We analyzed the numbers of neurons and other cells that make up the brain of 11 Glires, whose phylogenetic relationships are shown in figure . This dataset expands the original dataset of 6 rodent species [Herculano-Houzel et al., 2006
] and includes 10 rodent species belonging to 7 different families (naked mole-rat, Bathyergidae; mouse and rat, Muridae; hamster, Cricetidae; spiny rat, Echimyidae; guinea pig and capybara, Caviidae; prairie dog and grey squirrel, Sciuridae; agouti, Dasyproctidae), and the closely related rabbit (order Lagomorpha). The average data from this expanded dataset of 11 Glires are presented in table divided into four structures: cerebral cortex (grey and white matter combined), cerebellum (grey and white matter combined, including deep nuclei), RoB, and olfactory bulb.
Across the 11 species examined, from the naked mole-rat to the capybara, body mass varies 2,039×, from slightly over 20 g in the former to almost 50,000 g in the latter. Brain mass, in turn, is only 191× larger in the capybara than in the naked mole-rat; cortical mass, 262×; cerebellar mass, 138×, and the RoB, 124×. In contrast, the numbers of neurons in these structures vary disproportionately to brain mass: numbers of neurons are only 58× larger in the capybara brain than in the naked mole-rat; 50× larger in the cerebral cortex; 74× larger in the cerebellum, and 22× larger in the RoB (table ). The percentage of neurons in the whole brain decreases significantly with increasing brain size, from a maximum of 65.3% in the mouse to a minimum of 33.6% in the capybara (Spearman correlation coefficient: −0.882, p = 0.0053).
Conformity to the Cellular Scaling Rules Identified for the Previous Dataset
To examine whether the cellular composition of the brains of the present 4 rodent and 1 Lagomorpha species conform to the rules identified previously, we first recalculated the cellular scaling rules that apply to the original set of 6 rodent species [Herculano-Houzel et al., 2006
] by using species averages, instead of the individual values, and now excluding the olfactory bulb from the RoB. These average scaling rules are shown in online supplementary table 1
(for all online suppl. material, see www.karger.com/doi/10.1159/000330825
). We find that the exponents recalculated from the species averages are very similar to those reported originally from individual values: 1.748, 1.314 and 1.627 against the original 1.760, 1.370 and 1.772 for the cerebral cortex, cerebellum and RoB, respectively. Because accounting for phylogenetic relatedness in the dataset does not modify the scaling exponents significantly (online suppl. table 2
, previous dataset), with differences of typically only 1–2%, we used the uncorrected scaling functions, obtained directly from the dataset, for further analysis.
Next, we determined how the average numbers of neurons and other cells in each brain structure of the current 5 species depart from the expected values obtained by applying to each species the scaling rules obtained for the previous rodent dataset (power functions shown in online suppl. table 3
). For comparison, we also calculated how much the numbers of neurons and other cells depart from the expected values for the brain structures of each of the species in the previous study, given the mass of each structure. Percent deviations from the expected numbers of neurons and other cells were calculated as [100 × (observed – expected)] for each relationship.
Figure shows that the mass of the cerebral cortex, cerebellum and RoB in the new dataset conform to the expected values from the total brain mass in each species (fig. ). Additionally, we find that the spiny rat, the prairie dog, the grey squirrel and the rabbit have numbers of neuronal and other cells that conform to the scaling rules that apply to the previous set of species, with deviations from the expected values that are comparable to those found for the 6 species from which the scaling rules were obtained (fig. ). Although the squirrel has systematically more neurons and other cells in the cerebral cortex, cerebellum and RoB than expected from the mass of these structures (34.7, 17.5 and 22.4% more neurons, and 38.2, 65.7 and 86.3% more other cells, respectively), most of these deviations fall within the range observed for the previous species (fig. , sq).
Fig. 2 With the exception of the naked mole-rat, the current Glires deviate from the expected values in their cellular composition by as much as the rodent species studied earlier. The y-axis shows percent deviation from the values expected from the brain scaling (more ...)
Remarkably, however, we find that the naked mole-rat has about 50% fewer neurons than expected in the cerebral cortex and cerebellum; this is the largest deviation from the expected values observed for any of the 11 species (fig. ), with a corresponding deviation of neuronal density in these structures to about 50% less than expected, given that the mass of the cerebral cortex and cerebellum corresponds to the expected values from total brain mass. In contrast, the number of neurons in the RoB of the naked mole-rat deviates from the expected values for RoB mass by about as much as the species from which these scaling rules were derived (–32.1%, range: −48.9% in hamster to 57.2% in mouse). These findings indicate that the brains of 4 of the present species, including the closely related lagomorph, conform to the cellular scaling rules described previously for 6 other rodent species, while the naked mole-rat seems to be an outlier, with remarkably fewer neurons than expected in its cerebral cortex and cerebellum.
Updated Cellular Scaling Rules
Given the conformity of the spiny rat, prairie dog, squirrel and rabbit to the cellular scaling rules identified previously, we next determined the cellular scaling rules that apply to the brains of the expanded dataset of 10 Glires species (table ). The naked mole-rat was excluded from the calculations due to its apparent condition as an outlier in the scaling relationships. Importantly, we find that the updated scaling exponents are virtually identical to those identified previously for the smaller set of 6 rodent species (online suppl. table 1
), with the expected difference in the neuronal scaling rules that apply to the RoB, which now does not include the olfactory bulb. This similarity to the previous scaling rules further confirms that the 4 species added, including the rabbit, conform to the scaling rules that applied to the previous dataset. This conformity is further seen in the plots of the relationships between structure mass and number of neurons (fig. ). These plots, which depict the scaling rules calculated without the naked mole-rat, also illustrate how the numbers of neurons in the cerebral cortex and cerebellum of this species fall strikingly short of the expected number (fig. ), while its number of neurons in the RoB is closer to the expected one (fig. ). Indeed, adding the naked mole-rat to the analysis alters the neuronal scaling exponents for the cerebral cortex, cerebellum and RoB from 1.699, 1.305 and 1.568 to 1.519, 1.160 and 1.533, respectively. In contrast to the structure-specific neuronal scaling rules, the functions that relate structure mass to the number of other cells in the structure are remarkably similar to one another (fig. ). As for the original dataset, these exponents are not significantly affected when phylogenetic relatedness among the species is accounted for (online suppl. table 2
Updated cellular brain scaling rules calculated from average species values in the expanded Glires dataset
Fig. 3 Scaling of brain structure mass in the combined dataset as a function of numbers of neurons. Each point represents the average mass and number of neurons in the cerebral cortex (a, circles), cerebellum (b, squares) or RoB (c, triangles) of a Glires species. (more ...)
Fig. 4 Scaling of brain structure mass in the combined dataset as a function of numbers of other cells. Each point represents the average mass and number of other cells in the cerebral cortex (circles), cerebellum (squares) or RoB (triangles) of each Glires (more ...)
Separating the olfactory bulb from the RoB allows us to examine the cellular scaling rules that apply to that structure among Glires. We find that the mass of the two olfactory bulbs varies across species as a power function of its number of neurons raised to an exponent of 1.312, and as a power function of its number of other cells raised to an exponent of 1.307 (fig. ).
Fig. 5 Scaling of olfactory bulb mass in the combined dataset as a function of numbers of other cells. Each point represents the average mass and number of neurons (black symbols) or other cells (white symbols) in the two olfactory bulbs of each Glires species. (more ...)
In each structure, with the exception of the olfactory bulb, we find that neurons represent decreasing percentages of all cells in the structure with increasing structure mass across species (Spearman correlation coefficients: cerebral cortex, −0.927; cerebellum, −0.842; RoB, −0.879, all values of p < 0.02; olfactory bulb, p = 0.2997). Accordingly, the O/N ratio (number of other cells/number of neurons) for each structure increases significantly (p < 0.05) together with increasing structure mass from a minimum of 0.870 (mouse) to a maximum of 5.983 (capybara) in the cerebral cortex; a minimum of 0.121 (hamster) to a maximum of 0.493 (capybara) in the cerebellum, and a minimum of 1.242 (mouse) to a maximum of 9.638 (rabbit) in the RoB, with no significant correlation with structure mass in the olfactory bulb.
In all structures, neuronal densities decrease with increasing structure mass in nonoverlapping ways that can be described as different power functions of structure mass with negative exponents (table ; fig. ). In contrast, other cell densities are much more overlapping across structures, and do not vary significantly with structure mass (fig. ).
Fig. 6 Neuronal densities are varied and decrease with increasing structure mass, while other cell density is largely overlapping across structures. Each point represents the average mass and neuronal density (a, number of neurons/mg) or other cell density ( (more ...)
Relative Distribution of Brain Mass and Neurons
Among Glires, the distribution of brain mass changes significantly with increasing brain mass. The relative mass of the cerebral cortex, expressed as the percentage of whole brain mass, increases significantly with increasing brain mass (Spearman correlation coefficient: 0.830, p = 0.0127), while the relative mass of the RoB decreases significantly (Spearman correlation coefficient: −0.830, p = 0.0127) and the relative mass of the cerebellum fails to correlate with brain mass (Spearman correlation, p = 0.8553; naked mole-rat excluded from all calculations). However, the distribution of neurons across these brain structures does not change significantly with increasing brain mass, with no significant correlation found between brain mass and the percent of all brain neurons located in the cerebral cortex (p = 0.3000), cerebellum (p = 0.1035) or RoB (p = 0.0710). Indeed, relative mass is not correlated with relative number of neurons in the cerebral cortex (p = 0.9855) or in the RoB (p = 0.4437), and only marginally so in the cerebellum (p = 0.0325). This indicates that the relative size is misleading, and the distribution of brain mass is not a valid proxy for the distribution of neurons: relatively larger cerebral cortices in larger Glires brains do not hold relatively more neurons than in smaller brains.
We have recently shown that, despite the faster increase in the mass of the cerebral cortex compared to the cerebellum, numbers of neurons increase coordinately, and linearly, in these two structures across species. We find that, for the expanded dataset of Glires, numbers of neurons also increase coordinately in the two structures in a way that can be described as a power function of the number of neurons in the cerebral cortex with an exponent of 1.101 (which decreases to 1.031 after accounting for phylogenetic relatedness; p < 0.0001), or even better by a linear relationship of slope 3.914 (fig. ). Remarkably, although the number of neurons in the naked mole-rat cerebral cortex and cerebellum seem smaller than expected from the animal's brain mass (fig. ), they are still related in the same manner as in other Glires, such that the addition of the naked mole-rat to the dataset leaves the linear slope practically unaltered, at 3.987 (fig. ).
Fig. 7 Coordinated scaling of the numbers of neurons in the cerebellum and cerebral cortex of Glires. Each point represents the average number of neurons in the cerebellum (y-axis) and cerebral cortex (x-axis) of a species (black symbols = current dataset; white (more ...)
After calculating the scaling rules from the average species values, we find that in our previous dataset of 6 rodent species [Herculano-Houzel et al., 2006
], brain size increased as a power function of body mass with an exponent of 0.761 (p = 0.0006, 95% confidence interval: 0.551–0.971); this exponent is decreased to 0.639 after accounting for phylogenetic relatedness in the dataset (p = 0.0002). For the expanded dataset of 10 species (excluding the naked mole-rat), we find that whole brain mass varies as a power function of body mass with a similar exponent of 0.712 (p < 0.0001), which also decreases to 0.616 (p < 0.0001) after accounting for phylogenetic relations. The addition of the naked mole-rat hardly affects the scaling exponents, which become 0.704 before and 0.625 after correcting for phylogenetic relations, respectively (p < 0.0001). For consistency with the cellular scaling rules for the brain, we shall consider the uncorrected exponent calculated by excluding the naked mole-rat from the dataset.
The number of neurons in the whole brain and the different brain structures of Glires can be predicted from either body mass or brain mass according to the equations described in table . Observed numbers of neurons depart from the values predicted from body mass by an average of 30.0 ± 22.9%, while they depart from the values predicted from brain mass significantly less, by 18.6 ± 13.6% (2-tailed t test, p = 0.0060). Brain mass, therefore, is a better predictor of the number of brain neurons than body mass, which suggests that although brain and body mass are correlated across Glires, body mass is more variable than brain mass for a given number of brain neurons.
Scaling rules that predict brain neurons from body mass and brain mass calculated from average species values in the expanded Glires dataset