brain weight can be related to body weight with a simple function (brain weight = 0.12 x body weight in grains 7 ^), where the exponent gives the slope of the straight line that is obtained when log brain weight is plotted against log body weight. Because of the generally clear relationship between brain and body weight for comparisons across orders, it is understandable that in the neuropsychological literature (e.g., Kolb & Whishaw, 1990) the differences in brain weight between men and women have been attributed to body size differences. However, the matter is more complex than that.
'it is not possible, or even defensible, to define behavioural capacity in any precise way or to provide particular operational definitions. The term behavioural capacity can be used meaningfully only if it is allowed to denote the broadest possible collective of human abilities.
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When measurements are compared at different taxonomic levels, the slope of the log brain weight/log body weight function changes. Harvey (1988) shows this for comparisons at different taxonomic levels in primates. For instance, when the analysis is made at the genus level (i.e., mapping brain to body size lor individuals of the same genus) but of different species, the slope is less steeply inclined than the slope that is obtained at the subfamily level. When the analysis is performed at the species level, the slope that relates log brain and log body weight of different individuals belonging to the same species approaches zero. In other words, one cannot expect any clear relation between body weight and brain weight for individuals within a species. If this statement holds for humans, the attempt to account for sex differences in brain size in terms of differing body size is bound to be unsuccessful. In considering brain/body size relations within the human species, two aspects have to be considered. First, there is the general question of sampling problems, and, second, there is the more specific question of what points of reference can be used when comparing brain weights relative to individuals differing in body parameters. Sampling Problems Whenever the brains of different populations are compared, sampling problems enter the picture. On occasion, and this will be illustrated later when discussing the corpus callosum, sex comparisons are based on samples that are not comparable. However, it is unlikely that the basic finding of female brains being smaller than male brains can be reduced to sampling problems. The best available sample, that described by Pakkenberg and Voigt (1964), shows sex differences in brain size that are comparable in magnitude to the differences in cranial capacity between the sexes obtained by Passingham (1979) for a living sample in which men and women were matched according to social status. The usual problems of, for example, differences in nutritional status, do not enter the picture for that sample. Moreover, in other samples such as that of Jugoslavian brains described by Gjukic (1955), the overall brain weights (M = 1358 g, F = 1228 g) differ considerably from those obtained by Pakkenberg and Voigt (M = 1440 g, F = 1282 g), but the male/female differences arc strictly comparable. Similar statements can be made about the sample described by Ho, Roessmann, Straumfjord, and Monroe (1980a). In some studies, the differential between males and females is slightly less than that observed in the above studies (Ricklan & Tobias, 1986) but the difference is still very marked. Indeed, it was the very stability of the male/female differential that caused Ricklan and Tobias to comment on a relatively small departure. It is of interest to note that whatever can be said about the stability of the comparisons between males and females cannot be said about differences between brain size of various ethnic groups. Recent claims by Rushton (1988) about differences in brain size between what he calls different races are based on an essentially arbitrary selection of data from studies where the background of the samples is not known. The arbitrariness is illustrated by a comparison of the Pakkenberg and Voigt (1964) and Gjukic (1955) data. The average brain weight of Jugoslavian males and females differs from that of Danish males and females by a larger amount than the differences cited by Rushton between white and black (whatever that means) samples.
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The average weight of the brains of Jugoslavs is less than that given by Rushton tor blacks. Similarly puzzling figures can be obtained from the relatively well controlled study by Appel and Appcl (1942). In that study, the brains of Bavarians arc larger than the brains of Americans, and the brains of Bohemians (I assume not of the Jack Kerouac type) are again heavier than the brains of the former groups by amounts that exceed the differences between blacks and whites cited by Rushton. What Tobias wrote in 1970 about the sampling problems when comparing brain sizes across ethnic groups still is valid today. It is particularly important that the early nutritional status of the mothers in the various populations is comparable (Brown, 1966). What is the Appropriate Basis for Comparing the Brain Weight of Individuals That Differ in Body Parameters? Jerison (1979) makes his position with regard to humans quite clear: "In the human species it is likely that there is no relationship at all between brain size and body size in healthy adults of the same sex and ethnic group" (p. 39). His conclusion is based, in part, on his recalculation of the relation between body height and brain weight for the sample studied by Pakkenberg and Voigt (1964). In general, a relationship between height and brain weight has been found, but as older people arc smaller than younger people, researchers must control for the confounding influence of age. When Jerison (1979) calculated the correlation between body height and brain weight for a subsamplc of males within the age range of 28-41 years, a correlation coefficient of r = .05 was found. Passingham (1979) came to similar conclusions for a subsample of 198 males and 92 females aged between 18 and 45 years of age. In this case, the correlation for males was r = .20 and for females r = . 12. In spite of the discrepancy of values for the two analyses, which both had as a basis the Pakkenberg and Voigt (1964) data set, two aspects are noteworthy. First, the correlation between body height and brain weight for the female sample was not significant. Second, even in the case of the male subsamplc as defined by Passingham, the correlation accounts for only .04% of the variance. If body weight and brain weight are correlated, an even poorer correlation emerges for females. Passingham (1979) showed a correlation of r = .19 for males and of r = .025 for females. The slope relating body weight and brain weight, therefore, is not very steep for males and entirely flat for females. In other words, there is, within relatively well selected samples, no impressive relationship between body weight or height and brain weight. Both Jerison's and Passingham's analyses indicate the absolute necessity of controlling for age when relating brain and body parameters. There is some moderate agreement (Ho et al., 1980a) that body height is a better indicator of brain weight than body weight and that body surface might be a slightly better indicator than body height. A more detailed analysis of the Pakkenberg and Voigt (1964) data by Holloway (1980) reveals that the situation is even more complex than the above discussion suggests. Holloway separated out of the data set subgroups of males and females who were classified, on the basis of weight, as small or big (Holloway, 1980, Table 8). The females classifed as big averaged some 70.278 kg in weight and had an average brain weight of 1319.7 g. Females classified as small had an average
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body weight of 54.514 kg and an average brain weight of 1316.0 g. Thus, there was no appreciable difference in brain weight between the two groups differing drastically in body weight. In contrast, males classifed as big (body = 82.612 kg) had brains averaging 1480.8 g, whereas males classifed as small (body = 64.032 kg) had brains averaging 1438.9 g. This supports the general finding (Ho, Roessmann, Straumfjord, & Monroe, 1980b; Jerison, 1979; Passingham, 1979) that the relationship between body weight and brain weight tends to be more clearly expressed for males. However, it also has to be conceded that the brain sizes of the small and big males were not nearly as divergent as would be expected on the basis of body size differences. Holloway's (1980) data might be interpreted as revealing a male/female difference in body weight/brain allomctry because the big females, who were heavier than the small males, clearly had smaller brains than the small males. However, Holloway does not comment on the important fact that the average difference in height between the females classifed as big and small was only 1.2 cm. In the case of the males the difference in height between the two groups was 4.8 cm in favour of the big males. It is clear that in females, greater body weight does not necessarily indicate greater height. As far as the big female to small male comparison is concerned, it is to be noted that the small males, although lighter in weight, were still 7.3 cm taller than the big females. Holloway's failure to find convincing correlations between body weight or body height and brain weight for females is not surprising in view of the above facts. The inadequacy of brain/body parameter scaling is illustrated particularly clearly when brain size is expressed as ratio of the observed (E,,) to the expected brain weight, the encephulizaiion index, EQ (Jerison, 1973). The formula given above (Et. = kP") gives the expected brain weight for a modern mammal. For the average modern mammal the EQ (E,,/Ee) should be close to 1. Because of the problems expressing brain weight relative to body parameters, one would expect within-sex comparisons to make little sense. For instance, if one calculates EQs on the basis of the data provided by Holloway (1980), then in his distinction between big and small males, big males would have an EQ of 6.6, and small males would have an EQ of 7.5! A similar comparison for big and small females yields EQs of 6.6 and 7.7, respectively. Ironically, if the EQs for large numbers of human males and females are calculated, very similar values emerge. For instance, in Holloway's analysis of Pakkenberg and Voigt's (1964) sample, the HQ is 7.1 for the male group and 7.1 for the female group. Similarly, in Jerison's (1973) analysis of the 721 male and 935 female specimens in Gjukic's data set, the EQ is 7.9 for males and 7.4 for females. We find here the very peculiar situation that brain weight and body weight are not meaningfully related within the sexes, but between the sexes a meaningful relation is expressed in the KQ. That not too much unqualified reliance should be placed on the cnccphalization quotient is further indicated by the fact that nonanthropoid simians such as the Cebus monkey can have EQs in excess of those shown by early hominids (Bckoff, 1989). Similarly, the Malayan sunbear has an EQ that is almost three times the EQs of other bear species (Kruska, 1988), and that is comfortably in the primate range, without there being any evidence of unusual behavioural capacity in this species.
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It is of interest to note that Gould (1981, p. 106) used Broca's original data for sex and brain size comparisons and reduced the sex difference in brain weights from 181 g to 113 g by controlling for height and weight in a multiple regression. Gould used a direct scaling equation instead of calculating the EQ. Rather than concluding that the remaining difference represents a genuine betwecn-sex difference, Gould questioned (as others have done before him) whether weight or height arc adequate referents for body/brain size allometry. Holloway's (1980) analysis validates Gould's concern. Tf meaningful distinctions between the brain sizes of the sexes are to be made, some common reference points that arc valid within and between the sexes have to be found. Weight and height are not useful because they do not mean the same thing in males and females. A possible confounding factor is metabolic rate, because metabolic rate has been related to brain size (e.g., Harvey & Bennet, 1983). It is known that the basal metabolic rate of females is some 5% less than that of males (Guyton, 1986). There is little question that this factor relates to the different meanings of body weight in the two sexes; however, in terms of scaling metabolic rate to brain size, open questions remain (Harvey, 1988; Heusner, 1982). Because of the unresolved difficulties posed by human dimorphism, it would be informative to obtain information on brain size differences in species where dimorphism is minimal — even though a generally valid answer for mammals is not likely because there are marked differences between species. For instance, in mice, males tend to be larger than females but female brains are not smaller than male brains (Hahn, 1979; Wahlstcn, 1982). Moreover, the brain/body weight relations for various species of myomorph rodents vary unpredictably along the sex dimension, with steeper slopes of the log brain weight/log body weight plots for females in some species and males in others (Mann, Glickman, & Towe, 1988). Of special interest would be information on brain/body relations in gibbons, where sex dimorphism is minimal, and some species among the Viverridae (e.g., meerkat) and Hyacnidac (e.g., spoiled hyaena), where females are larger than males. Such information is not available. Up to this point, only brain size as such has been related to body parameters. Can anything be gained by relating the number of cortical neurons to rxxly parameters, and can this number in turn be related to sex differences in brain size? As in the case of brain weight comparisons, the underlying reasoning for comparisons of neuron numbers derives not from comparisons of individuals within species, but from comparisons of individuals from different mammalian orders. The number of neurons required to maintain the basic functions of a body of a given size can be estimated by using the brains of primitive inscctivores as a point of reference (Jerison, 1973). Presumably, any neurons in excess of this number are "extra" in the sense that they presumably add additional capacity. To obtain the number of extra neurons N r , one subtracts the basic insectivore brain number of neurons Nh = 10 x B 2 " (where B = .03B2M) from Jerison's estimate of the total number of cortical neurons (N = lO^H2'-'). Thus, Nc = N - N,,. This procedure will yield more extra neurons for larger brains in general. For instance, by this criterion (and based on the brain and body weights provided by Russell, 1979), a sheep will have more extra neurons than a fox, and a camel will have considerably more extra neurons than a chimpanzee. These comparisons show that differences in
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extra neuron numbers between different mammalian orders can have no obvious significance in terms of behavioural capacity (see also Holloway, 1974). That being so, it could hardly be argued that the differences in extra neuron numbers that are inevitably observed in between-sex comparisons within the human species have any such significance. The general criticisms of problems in scaling brain size and neuron number and body relative to each other do not invalidate more broadly based attempts to relate body and brain (cf. Jcrison, 1973), but it is clear that, for the purposes of comparing individuals within species and between sexes, within a species no meaningful basis of comparison exists at this time. This reduces the question of sex differences in brain size to the more general question of what differences in brain size could possibly mean. An immediate impulse would be to challenge the question in itself. Could one not be satisfied with the simple acknowledgement that the brain, like other organs, shows a natural variability in size, and that is that? But the very reference to other organs shows that such an objection cannot be sustained. After all, the size of other organs tends to be related to physiological capacity in one way or another. Would not the size of the brain be related to its natural functions? Thus, the question of whether brain size differences arc not related to behavioural capacity, however broadly defined, seems a reasonable question to ask. And, if there is no such relation, what role docs brain size as such play in one's conception of cortical function? These two questions will be considered in the next two sections. 2. BRAIN SIZE AND BEHAVIOUR The pervasive expectation that larger brain size is linked to greater behavioural capacity, as based on companions of diffcrnt mammalian orders (Jerison, 1979), has evidently, and in spite of the explicit disclaimers by Jerison, been applied directly to comparisons within the human species (Rushton, 1988). The evidence that links behavioural capacity to brain size in humans is remarkably limited. Of the few published studies, only Passingham's (1979) work meets minimal methodological demands. Passingham related brain size to occupational groupings for a sample of individuals who had died but whose previous occupations were known. He also had a sample of living individuals whose IQ could be measured and related to body parameters and brain size estimates inferred via cranial measurements. If the exact measurement of a brain obtained by autopsy presents a problem, the estimation of brain parameters from outside the skull is even more uncertain. However measured, the relationship between brain size and IQ or occupational class is not impressive. For instance, once height has been partiallcd out, cranial capacity accounts for only .009% of the variance observed in the IQ measure! Eor the living sample, the estimates of female cranial capacity were, in keeping with studies where brains themselves are measured, considerably lower than the estimates for male cranial capacity, but the IQ measure shows no significant sex differences. The fact that the two sexes were similar in IQ, in spite of very drastic differences in cranial capacity, raises considerable doubts about Rushton's attempts to relate IQ differences between different ethnic/racial groups to differences in cranial capacity. This is so because even the questionable differences claimed by Rushton are not as large as the betweensex differences seen within any comparison group.
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Here, as in other similar comparisons, the fundamental lack of a theoretical basis for brain size comparisons is apparent. If IQ, or, to be generous, the underlying range of intellectual abilities thought to be reflected in IQ, is subject to selection in a biological sense, then it has to be shown that greater IQ confers greater reproductive fitness. While nobody would want to argue that a Wcchsler IQ of, let us say, more than 2 SD below the norm would not be clearly associated with a reduced reproductive potential in the sort of sample that was used to establish standarized norms, the case is much harder to make for IQ values above this level. If, within the normally observed range of human brain size, there are no compelling links between brain size and behavioural capacity, is there anything that can be said about extremes in human brain size? Glees (1988) reports on a person with microcephalia, with a verified brain weight of 395 g. Glees notes "...I could only admire his enormous dexterity and skill in moving and climbing, and his pleasant, friendly behavior" (p. 102). Passingham (1982), in his review of some of the literature, notes a person with a brain weight of 517 g was said to have good speech, although the sources Passingham cites agree that there was mental retardation. It does not appear as if small brain sizes of this sort are compatible with a normal range of behavioural capacities, however measured. Distributional data tell the same story. The Pakkenberg and Voigt (1964) data show that even in the sample of females, there were practically no brains weighing less than 900 g, and this is true for the males as well (Passingham, 1982, p. 120). This is important because if the lower limit for "normal" brain size was significantly below 900 g, the high metabolic cost of maintaining brain tissue would surely favour lower brain size. It is suggested here that there probably is a lower limit to the size of the brain that is capable of the range of abilities we associate with the average individual. Distribution curves suggest that somewhere between 900 and 700 g there is a transition from a "full" behavioural capacity brain to a "reduced" behavioural capacity brain. This is also in agreement with conclusions reached by Dart (1956). At the other end of the spectrum, it is clear that brains in excess of 1700 g are very rare (Passingham, 1979). Warkany, Lcmire, and Cohen (1981) feel that adult brain weights exceeding 1500 gm are already in the "excessive" range. This is probably too stringent a criterion, but it is clear that megcncephaly is associated with dysfunction just as microcephaly is. As with cases of microcephaly, the literature reports persons who depart from the mean by some 2-3 SDs but who have normal intelligence. The conclusions to be drawn arc quite simple. There is no obvious relation between brain size and behavioural capacity, within generously defined limits. What, then, is the meaning of individual differences in brain size? Do current theories of cortical function lead us to expect that larger brains can do more, and, if so, why aren't brains larger than they arc? 3. LIMITS TO BRAIN SIZE AND THE SIGNIFICANCE OF BRAIN SIZE IN THEORIES OP CORTICAL FUNCTION There is some reason to believe that the brain size of Homo Sapiens has not increased within the time span covered by the historical record. What are the factors
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that determine the upper limits of size in normally functioning brains? One limitation might be the familiar factor of metabolic cost. An argument has been made (Epstein & Epstein, 1978) that the size of the infant's head at birth is not limited by the dimension of the birth canal but by the metabolically sustainable brain mass. If so, this is liable to be an important factor in delimiting overall brain size relative to body size. It can be stated a priori that this factor is not important in the determination of sex differences in brain size because the metabolic rate in adult females (Guyton, 1986) is lower than that of males. In order to account for smaller female brains, it would have to be assumed that the metabolic rate of female infants is higher than that of males. There is no evidence in support of this. But there might be other factors that delimit brain size at the upper end. As the work by Rockcl, Hiorns, and Powell (1980) indicates, the basic number of neurons in a unit-sized slab of cortex that extends through all cortical layers does not differ much between various mammalian orders. What does differ is the degree to which cortical elements are interconnected. One index of this is the ratio of white matter to gray matter. Hofman's work (1985, 1988) indicates that the human brain has, compared to other primates, a significantly greater proportion of white matter, suggesting that a premium is placed on interconnectedness. The implication is clear. If the only way of increasing behavioural capacity is by increasing the surface of the cortical sheet while maintaining the same organizational principles of interconnectedness, the disproportionate growth of white matter that subserves intra- and interhemispherie connections will, in the end, limit the amount of cortical surface that can be added. In other words, there is a clear limit to the amount of cortex that can be added to the human brain if normal interconnectivity patterns are to prevail. But this approach begs the question. What conceivable advantage would be derived by adding physiologically expensive extra neural tissue in terms of brain function? Is there any theory of brain function that would a priori envisage advantages of more cortical mass? The answer to this question is more difficult than one might expect because, in a way, it presupposes that there is an understanding of how the cortex works. Such an understanding is not presently available. However, several recent models of cortical function allow at least a tentative exploration of where the answer to the question, how does more or less cortical surface relate to behavioural capacity in the widest sense, might lead. In the following, the assumption of a minimal cortical mass (900 g overall weight or even somewhat less) necessary for the full range of brain function in adult humans underlies all speculations. Ihe Modular Model Neurophysiologists tell us that the cortex is composed of vertically oriented smallest functional units that are called columns (Mountcastle, 1978). Each column is characterized by a unique set of input/output relations. Groups of columns are organized to form larger units that have in common the processing of a particular kind of sensory or motor function. The larger units, in turn, are interconnected for the purpose of, tor example, bringing together information from different modalities. So far, the view of a mosaic of vertically oriented units that arc interconnected towards some common function has been demonstrated only tor sensory and motor functions. After initial mapping of the somatosensory cortices that left many uncharged regions, it appears
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that more and more of the cortical surface can be filled by modules engaged in specific types of processing (Kaas, 1982). Ultimately, it is possible that the entire cortex can be represented as a mosaic of specific processing units that are interconnected. At the first approximation, "more" mapping units on the primary sensory or motor cortex mean finer resolution of sensory analysis or finer resolution of movement. But even here, it is totally unclear what more means in functional terms. For instance, it has been shown that the surface extent of the visual cortical area VI of a given macaque may be twice that of another animal (Van Essen, Newsomc, & Maunsell, 1984). What does this mean in terms of behavioural capacity in the visual domain of the individual animals who so differ? Indeed, beyond stating that more modules allow finer mapping of detail at the primary level and greater flexibility of interconnectivity at higher levels one cannot go. How this translates into behavioural capacity once a certain minimal level of mapping and interconnectivity is available remains to be determined, and whether additional units would increase the capacity of the system remains unanswered. It should be noted that there is more to the cortex (or, in Braitenberg's 1989 terms, less) than described by the modular scheme. Superimposed on the existing network of cortical modules is a system of broad interconnectivity that is likely involved in distributed functions that transcend any one modular mechanism. To the extent that this system of interconnections is based on the existing modular framework, that is, it does not involve separate and additional cortical areas beyond the ones that are already there, there is no a priori expectation that additional cortical mass would yield additional behavioural capacity in the sense of more or better or faster. The Purcellation Hypothesis Ebbeson (1984) addressed the question of how new functional circuits can arise in the brain. His parcellation hypothesis, oversimplified here in order to clarify exposition, suggests that new functional circuits are selected from already existing undiffcrentiated cortex. Implicit in the model is the assumption that in the evolution of the brain, the selection towards more cortical substrate has a selective advantage because it allows the development of as yet unanticipated additional capacity. Again, the addition of cortical tissue cannot be unlimited because whatever is there has to be integrated within the existing organization of intercortical and cxtracortical networks. Nevertheless, it can clearly be seen that this model does give a justification to an assumption that, within limits, more is belter. The Theory of Neuronul Group Selection This theory, advanced by Hdclman (1987), takes populations of neurons as the operative functional networks. Uoth Edclman's theory — the advanced state of development of his conceptions deserves the status of theory rather than model — and Ebbcson's (1984) model emphasize selection of already present units in the genesis of something that is functionally new. hxielman addresses the question of how external sensory events can be integrated into a perceptual experience by suggesting that these events select from the neural substrate those elements capable of responding to them. Edclman's theory about cortical function derives from his work on antibodies. With antibodies, there is the question: docs a foreign protein (antigen) that enters the body,
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and to which antibodies arc formed, instruct the antibody system to produce antibodies against this antigen, or does the antigen select among existing antibodies those that are capable of responding to it? The latter mechanism seems to apply. In analogy, a given sensory event selects from the primary sensory analyzers those that are capable of responding to it. The part of Edelman's theory that is of interest to the question of overall brain size will be considered here. Hdclman (1987) points out that the sensory system can be arranged in one of two extreme forms. First, the cortical repertoires that respond to incoming sensory events can be few in number and relatively unselectivc. That is, they can respond to a great number of sensory events, but because the potential number of different incoming events is huge they will not be able to discriminate very well between different sensory events. In analogy to the immune system, this would correspond to a small repertoire of antibodies that react relatively indiscriminately against a variety of antigens and can therefore cover a great range of these. The other extreme would be that for every possible sensory event there is a repertoire of cells that respond just to that particular event and to no other. In analogy to the immune system, this would imply the existence of a huge library of existing antibodies that are capable of responding to any conceivable antigen. Obviously, with regard to sensory events, a compromise has to be made between a system that is capable of responding to most anything, but is of little use because it offers few possibilities of discrimination, and a system that is enormously large and that can respond to all possible sensory events. Edelman's assumption about his selective ncuronal networks is that recognition (discrimination) can never be perfect and that "...there must be some number above which increasing the size of the repertoire will lead to no further gain; other mechanisms must be brought into play to improve performance" (Edelman, 1987, p. 56). Here, then, is a clear case of a situation in which more in terms of numbers of cortical units does not necessarily bring functional gains. The entire thrust of the present argument is that even relatively small brains have huge numbers of neurons. Researchers who took neurophysiology and ncuroanatomy courses as students may recall that only 10-20 years ago the total number of neurons was given as 10 billion, and neural computation theoreticians at the time thought this quite an adequate number for any operations the brain might carry out. Jerison's (1973, 1979) formulae estimate some 10 billion cortical neurons for the average brain. However, if recent methods and counts by Rockcl et al. (1980) are used as a basis, rather more impressive numbers emerge. Assuming that there are some 110 cortical cells in a slab of cortex with a surface measuring 24 x 30 micrometers, and estimating the area of the cortical surface with the formula given by Jerison (1979, p. 33), the estimated number of cortical neurons is even a small human brain of 1000 g is in the order of 32 billion. Even a brain of 900 g will have in excess of 29 billion cortical neurons.2 -The estimates of the total cortical surface area may he off the mark by a considerable margin- Cherniak (1990), supported by Jouandet el al. (1989), suggests (hat the average human cortical surface area is probably well below 2(XX) em-. On the basis ol estimates of the volume of neurons and their processes, Cherniak (urther argues thai the number of synapses per neuron is likely overestimated, or the number of neurons altogether, or both, because volume estimates for neurons and components are not compatible with estimates for numbers of neurons and available cortical volume. I lowcvcr. to further complicate the picture, t'hemiak's ncuronal volume calculations themselves arc open to question because he appears to base estimates on pyramidal neuron parameters. The majority of cortical neurons, however, are the much smaller stellate neurons.
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Computational Neural Networks Even those most enthusiastic about the potential of computational approaches acknowledge that the question of how real neural networks operate is difficult to answer at this point because much needed information is lacking (Churchland & Seijnowski, 1989). Much of the concern of network modellers has been directed at conceptually manageable problems, such as analysis of sensory events and computational models that guide movement in three dimensional space. For processing at this level, even small brains appear to posses ample resources. At higher levels of complexity that involve learning and recall (McNaughton, 1989), there are concerns about limits to storage capacity. For instance, in the model that uses associative correlation matrices as a metaphor for computational systems, it is clear that the capacity of the matrix increases with the dimensionality of the input channels, as McNaughton points out. He also points out that for real neural systems there might be definite limits to storage capacity. These limits are posed not by limits in the overall size of the brain, but by the general problems of intcrconncctivity. As the overall size of a given network increases, processing time also increases. The time element is of importance to an organism that lives in real time, in a real world, and will therefore impose restraints on the size of operating neural networks. It should be noted that all these models do in one way or another involve all levels of the cortical and subcortical (Braitenberg, 1989) systems in an interactive mode that does not posit separate higher regions. This is an important point. While there are higher order representations, so-called higher order cognitive processes do not take place in a uniquely reserved separate part of the brain. For instance, in Edelman's (1987) theory, there are neuronal groups that form primary and secondary (higher order) repertoires. The secondary repertoire is not formed by a different and separate neuron population, but is formed by neurons that are part of the primary repertoire and that form a functionally defined new entity. It is clear that this model of processing, which allows for different functional processes at anatomically overlapping loci, does not allow for any simple equation of "larger brain = greater capacity at functionally more complex levels." All of this is permissive of the concept of a necessary and sufficient cortical mass, with an emphasis more on interconnectivity than absolute cortical mass. In summary, while this attempt to relate cortical mass to behavioural capacity is tentative and informal, it docs suggest that there is certainly no clear indication of more being better. All current major models of cortical functioning place heavy emphasis on interconncctedncss of cortical neurons, and it seems that the very demands of interconnecting huge numbers of neurons arc the principal likely cause for constraints to unlimited addition of conical mass. Further, formal quantitative models are needed to determine possible tradeoffs between speed of operation and comprehensiveness of cortical operations that may, ultimately, determine whether or not small and large brains each have different functional advantages. The emphasis on interconnectedncss relates importantly to the question of whether there exists a sex difference in the size of the corpus callosum, because this commissure can be seen as symbolic of cortical interconnectivity as such (Peters, 1988).
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The Corpus Callosum as General Indicator of Cortical Interconnectivity Although work on sex differences in the anterior commissure is available (Allen & Gorsky, 1986), much more information is available on the corpus callosum. The literature on sex differences in callosal size is contradictory. At one extreme, some reports (e.g., Lacostc & Holloway, 1982) suggest that in humans the corpus callosum is absolutely larger in females. A similar pattern has even been claimed for other primates (Lacoste & Woodward, 1988). At the other extreme, Witelson (1985, 1989) and Clarke, Kraftsik, Van dcr Loos, and Innocent! (1989) claim that the corpus callosum of males is larger. In the case of the Clarke et al. study, there was a serious problem of matching sex samples appropriately. In the infant group where sex differences were shown, 6 out of 10 males were 6 months of age or older, whereas only 4 out of 12 females were 6 months or older. At this stage, age differences mean much in terms of brain development. For the adult sample, the average age of the 22 males was 62.0 years and that ol the 16 females was 82.1 years. It is interesting to note that for the two samples of subjects (fetuses and post-mortem cases) where the ages of subjects were exactly matched, no sex differences in callosal size were reported. Witelson's (1985, 1989) claim for a larger corpus callosum rests on a subsample of six non-right-handed males; in the other, larger, group of right-handers no sex differences were shown. The average brain weight of her six non-right-handed subjects, all of whom had died of cancer, was 1551 g- This figure is extraordinarily high for any group; it is impossibly high when the cause of death is considered. When brain weights are ordered according to cause of death, cancer patients arc among those with the most reduced brain weights at death (Appel & Appel, 1942). A cautious interpretation of the evidence, based also on the extensive literature review provided by Witelson (1989), leads to the conclusion that, in spite of differences in brain weight between the sexes, there is no evidence of a corresponding sealing of the corpus callosum: The absolute size of the corpus callosum appears similar for the sexes, and this suggests a comparative level of interconnectivity. Another reason for the similarity in callosal size across the sexes could perhaps be found in similar neuron counts for brains differing in size. There is very little evidence to answer this question. However, Zamenhof, Van Marthens, and Bursztyn (1971) suggest that brain size differences between larger and smaller chick and rat brains may be due to differences in supportive tissue mass rather than differences in neuron and glial cell counts. In humans, there is also suggestive evidence that small brain sizes need not mean small neuron counts. Dart (1956), in a discussion of a brain that weighed only 851 g, states that "...in Inaba's individual the brain had amazingly compensated for its reduction in size by a threefold increase in the relative number of nerve cells present" (p. 26). Equality of cell numbers does not, of course, mean similarity in interconnectivity, but in the absence of information on either factor in comparisons of large and small brains within the human species, the need for studies of fine structure in large and small brains appears ever more urgent. CONCLUSION Within sexes, and for healthy individuals in the age range where brain development is completed and aging effects have nol yet set in, there is only a very small
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relationship between body weight and size parameters and brain size for males, and no relationship for females. Having said this, there is a sizable difference in brain size between the sexes that cannot be entirely accounted for by the conventionally used reference parameters of body height and body weight. It is concluded that the dimorphism in body parameters is such that the sealars weight and height, singly or in conjunction, do not allow a reasonable common metric that can be used to relate brain weight to body parameters across the sexes. In the absence of a meaningful relative comparison, the significance of the absolute differences in brain size that, in contrast to other neuroanatomical indices (Janowsky, 1989), are very marked across the sexes cannot be ascertained. The general question of the significance of differences in brain size, regardless of whether they occur within or between sexes, finds no better answer. Large differences in brain size exist between individuals, and there is no obvious relation between such differences and any behavioural indices as have been studied. Any further examination of the question will have to focus (a) on the differences in fine anatomy between large and small brains and (b) on the more general possibility that in terms of cortical function, the general limits of what can be done with the basic mammalian cortex have been reached in the human brain. 1 It has been suggested that, even within the normal range of human brain sizes, there might already be some tradeoffs between advantages offered by speed and efficiency and the advantages offered by greater size of the available neural network. References Allen, I..S-, & Gorsky, R.A. (1986). Sexual dimorphism of the human anterior commissure. Analom ical Record, 214, 3A. Appcl, F.W.. & Appcl. Iv.M. (1942). Intracranial variation in the weight of the human brain. Human Biology. 14, 235-250. Bckoff, M. (1989). Tools, terms, and lelcncephaloiis: Neural correlates of "complex" and "intelligent" behavior. Behavioral arul Brain Sciencex, 12, 591-593. Braitcnherg, V. (1989). Sonic arguments lor a theory of cell assemblies in the cerebral cortex. In I.. Nadcl, L.A. Cooper, P. Culiocovcr, & M. Harnish (F.ds), Neural connections, menial compulation (pp. 137 145). Cambridge: MIT Prcss. Brown, R.H. (1966). Organ weight in malnutrition with special reference to brain weight. Developmental Medicine and Child Neurology, 8, 512 522. Chcrniak, C. (1990). The bounded brain: Toward quantitative neuroanalomy. Journal of Cognitive Neuroxcience. 2, 58-68. Churchland, P S . , & Seijnowski. T.J. (1989). Neural representation and neural compulation. In L. Nadel, L.A. Gx>per, P. Culiocovcr, & M Harnish (Rds.) Neural connections, mental compulation (pp. 15-48). Cambridge: MIT Press. Clarke, S., Kraftsik, R-, Van der Loos. H , & Innocenli. Ci.M. (I9K9). Forms and measures of the adult anil developing corpus eallosum: Is there sexual dimorphism? Pie Journal oj Comparative Neurology. 2X0. 213-230.
'if this premise is correct, there are no mammalian brains as large or larger than human brains that exceed the latter in complexity of interconnections. Detailed work on whale brains shows a simple cortical structure with a relatively and absolutely small corpus eallosum (Morgane, Jacobs. & Galaburda, 1986). It is likely that work on other extremely large brains, such as those of elephants, will also show a more coarsegrained cortex and poorer intcrconnectivity in absolute lernis. In such large animals, the very distances that have to be .spanned will require cell bodies IO l>c larger in order lo sustain the long ax
Sex Differences in Human Brain Size and the General Meaning of Differences in Brain Size Michael Peters University of Guelph ABSTRACT Contrary to commonly held convictions, there is no clear association between brain size and body parameters in humans. Within sexes, once age and health status are controlled for, there is no significant association between brain size and body height for females. For males, body height accounts for no more than .04% of the variance in brain size. The relation between brain weight and body weight is even less clearly defined. Nevertheless, there are large and significant differences in brain size between the sexes. If no adequate body parameters can be found that scale to brain size within the sexes, the marked dimorphism between males and females makes it even more difficult to find a common set of parameters that allow evaluation of brain size differences between sexes. Within and across sexes, there is no convincing link between a limited measure of behavioural capacity (1Q) and brain size. This leads to the more general question: Why would one expect such a link, and, if it is not found, what docs this mean in the context of general theories of cortical function? RKSUMK Contraircment aux croyances populaires, il n'y a pas chcz l'humain de relations claircs entre la taille du cerveaux et les paramctrcs corporcls. Dans le meme sexe, unc fois l'age et I'etat de sante controles, il n'y a pas de relation significative cntrc la taille du cerveau et la grandeur en cc qui concerne les femelles. Chez les males, la grandeur tient compte pour environ .04% dc la variance dans la taille du cerveau. La relation poids du cerveau ct poids du corps est encore moins bien definie. Neanmoins, des differences significatives existent entre les sexes en cc qui concerne la taille du ccrvcau. S'il s'avfere difficile de trouvcr des paramctres corporels adcquals qui eorrelent la taille du ccrvcau avee le sexe, le dimorphisme marque entre les males ct les femelles rend encore plus difficile la mise en evidence d'un ensemble commun de paramelres qui permet 1'evaluation dc differences entre les sexes dans la taille du cerveau. Unc analyse intra et intersexes indique qu'il n'y a pas dc lien convaincant entre une mesure limitec dc capacitc comportementale (i.e., QI) el la taille du cerveau. Ce qui nous mine a une question plus generale: pourquoi devrions-nous nous attendre a un tel lien, et, s'il n'est pas trouve, qu'estce que cela pourrait significr dans 1c contexte des theories generates du fonctionncment cerebral. Those who study brain/body size relations in modern and extinct mammals (cf. Jerison & Jerison, 1988) state specifically that within-spedes brain/body size comparisons do not have the same meaning as between-species comparisons. Unfortunately, psychologists who make claims about the relation between brain size and intelligence (cf. Rushton, 1988) and those who attack such claims do not take this distinction into consideration. Because of this, there is a general assumption that brain and body size are related within
This work was supported by Natural Science and Engineering Research Council of Canada Grant No. A 7054. Please address correspondence to Michael Peters, Phd, Dcpt. Psychology. University of Guelph, Guelph, Ontario, Canada NIG 2W1. E-mail: [email protected] 507
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species just as they are between species. In addition, there is a belief, based on evolutionary trends in mammals, and particularly hominids, that larger brains stand for greater behavioural capacity1. Again, the assumption is that trends valid for between-specics comparisons are valid for within-specics comparisons. Are these assumptions justified, and, if not, what are the implications, especially in terms of the large sex differences in brain size? These questions will be considered below. In Part 1, the nature of the available evidence that relates brain size to body size will be discussed. In Part 2, the scant evidence on the relation between brain size and intelligence will be reviewed, followed in Part 3 by a consideration of the significance of brain size in the context of current theories of cortical function. It should be noted that the entire discussion will be limited strictly to brain size as such. No consideration will be given to the possibility of different organizational patterns in male and female brains (Kimura, 1987) because this docs not relate to brain size in any obvious way. 1. BRAIN/BODY SIZE RELATIONS Gould (1981) illustrated how anatomical information on differences in brain size between races and sexes was used in a pernicious way to confirm existing prejudices in terms of mental capacity. Although brain size differences between races are not at all firmly established (Tobias, 1970), the differences in brain size between the sexes are sizable and confirmed across various samples. They do have to be accounted for. An obvious possibility is that the sex differences in brain size are related to differences in body size. After all, one would expect that brain size is scaled in some way to body size so that females, being some 12-15% smaller in body si/.c than males, would be expected to have smaller brains than males. Similarly, it is assumed that within the sexes, brain size is scaled to body size. What is the evidence for such scaling? In order to answer this question, the allometry of brain/body relations has to be considered in some detail. The term allometry refers here to the evaluation of changes in the size of the brain relative to body size. The Expected Brain Size for a Mammal of a Given Size Empirical work such as described in Jcrison's (1973) path-breaking book on the evolution of brain and intelligence shows that when the brains of large numbers of individuals of different modern mammalian orders are measured, brain weight can be related to body weight with a simple function (brain weight = 0.12 x body weight in grains 7 ^), where the exponent gives the slope of the straight line that is obtained when log brain weight is plotted against log body weight. Because of the generally clear relationship between brain and body weight for comparisons across orders, it is understandable that in the neuropsychological literature (e.g., Kolb & Whishaw, 1990) the differences in brain weight between men and women have been attributed to body size differences. However, the matter is more complex than that.
'it is not possible, or even defensible, to define behavioural capacity in any precise way or to provide particular operational definitions. The term behavioural capacity can be used meaningfully only if it is allowed to denote the broadest possible collective of human abilities.
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When measurements are compared at different taxonomic levels, the slope of the log brain weight/log body weight function changes. Harvey (1988) shows this for comparisons at different taxonomic levels in primates. For instance, when the analysis is made at the genus level (i.e., mapping brain to body size lor individuals of the same genus) but of different species, the slope is less steeply inclined than the slope that is obtained at the subfamily level. When the analysis is performed at the species level, the slope that relates log brain and log body weight of different individuals belonging to the same species approaches zero. In other words, one cannot expect any clear relation between body weight and brain weight for individuals within a species. If this statement holds for humans, the attempt to account for sex differences in brain size in terms of differing body size is bound to be unsuccessful. In considering brain/body size relations within the human species, two aspects have to be considered. First, there is the general question of sampling problems, and, second, there is the more specific question of what points of reference can be used when comparing brain weights relative to individuals differing in body parameters. Sampling Problems Whenever the brains of different populations are compared, sampling problems enter the picture. On occasion, and this will be illustrated later when discussing the corpus callosum, sex comparisons are based on samples that are not comparable. However, it is unlikely that the basic finding of female brains being smaller than male brains can be reduced to sampling problems. The best available sample, that described by Pakkenberg and Voigt (1964), shows sex differences in brain size that are comparable in magnitude to the differences in cranial capacity between the sexes obtained by Passingham (1979) for a living sample in which men and women were matched according to social status. The usual problems of, for example, differences in nutritional status, do not enter the picture for that sample. Moreover, in other samples such as that of Jugoslavian brains described by Gjukic (1955), the overall brain weights (M = 1358 g, F = 1228 g) differ considerably from those obtained by Pakkenberg and Voigt (M = 1440 g, F = 1282 g), but the male/female differences arc strictly comparable. Similar statements can be made about the sample described by Ho, Roessmann, Straumfjord, and Monroe (1980a). In some studies, the differential between males and females is slightly less than that observed in the above studies (Ricklan & Tobias, 1986) but the difference is still very marked. Indeed, it was the very stability of the male/female differential that caused Ricklan and Tobias to comment on a relatively small departure. It is of interest to note that whatever can be said about the stability of the comparisons between males and females cannot be said about differences between brain size of various ethnic groups. Recent claims by Rushton (1988) about differences in brain size between what he calls different races are based on an essentially arbitrary selection of data from studies where the background of the samples is not known. The arbitrariness is illustrated by a comparison of the Pakkenberg and Voigt (1964) and Gjukic (1955) data. The average brain weight of Jugoslavian males and females differs from that of Danish males and females by a larger amount than the differences cited by Rushton between white and black (whatever that means) samples.
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The average weight of the brains of Jugoslavs is less than that given by Rushton tor blacks. Similarly puzzling figures can be obtained from the relatively well controlled study by Appel and Appcl (1942). In that study, the brains of Bavarians arc larger than the brains of Americans, and the brains of Bohemians (I assume not of the Jack Kerouac type) are again heavier than the brains of the former groups by amounts that exceed the differences between blacks and whites cited by Rushton. What Tobias wrote in 1970 about the sampling problems when comparing brain sizes across ethnic groups still is valid today. It is particularly important that the early nutritional status of the mothers in the various populations is comparable (Brown, 1966). What is the Appropriate Basis for Comparing the Brain Weight of Individuals That Differ in Body Parameters? Jerison (1979) makes his position with regard to humans quite clear: "In the human species it is likely that there is no relationship at all between brain size and body size in healthy adults of the same sex and ethnic group" (p. 39). His conclusion is based, in part, on his recalculation of the relation between body height and brain weight for the sample studied by Pakkenberg and Voigt (1964). In general, a relationship between height and brain weight has been found, but as older people arc smaller than younger people, researchers must control for the confounding influence of age. When Jerison (1979) calculated the correlation between body height and brain weight for a subsamplc of males within the age range of 28-41 years, a correlation coefficient of r = .05 was found. Passingham (1979) came to similar conclusions for a subsample of 198 males and 92 females aged between 18 and 45 years of age. In this case, the correlation for males was r = .20 and for females r = . 12. In spite of the discrepancy of values for the two analyses, which both had as a basis the Pakkenberg and Voigt (1964) data set, two aspects are noteworthy. First, the correlation between body height and brain weight for the female sample was not significant. Second, even in the case of the male subsamplc as defined by Passingham, the correlation accounts for only .04% of the variance. If body weight and brain weight are correlated, an even poorer correlation emerges for females. Passingham (1979) showed a correlation of r = .19 for males and of r = .025 for females. The slope relating body weight and brain weight, therefore, is not very steep for males and entirely flat for females. In other words, there is, within relatively well selected samples, no impressive relationship between body weight or height and brain weight. Both Jerison's and Passingham's analyses indicate the absolute necessity of controlling for age when relating brain and body parameters. There is some moderate agreement (Ho et al., 1980a) that body height is a better indicator of brain weight than body weight and that body surface might be a slightly better indicator than body height. A more detailed analysis of the Pakkenberg and Voigt (1964) data by Holloway (1980) reveals that the situation is even more complex than the above discussion suggests. Holloway separated out of the data set subgroups of males and females who were classified, on the basis of weight, as small or big (Holloway, 1980, Table 8). The females classifed as big averaged some 70.278 kg in weight and had an average brain weight of 1319.7 g. Females classified as small had an average
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body weight of 54.514 kg and an average brain weight of 1316.0 g. Thus, there was no appreciable difference in brain weight between the two groups differing drastically in body weight. In contrast, males classifed as big (body = 82.612 kg) had brains averaging 1480.8 g, whereas males classifed as small (body = 64.032 kg) had brains averaging 1438.9 g. This supports the general finding (Ho, Roessmann, Straumfjord, & Monroe, 1980b; Jerison, 1979; Passingham, 1979) that the relationship between body weight and brain weight tends to be more clearly expressed for males. However, it also has to be conceded that the brain sizes of the small and big males were not nearly as divergent as would be expected on the basis of body size differences. Holloway's (1980) data might be interpreted as revealing a male/female difference in body weight/brain allomctry because the big females, who were heavier than the small males, clearly had smaller brains than the small males. However, Holloway does not comment on the important fact that the average difference in height between the females classifed as big and small was only 1.2 cm. In the case of the males the difference in height between the two groups was 4.8 cm in favour of the big males. It is clear that in females, greater body weight does not necessarily indicate greater height. As far as the big female to small male comparison is concerned, it is to be noted that the small males, although lighter in weight, were still 7.3 cm taller than the big females. Holloway's failure to find convincing correlations between body weight or body height and brain weight for females is not surprising in view of the above facts. The inadequacy of brain/body parameter scaling is illustrated particularly clearly when brain size is expressed as ratio of the observed (E,,) to the expected brain weight, the encephulizaiion index, EQ (Jerison, 1973). The formula given above (Et. = kP") gives the expected brain weight for a modern mammal. For the average modern mammal the EQ (E,,/Ee) should be close to 1. Because of the problems expressing brain weight relative to body parameters, one would expect within-sex comparisons to make little sense. For instance, if one calculates EQs on the basis of the data provided by Holloway (1980), then in his distinction between big and small males, big males would have an EQ of 6.6, and small males would have an EQ of 7.5! A similar comparison for big and small females yields EQs of 6.6 and 7.7, respectively. Ironically, if the EQs for large numbers of human males and females are calculated, very similar values emerge. For instance, in Holloway's analysis of Pakkenberg and Voigt's (1964) sample, the HQ is 7.1 for the male group and 7.1 for the female group. Similarly, in Jerison's (1973) analysis of the 721 male and 935 female specimens in Gjukic's data set, the EQ is 7.9 for males and 7.4 for females. We find here the very peculiar situation that brain weight and body weight are not meaningfully related within the sexes, but between the sexes a meaningful relation is expressed in the KQ. That not too much unqualified reliance should be placed on the cnccphalization quotient is further indicated by the fact that nonanthropoid simians such as the Cebus monkey can have EQs in excess of those shown by early hominids (Bckoff, 1989). Similarly, the Malayan sunbear has an EQ that is almost three times the EQs of other bear species (Kruska, 1988), and that is comfortably in the primate range, without there being any evidence of unusual behavioural capacity in this species.
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It is of interest to note that Gould (1981, p. 106) used Broca's original data for sex and brain size comparisons and reduced the sex difference in brain weights from 181 g to 113 g by controlling for height and weight in a multiple regression. Gould used a direct scaling equation instead of calculating the EQ. Rather than concluding that the remaining difference represents a genuine betwecn-sex difference, Gould questioned (as others have done before him) whether weight or height arc adequate referents for body/brain size allometry. Holloway's (1980) analysis validates Gould's concern. Tf meaningful distinctions between the brain sizes of the sexes are to be made, some common reference points that arc valid within and between the sexes have to be found. Weight and height are not useful because they do not mean the same thing in males and females. A possible confounding factor is metabolic rate, because metabolic rate has been related to brain size (e.g., Harvey & Bennet, 1983). It is known that the basal metabolic rate of females is some 5% less than that of males (Guyton, 1986). There is little question that this factor relates to the different meanings of body weight in the two sexes; however, in terms of scaling metabolic rate to brain size, open questions remain (Harvey, 1988; Heusner, 1982). Because of the unresolved difficulties posed by human dimorphism, it would be informative to obtain information on brain size differences in species where dimorphism is minimal — even though a generally valid answer for mammals is not likely because there are marked differences between species. For instance, in mice, males tend to be larger than females but female brains are not smaller than male brains (Hahn, 1979; Wahlstcn, 1982). Moreover, the brain/body weight relations for various species of myomorph rodents vary unpredictably along the sex dimension, with steeper slopes of the log brain weight/log body weight plots for females in some species and males in others (Mann, Glickman, & Towe, 1988). Of special interest would be information on brain/body relations in gibbons, where sex dimorphism is minimal, and some species among the Viverridae (e.g., meerkat) and Hyacnidac (e.g., spoiled hyaena), where females are larger than males. Such information is not available. Up to this point, only brain size as such has been related to body parameters. Can anything be gained by relating the number of cortical neurons to rxxly parameters, and can this number in turn be related to sex differences in brain size? As in the case of brain weight comparisons, the underlying reasoning for comparisons of neuron numbers derives not from comparisons of individuals within species, but from comparisons of individuals from different mammalian orders. The number of neurons required to maintain the basic functions of a body of a given size can be estimated by using the brains of primitive inscctivores as a point of reference (Jerison, 1973). Presumably, any neurons in excess of this number are "extra" in the sense that they presumably add additional capacity. To obtain the number of extra neurons N r , one subtracts the basic insectivore brain number of neurons Nh = 10 x B 2 " (where B = .03B2M) from Jerison's estimate of the total number of cortical neurons (N = lO^H2'-'). Thus, Nc = N - N,,. This procedure will yield more extra neurons for larger brains in general. For instance, by this criterion (and based on the brain and body weights provided by Russell, 1979), a sheep will have more extra neurons than a fox, and a camel will have considerably more extra neurons than a chimpanzee. These comparisons show that differences in
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extra neuron numbers between different mammalian orders can have no obvious significance in terms of behavioural capacity (see also Holloway, 1974). That being so, it could hardly be argued that the differences in extra neuron numbers that are inevitably observed in between-sex comparisons within the human species have any such significance. The general criticisms of problems in scaling brain size and neuron number and body relative to each other do not invalidate more broadly based attempts to relate body and brain (cf. Jcrison, 1973), but it is clear that, for the purposes of comparing individuals within species and between sexes, within a species no meaningful basis of comparison exists at this time. This reduces the question of sex differences in brain size to the more general question of what differences in brain size could possibly mean. An immediate impulse would be to challenge the question in itself. Could one not be satisfied with the simple acknowledgement that the brain, like other organs, shows a natural variability in size, and that is that? But the very reference to other organs shows that such an objection cannot be sustained. After all, the size of other organs tends to be related to physiological capacity in one way or another. Would not the size of the brain be related to its natural functions? Thus, the question of whether brain size differences arc not related to behavioural capacity, however broadly defined, seems a reasonable question to ask. And, if there is no such relation, what role docs brain size as such play in one's conception of cortical function? These two questions will be considered in the next two sections. 2. BRAIN SIZE AND BEHAVIOUR The pervasive expectation that larger brain size is linked to greater behavioural capacity, as based on companions of diffcrnt mammalian orders (Jerison, 1979), has evidently, and in spite of the explicit disclaimers by Jerison, been applied directly to comparisons within the human species (Rushton, 1988). The evidence that links behavioural capacity to brain size in humans is remarkably limited. Of the few published studies, only Passingham's (1979) work meets minimal methodological demands. Passingham related brain size to occupational groupings for a sample of individuals who had died but whose previous occupations were known. He also had a sample of living individuals whose IQ could be measured and related to body parameters and brain size estimates inferred via cranial measurements. If the exact measurement of a brain obtained by autopsy presents a problem, the estimation of brain parameters from outside the skull is even more uncertain. However measured, the relationship between brain size and IQ or occupational class is not impressive. For instance, once height has been partiallcd out, cranial capacity accounts for only .009% of the variance observed in the IQ measure! Eor the living sample, the estimates of female cranial capacity were, in keeping with studies where brains themselves are measured, considerably lower than the estimates for male cranial capacity, but the IQ measure shows no significant sex differences. The fact that the two sexes were similar in IQ, in spite of very drastic differences in cranial capacity, raises considerable doubts about Rushton's attempts to relate IQ differences between different ethnic/racial groups to differences in cranial capacity. This is so because even the questionable differences claimed by Rushton are not as large as the betweensex differences seen within any comparison group.
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Here, as in other similar comparisons, the fundamental lack of a theoretical basis for brain size comparisons is apparent. If IQ, or, to be generous, the underlying range of intellectual abilities thought to be reflected in IQ, is subject to selection in a biological sense, then it has to be shown that greater IQ confers greater reproductive fitness. While nobody would want to argue that a Wcchsler IQ of, let us say, more than 2 SD below the norm would not be clearly associated with a reduced reproductive potential in the sort of sample that was used to establish standarized norms, the case is much harder to make for IQ values above this level. If, within the normally observed range of human brain size, there are no compelling links between brain size and behavioural capacity, is there anything that can be said about extremes in human brain size? Glees (1988) reports on a person with microcephalia, with a verified brain weight of 395 g. Glees notes "...I could only admire his enormous dexterity and skill in moving and climbing, and his pleasant, friendly behavior" (p. 102). Passingham (1982), in his review of some of the literature, notes a person with a brain weight of 517 g was said to have good speech, although the sources Passingham cites agree that there was mental retardation. It does not appear as if small brain sizes of this sort are compatible with a normal range of behavioural capacities, however measured. Distributional data tell the same story. The Pakkenberg and Voigt (1964) data show that even in the sample of females, there were practically no brains weighing less than 900 g, and this is true for the males as well (Passingham, 1982, p. 120). This is important because if the lower limit for "normal" brain size was significantly below 900 g, the high metabolic cost of maintaining brain tissue would surely favour lower brain size. It is suggested here that there probably is a lower limit to the size of the brain that is capable of the range of abilities we associate with the average individual. Distribution curves suggest that somewhere between 900 and 700 g there is a transition from a "full" behavioural capacity brain to a "reduced" behavioural capacity brain. This is also in agreement with conclusions reached by Dart (1956). At the other end of the spectrum, it is clear that brains in excess of 1700 g are very rare (Passingham, 1979). Warkany, Lcmire, and Cohen (1981) feel that adult brain weights exceeding 1500 gm are already in the "excessive" range. This is probably too stringent a criterion, but it is clear that megcncephaly is associated with dysfunction just as microcephaly is. As with cases of microcephaly, the literature reports persons who depart from the mean by some 2-3 SDs but who have normal intelligence. The conclusions to be drawn arc quite simple. There is no obvious relation between brain size and behavioural capacity, within generously defined limits. What, then, is the meaning of individual differences in brain size? Do current theories of cortical function lead us to expect that larger brains can do more, and, if so, why aren't brains larger than they arc? 3. LIMITS TO BRAIN SIZE AND THE SIGNIFICANCE OF BRAIN SIZE IN THEORIES OP CORTICAL FUNCTION There is some reason to believe that the brain size of Homo Sapiens has not increased within the time span covered by the historical record. What are the factors
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that determine the upper limits of size in normally functioning brains? One limitation might be the familiar factor of metabolic cost. An argument has been made (Epstein & Epstein, 1978) that the size of the infant's head at birth is not limited by the dimension of the birth canal but by the metabolically sustainable brain mass. If so, this is liable to be an important factor in delimiting overall brain size relative to body size. It can be stated a priori that this factor is not important in the determination of sex differences in brain size because the metabolic rate in adult females (Guyton, 1986) is lower than that of males. In order to account for smaller female brains, it would have to be assumed that the metabolic rate of female infants is higher than that of males. There is no evidence in support of this. But there might be other factors that delimit brain size at the upper end. As the work by Rockcl, Hiorns, and Powell (1980) indicates, the basic number of neurons in a unit-sized slab of cortex that extends through all cortical layers does not differ much between various mammalian orders. What does differ is the degree to which cortical elements are interconnected. One index of this is the ratio of white matter to gray matter. Hofman's work (1985, 1988) indicates that the human brain has, compared to other primates, a significantly greater proportion of white matter, suggesting that a premium is placed on interconnectedness. The implication is clear. If the only way of increasing behavioural capacity is by increasing the surface of the cortical sheet while maintaining the same organizational principles of interconnectedness, the disproportionate growth of white matter that subserves intra- and interhemispherie connections will, in the end, limit the amount of cortical surface that can be added. In other words, there is a clear limit to the amount of cortex that can be added to the human brain if normal interconnectivity patterns are to prevail. But this approach begs the question. What conceivable advantage would be derived by adding physiologically expensive extra neural tissue in terms of brain function? Is there any theory of brain function that would a priori envisage advantages of more cortical mass? The answer to this question is more difficult than one might expect because, in a way, it presupposes that there is an understanding of how the cortex works. Such an understanding is not presently available. However, several recent models of cortical function allow at least a tentative exploration of where the answer to the question, how does more or less cortical surface relate to behavioural capacity in the widest sense, might lead. In the following, the assumption of a minimal cortical mass (900 g overall weight or even somewhat less) necessary for the full range of brain function in adult humans underlies all speculations. Ihe Modular Model Neurophysiologists tell us that the cortex is composed of vertically oriented smallest functional units that are called columns (Mountcastle, 1978). Each column is characterized by a unique set of input/output relations. Groups of columns are organized to form larger units that have in common the processing of a particular kind of sensory or motor function. The larger units, in turn, are interconnected for the purpose of, tor example, bringing together information from different modalities. So far, the view of a mosaic of vertically oriented units that arc interconnected towards some common function has been demonstrated only tor sensory and motor functions. After initial mapping of the somatosensory cortices that left many uncharged regions, it appears
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that more and more of the cortical surface can be filled by modules engaged in specific types of processing (Kaas, 1982). Ultimately, it is possible that the entire cortex can be represented as a mosaic of specific processing units that are interconnected. At the first approximation, "more" mapping units on the primary sensory or motor cortex mean finer resolution of sensory analysis or finer resolution of movement. But even here, it is totally unclear what more means in functional terms. For instance, it has been shown that the surface extent of the visual cortical area VI of a given macaque may be twice that of another animal (Van Essen, Newsomc, & Maunsell, 1984). What does this mean in terms of behavioural capacity in the visual domain of the individual animals who so differ? Indeed, beyond stating that more modules allow finer mapping of detail at the primary level and greater flexibility of interconnectivity at higher levels one cannot go. How this translates into behavioural capacity once a certain minimal level of mapping and interconnectivity is available remains to be determined, and whether additional units would increase the capacity of the system remains unanswered. It should be noted that there is more to the cortex (or, in Braitenberg's 1989 terms, less) than described by the modular scheme. Superimposed on the existing network of cortical modules is a system of broad interconnectivity that is likely involved in distributed functions that transcend any one modular mechanism. To the extent that this system of interconnections is based on the existing modular framework, that is, it does not involve separate and additional cortical areas beyond the ones that are already there, there is no a priori expectation that additional cortical mass would yield additional behavioural capacity in the sense of more or better or faster. The Purcellation Hypothesis Ebbeson (1984) addressed the question of how new functional circuits can arise in the brain. His parcellation hypothesis, oversimplified here in order to clarify exposition, suggests that new functional circuits are selected from already existing undiffcrentiated cortex. Implicit in the model is the assumption that in the evolution of the brain, the selection towards more cortical substrate has a selective advantage because it allows the development of as yet unanticipated additional capacity. Again, the addition of cortical tissue cannot be unlimited because whatever is there has to be integrated within the existing organization of intercortical and cxtracortical networks. Nevertheless, it can clearly be seen that this model does give a justification to an assumption that, within limits, more is belter. The Theory of Neuronul Group Selection This theory, advanced by Hdclman (1987), takes populations of neurons as the operative functional networks. Uoth Edclman's theory — the advanced state of development of his conceptions deserves the status of theory rather than model — and Ebbcson's (1984) model emphasize selection of already present units in the genesis of something that is functionally new. hxielman addresses the question of how external sensory events can be integrated into a perceptual experience by suggesting that these events select from the neural substrate those elements capable of responding to them. Edclman's theory about cortical function derives from his work on antibodies. With antibodies, there is the question: docs a foreign protein (antigen) that enters the body,
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and to which antibodies arc formed, instruct the antibody system to produce antibodies against this antigen, or does the antigen select among existing antibodies those that are capable of responding to it? The latter mechanism seems to apply. In analogy, a given sensory event selects from the primary sensory analyzers those that are capable of responding to it. The part of Edelman's theory that is of interest to the question of overall brain size will be considered here. Hdclman (1987) points out that the sensory system can be arranged in one of two extreme forms. First, the cortical repertoires that respond to incoming sensory events can be few in number and relatively unselectivc. That is, they can respond to a great number of sensory events, but because the potential number of different incoming events is huge they will not be able to discriminate very well between different sensory events. In analogy to the immune system, this would correspond to a small repertoire of antibodies that react relatively indiscriminately against a variety of antigens and can therefore cover a great range of these. The other extreme would be that for every possible sensory event there is a repertoire of cells that respond just to that particular event and to no other. In analogy to the immune system, this would imply the existence of a huge library of existing antibodies that are capable of responding to any conceivable antigen. Obviously, with regard to sensory events, a compromise has to be made between a system that is capable of responding to most anything, but is of little use because it offers few possibilities of discrimination, and a system that is enormously large and that can respond to all possible sensory events. Edelman's assumption about his selective ncuronal networks is that recognition (discrimination) can never be perfect and that "...there must be some number above which increasing the size of the repertoire will lead to no further gain; other mechanisms must be brought into play to improve performance" (Edelman, 1987, p. 56). Here, then, is a clear case of a situation in which more in terms of numbers of cortical units does not necessarily bring functional gains. The entire thrust of the present argument is that even relatively small brains have huge numbers of neurons. Researchers who took neurophysiology and ncuroanatomy courses as students may recall that only 10-20 years ago the total number of neurons was given as 10 billion, and neural computation theoreticians at the time thought this quite an adequate number for any operations the brain might carry out. Jerison's (1973, 1979) formulae estimate some 10 billion cortical neurons for the average brain. However, if recent methods and counts by Rockcl et al. (1980) are used as a basis, rather more impressive numbers emerge. Assuming that there are some 110 cortical cells in a slab of cortex with a surface measuring 24 x 30 micrometers, and estimating the area of the cortical surface with the formula given by Jerison (1979, p. 33), the estimated number of cortical neurons is even a small human brain of 1000 g is in the order of 32 billion. Even a brain of 900 g will have in excess of 29 billion cortical neurons.2 -The estimates of the total cortical surface area may he off the mark by a considerable margin- Cherniak (1990), supported by Jouandet el al. (1989), suggests (hat the average human cortical surface area is probably well below 2(XX) em-. On the basis ol estimates of the volume of neurons and their processes, Cherniak (urther argues thai the number of synapses per neuron is likely overestimated, or the number of neurons altogether, or both, because volume estimates for neurons and components are not compatible with estimates for numbers of neurons and available cortical volume. I lowcvcr. to further complicate the picture, t'hemiak's ncuronal volume calculations themselves arc open to question because he appears to base estimates on pyramidal neuron parameters. The majority of cortical neurons, however, are the much smaller stellate neurons.
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Computational Neural Networks Even those most enthusiastic about the potential of computational approaches acknowledge that the question of how real neural networks operate is difficult to answer at this point because much needed information is lacking (Churchland & Seijnowski, 1989). Much of the concern of network modellers has been directed at conceptually manageable problems, such as analysis of sensory events and computational models that guide movement in three dimensional space. For processing at this level, even small brains appear to posses ample resources. At higher levels of complexity that involve learning and recall (McNaughton, 1989), there are concerns about limits to storage capacity. For instance, in the model that uses associative correlation matrices as a metaphor for computational systems, it is clear that the capacity of the matrix increases with the dimensionality of the input channels, as McNaughton points out. He also points out that for real neural systems there might be definite limits to storage capacity. These limits are posed not by limits in the overall size of the brain, but by the general problems of intcrconncctivity. As the overall size of a given network increases, processing time also increases. The time element is of importance to an organism that lives in real time, in a real world, and will therefore impose restraints on the size of operating neural networks. It should be noted that all these models do in one way or another involve all levels of the cortical and subcortical (Braitenberg, 1989) systems in an interactive mode that does not posit separate higher regions. This is an important point. While there are higher order representations, so-called higher order cognitive processes do not take place in a uniquely reserved separate part of the brain. For instance, in Edelman's (1987) theory, there are neuronal groups that form primary and secondary (higher order) repertoires. The secondary repertoire is not formed by a different and separate neuron population, but is formed by neurons that are part of the primary repertoire and that form a functionally defined new entity. It is clear that this model of processing, which allows for different functional processes at anatomically overlapping loci, does not allow for any simple equation of "larger brain = greater capacity at functionally more complex levels." All of this is permissive of the concept of a necessary and sufficient cortical mass, with an emphasis more on interconnectivity than absolute cortical mass. In summary, while this attempt to relate cortical mass to behavioural capacity is tentative and informal, it docs suggest that there is certainly no clear indication of more being better. All current major models of cortical functioning place heavy emphasis on interconncctedncss of cortical neurons, and it seems that the very demands of interconnecting huge numbers of neurons arc the principal likely cause for constraints to unlimited addition of conical mass. Further, formal quantitative models are needed to determine possible tradeoffs between speed of operation and comprehensiveness of cortical operations that may, ultimately, determine whether or not small and large brains each have different functional advantages. The emphasis on interconnectedncss relates importantly to the question of whether there exists a sex difference in the size of the corpus callosum, because this commissure can be seen as symbolic of cortical interconnectivity as such (Peters, 1988).
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The Corpus Callosum as General Indicator of Cortical Interconnectivity Although work on sex differences in the anterior commissure is available (Allen & Gorsky, 1986), much more information is available on the corpus callosum. The literature on sex differences in callosal size is contradictory. At one extreme, some reports (e.g., Lacostc & Holloway, 1982) suggest that in humans the corpus callosum is absolutely larger in females. A similar pattern has even been claimed for other primates (Lacoste & Woodward, 1988). At the other extreme, Witelson (1985, 1989) and Clarke, Kraftsik, Van dcr Loos, and Innocent! (1989) claim that the corpus callosum of males is larger. In the case of the Clarke et al. study, there was a serious problem of matching sex samples appropriately. In the infant group where sex differences were shown, 6 out of 10 males were 6 months of age or older, whereas only 4 out of 12 females were 6 months or older. At this stage, age differences mean much in terms of brain development. For the adult sample, the average age of the 22 males was 62.0 years and that ol the 16 females was 82.1 years. It is interesting to note that for the two samples of subjects (fetuses and post-mortem cases) where the ages of subjects were exactly matched, no sex differences in callosal size were reported. Witelson's (1985, 1989) claim for a larger corpus callosum rests on a subsample of six non-right-handed males; in the other, larger, group of right-handers no sex differences were shown. The average brain weight of her six non-right-handed subjects, all of whom had died of cancer, was 1551 g- This figure is extraordinarily high for any group; it is impossibly high when the cause of death is considered. When brain weights are ordered according to cause of death, cancer patients arc among those with the most reduced brain weights at death (Appel & Appel, 1942). A cautious interpretation of the evidence, based also on the extensive literature review provided by Witelson (1989), leads to the conclusion that, in spite of differences in brain weight between the sexes, there is no evidence of a corresponding sealing of the corpus callosum: The absolute size of the corpus callosum appears similar for the sexes, and this suggests a comparative level of interconnectivity. Another reason for the similarity in callosal size across the sexes could perhaps be found in similar neuron counts for brains differing in size. There is very little evidence to answer this question. However, Zamenhof, Van Marthens, and Bursztyn (1971) suggest that brain size differences between larger and smaller chick and rat brains may be due to differences in supportive tissue mass rather than differences in neuron and glial cell counts. In humans, there is also suggestive evidence that small brain sizes need not mean small neuron counts. Dart (1956), in a discussion of a brain that weighed only 851 g, states that "...in Inaba's individual the brain had amazingly compensated for its reduction in size by a threefold increase in the relative number of nerve cells present" (p. 26). Equality of cell numbers does not, of course, mean similarity in interconnectivity, but in the absence of information on either factor in comparisons of large and small brains within the human species, the need for studies of fine structure in large and small brains appears ever more urgent. CONCLUSION Within sexes, and for healthy individuals in the age range where brain development is completed and aging effects have nol yet set in, there is only a very small
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relationship between body weight and size parameters and brain size for males, and no relationship for females. Having said this, there is a sizable difference in brain size between the sexes that cannot be entirely accounted for by the conventionally used reference parameters of body height and body weight. It is concluded that the dimorphism in body parameters is such that the sealars weight and height, singly or in conjunction, do not allow a reasonable common metric that can be used to relate brain weight to body parameters across the sexes. In the absence of a meaningful relative comparison, the significance of the absolute differences in brain size that, in contrast to other neuroanatomical indices (Janowsky, 1989), are very marked across the sexes cannot be ascertained. The general question of the significance of differences in brain size, regardless of whether they occur within or between sexes, finds no better answer. Large differences in brain size exist between individuals, and there is no obvious relation between such differences and any behavioural indices as have been studied. Any further examination of the question will have to focus (a) on the differences in fine anatomy between large and small brains and (b) on the more general possibility that in terms of cortical function, the general limits of what can be done with the basic mammalian cortex have been reached in the human brain. 1 It has been suggested that, even within the normal range of human brain sizes, there might already be some tradeoffs between advantages offered by speed and efficiency and the advantages offered by greater size of the available neural network. References Allen, I..S-, & Gorsky, R.A. (1986). Sexual dimorphism of the human anterior commissure. Analom ical Record, 214, 3A. Appcl, F.W.. & Appcl. Iv.M. (1942). Intracranial variation in the weight of the human brain. Human Biology. 14, 235-250. Bckoff, M. (1989). Tools, terms, and lelcncephaloiis: Neural correlates of "complex" and "intelligent" behavior. Behavioral arul Brain Sciencex, 12, 591-593. Braitcnherg, V. (1989). Sonic arguments lor a theory of cell assemblies in the cerebral cortex. In I.. Nadcl, L.A. Cooper, P. Culiocovcr, & M. Harnish (F.ds), Neural connections, menial compulation (pp. 137 145). Cambridge: MIT Prcss. Brown, R.H. (1966). Organ weight in malnutrition with special reference to brain weight. Developmental Medicine and Child Neurology, 8, 512 522. Chcrniak, C. (1990). The bounded brain: Toward quantitative neuroanalomy. Journal of Cognitive Neuroxcience. 2, 58-68. Churchland, P S . , & Seijnowski. T.J. (1989). Neural representation and neural compulation. In L. Nadel, L.A. Gx>per, P. Culiocovcr, & M Harnish (Rds.) Neural connections, mental compulation (pp. 15-48). Cambridge: MIT Press. Clarke, S., Kraftsik, R-, Van der Loos. H , & Innocenli. Ci.M. (I9K9). Forms and measures of the adult anil developing corpus eallosum: Is there sexual dimorphism? Pie Journal oj Comparative Neurology. 2X0. 213-230.
'if this premise is correct, there are no mammalian brains as large or larger than human brains that exceed the latter in complexity of interconnections. Detailed work on whale brains shows a simple cortical structure with a relatively and absolutely small corpus eallosum (Morgane, Jacobs. & Galaburda, 1986). It is likely that work on other extremely large brains, such as those of elephants, will also show a more coarsegrained cortex and poorer intcrconnectivity in absolute lernis. In such large animals, the very distances that have to be .spanned will require cell bodies IO l>c larger in order lo sustain the long ax
