We analyzed 57 spinal cord specimens from 8 primate species and 1 Scandentia species. Our list of primate species contains 3 species of closely related Old World monkeys (M. mulatta, M. radiata and M. fascicularis), 3 species of New World monkeys, including both the Callithricidae radiation (C. jacchus) and the Cebidae radiation (A. trivirgatus and S. sciureus), and 2 species of prosimians, 1 from the Lorisiform radiation (O.r garnetti) and 1 from the Lemuriform radiation (Microcebus sp.; fig. , table ). Since removal of the tree shrew (T. glis) from the analyses typically resulted in only minor changes, all scaling relationships presented hitherto apply to the 8 primate species combined with the closely-related tree shrew (see table for comparison with relationships for primates only). Since scaling exponents were little affected by correcting for phylogenetic relatedness in the dataset (table ), the exponents reported below refer to the uncorrected relationships.
Spinal Cord Increases More Slowly than Body Mass
Average body size in our data set (table ) varies 141- fold from the mouse lemur (60 g) to the rhesus macaque (8,470 g) whereas spinal cord mass varies 36-fold, total cell number varies by 17-fold and the number of neurons varies 6-fold. Spinal cord mass varies as a power function of body mass with an exponent of 0.733, significantly below linearity (95% confidence interval, CI, 0.652–0.813; fig. ). Although in a previous data set we found a sample of primates to have larger brains linearly proportional to body mass [Herculano-Houzel et al., 2007
], for the current sample, we find that brain size increases as a similar power function of body mass to an exponent of 0.753 (CI, 0.559–0.947; fig. ). Accordingly, brain mass increases approximately linearly with spinal cord mass (exponent, 1.009; CI, 0.660–1.231). We find that the relative mass of the spinal cord, expressed as a percentage of body mass, decreases from 0.4% in the mouse lemur to 0.1% in the rhesus monkey (Spearman correlation r = −0.950, p = 0.0072; table ), varying as a power function of body mass raised to an exponent of −0.267 (CI, −0.348 to −0.187; table ).
Fig. 3 Spinal cord and brain mass increase as power functions of body mass. Each point represents the average spinal cord (a) or brain mass (b; ordinate) and average body mass (abscissa) for each of 8 primate species and the tree shrew. Plotted lines are power (more ...)
Cellular Scaling Rules for Primate Spinal Cord
The spinal cord gains mass faster than it gains neurons or nonneurons, proportionally to its total number of neurons raised to an exponent of 1.977 (CI, 1.601–2.354), and to the total number of nonneurons with an exponent of 1.222 (CI, 1.113–1.330; fig. ). The vast majority of the cells in the spinal cord are nonneuronal, with neurons representing fewer than 10% of cells for all species (table ). This finding is in stark contrast to the primate brain where, using identical methods, the percentage of cells that are neurons was found to be 45% or greater [Herculano-Houzel et al., 2007
]. Indeed, larger spinal cords are composed of a gradually smaller percentage of neurons (table ), which varies as a power function of cord mass with an exponent of −0.317 (p = 0.0005). Nonneurons increase at a faster rate than neurons in larger spinal cords (fig. ), with the ratio of nonneuronal to neuronal cells (NN/N ratio) increasing with spinal cord mass with an exponent of 0.333 (p = 0.0006), and spinal cord length with an approximately linear exponent (r2
= 0.844, p = 0.0096).
Fig. 4 Cellular scaling rules for the spinal cord. Cord mass (ordinate) increases as power functions of total number of neurons (a) and total number of other (nonneuronal) cells (b) in the spinal cord (abscissa). Each point represents the average values for (more ...)
Spinal Cord Neuronal Composition Is Linearly Related to Cord Length
Spinal cord mass, as expected of a three-dimensional structure, increases in our sample approximately as the cube of one-dimensional cord length (raised to an exponent of 2.923; CI, 2.128–3.718; fig. ). Spinal cord length increases with body mass raised to an exponent of 0.230 significantly below 1/3 (CI, 0.171–00.289; fig. ), which is consistent with the finding that body mass increases at a faster rate than spinal cord mass. Remarkably, the number of neurons in the spinal cord also varies with body mass raised to approximately the 1/3 power (exponent = 0.360; CI, 0.304–0.416; fig. ). The proximity to an exponent of 1/3 suggests that the number of neurons in the spinal cord is linearly proportional to cord length. Indeed, we find that the number of neurons in the spinal cord increases linearly with cord length (r2 = 0.918, p = 0.0026; fig. ), with approximately 43,000 neurons/mm of spinal cord. Accordingly, the average number of neurons per linear millimeter of spinal cord does not covary significantly with cord length or with cord mass (Spearman correlation, p = 0.3379 and 0.1797, respectively). In contrast to the invariant number of neurons per millimeter of spinal cord, the total number of nonneuronal cells increases steeply with cord length (raised to the power of 2.424; CI, 1.564–3.285; fig. ).
Fig. 5 Spinal cord mass and length scaling. a Spinal cord mass varies with cord length raised to an exponent of close to 3.0. b Spinal cord length varies with body mass raised to an exponent that is significantly smaller than 1/3 (95% CI, 0.171–0.289). (more ...)
Fig. 6 Cellular composition of the spinal cord scales with cord length. The total number of spinal cord neurons increases with body mass raised to the power of 0.360, close to 1/3 (a), and as a linear function of spinal cord length (b), with on average 43,075 (more ...)
The finding that the spinal cord cellular composition scales with cord length raises the intriguing possibility that variations in brain mass and composition across species are primarily related to cord length, rather than body mass. To examine this possibility, we compared the residuals of body mass, cord mass and cord length regressed onto brain mass (normalized for body mass, cord mass and cord length, respectively) for each of the species in our sample and in a previous dataset [MacLarnon, 1996
]. In both datasets, we find that the smallest normalized residuals are obtained for cord length (fig. ; our dataset, cord length × body mass, p = 0.0067; cord length × cord mass, p = 0.0184; MacLarnon dataset, p = 0.0243 and p = 0.0153, respectively; Mann-Whitney comparison of the absolute values of the normalized residuals). Similarly, we find smaller normalized residuals of cord length than of body mass onto brain number of neurons in our dataset (fig. , p = 0.0451, Mann-Whitney comparison of absolute residuals). These findings indicate that brain mass and neuronal composition are more directly related to spinal cord length than to body mass, and body mass seems free to vary to a much larger extent.
Fig. 7 Spinal cord length is more directly related than body mass to brain mass and number of neurons. a Normalized residuals for body mass (open circles), spinal cord mass (open triangles) and spinal cord length (filled circles) calculated onto brain mass for (more ...)
Cell Densities Decrease in Larger Spinal Cords
The large exponent of 1.977 relating spinal cord mass to number of neurons, well above linearity, suggests that average neuronal cell size (which includes the soma, axon and all dendrites) increases rapidly in the spinal cord as it gains neurons. Considering that cord mass varies with the product of its number of neurons and average neuronal mass, and assuming that the latter varies as a power function of the number of neurons, the exponent of this function can be estimated as 1.977–1 = 0.977. The proximity to linearity suggests that average neuronal size increases in the spinal cord proportionally with its number of neurons, and therefore also linearly with cord length. Consistently with the expected increase in average neuronal size, neuronal density decreases rapidly as a function of increasing cord mass, with an exponent of −0.515 (CI, −0.611 to −0.420; fig. ). Neuronal density decreases linearly with cord length (r2 = 0.971, p = 0.0003; fig. ), which is in line with the linear increase in neuronal cell size with number of neurons predicted above. Nonneuronal density also varies as a power function of cord mass but with a smaller exponent of −0.181 (CI, −0.247 to −0.114; fig. ).
Fig. 8 Scaling of neuronal and nonneuronal densities in the spinal cord. a, b Neuronal density in the spinal cord, calculated as the number of neurons per milligram of spinal cord, decreases with approximately the square root of spinal cord mass (a; p < (more ...)
Intraspecies Spinal Cord Comparisons
We collected a substantial number of spinal cords from 3 species: tree shrews (n = 14), galagos (n = 15), and owl monkeys (n = 12). These numbers were sufficient to investigate changes in the spinal cord within each species (table ). Although body mass was significantly larger in male than in female tree shrews and galagos (by 17 and 37%, respectively; Mann-Whitney U test, p = 0.0449 and p = 0.0051), no significant differences were found between males and females in all 3 species in spinal cord mass, total number of neurons or nonneurons, or the percentage of cells that were neurons (Mann-Whitney, all values of p > 0.05; not shown). No significant age correlations were found either, as we compared age to spinal cord mass, total number of neurons and nonneurons, and the percentage of cells that were neurons (Spearman correlation, p > 0.05).
Deviations from expected cellular composition of the spinal cord
Within each species, the mass of the spinal cord varied between the largest and smallest cords by 1.7× in tree shrews, 2.0× in galagos, and 3.1× in owl monkeys. This variation, however, was not significantly correlated with intraspecific variation in numbers of neurons or nonneuronal cells in the spinal cord or with individual body size (Spearman correlation, all p > 0.05), except that cord mass varied among owl monkey individuals as a power function of the number of nonneuronal cells with an exponent of 1.332 (p = 0.0024; not shown), close to the exponent of 1.222 that applies across species. Within each of the 3 species, the density of nonneuronal cells in the spinal cord was found to vary as a power function of spinal cord mass with similar exponents of −0.599, −0.563 and −0.525 (p = 0.0068, 0.0221 and 0.0010, for tree shrew, galago and owl monkey, respectively; fig. ) while neuronal density in the cord covaried significantly with cord mass only across owl monkeys (exponent −0.890, p = 0.0003; not shown).
Fig. 9 Intraspecific scaling of nonneuronal density in the spinal cord. Nonneuronal density in the spinal cord, calculated as the number of nonneuronal cells per milligram of spinal cord, decreases as similar power functions of increasing spinal cord mass across (more ...)
Spinal Cord Relationships with the Brain
We were interested in examining how brain cellular composition scales with the spinal cord. For suitable brain data sets, we chose those of Herculano-Houzel et al. 
and Gabi et al. [2010
, this issue] because they used identical methods. The spinal cord and combined brain data sets have 9 species in common: mouse lemur, tree shrew, galago, common marmoset, owl monkey, squirrel monkey, bonnet monkey, long-tailed monkey and rhesus macaque. As mentioned above, brain mass and spinal cord mass are linearly correlated (fig. ). As a result, spinal cord mass represents on average 11.2 ± 3.8% of total CNS mass, and this value does not covary with body or CNS mass (Spearman correlation, p = 0.7773 and p = 0.4229, respectively).
Fig. 10 Brain mass increases linearly with cord mass. Graphs depict how the mass of the whole brain (a), cerebral cortex (b), cerebellum (c) and remaining areas of the brain (d) scale as power functions of spinal cord mass with exponents close to 1.0 or slightly (more ...)
When the brain is separated into cerebral cortex (including white matter), cerebellum and rest of the brain (without the olfactory bulb), cortical mass is found to increase slightly faster than spinal cord mass (as a power function with exponent 1.124; CI, 0.789–1.460; fig. ), cerebellar mass increases slightly slower than spinal cord mass (as a power function of cord mass with an exponent of 0.874; CI, 0.550–1.198; fig. ) and the mass of the rest of the brain increases more slowly than spinal cord mass (as a power function of cord mass with exponent of 0.707; CI, 0.461–00.953; fig. ).
Scaling relationships between numbers of neurons in the brain and spinal cord are, however, strikingly different from the mass relationships above. This difference can be illustrated by the finding that while the macaque monkey contains 6× more neurons in the spinal cord than the mouse lemur, its brain has 25× more neurons than the mouse lemur brain (table ). Overall, the number of neurons in the brain scales with the number of neurons in the spinal cord raised to an exponent of 1.689 (CI, 0.965–2.414; fig. ). As a result, the fraction of CNS neurons in the spinal cord decreases from at most 1% in smaller animals to close to 0.1% in larger animals, varying with CNS mass raised to the power of −0.427 (CI, −0.659 to −0.194). The number of neurons in the cerebral cortex increases very rapidly as the spinal cord gains neurons, varying as a power function of average number of neurons in the spinal cord with an exponent of 2.112 (CI, 1.099–3.124; fig. ). The number of neurons in the cerebellum also increases much faster than the number of neurons in the spinal cord as a power function of average number of neurons in the spinal cord with an exponent of 1.621 (CI, 0.953–2.289; fig. ). In contrast, the number of neurons in the remaining areas, which include the entire brainstem up to the basal ganglia, increases practically linearly with the number of neurons in the spinal cord (power function exponent, 0.996; CI, 0.423–1.559; fig. ).
Fig. 11 Numbers of neurons in the brain, cerebral cortex and cerebellum increase faster than number of neurons in the spinal cord. Graphs depict how numbers of neurons in the whole brain (a), cerebral cortex (b), cerebellum (c) scaleas power functions of the (more ...)