Cellular scaling rules for the brains of an extended number of primate species

Abstract

What are the rules relating the size of the brain and its structures to the number of cells that compose them and their average sizes? We have shown previously that the cerebral cortex, cerebellum and the remaining brain structures increase in size as a linear function of their numbers of neurons and non-neuronal cells across 6 species of primates. Here we describe that the cellular composition of the same brain structures of 5 other primate species, as well as humans, conform to the scaling rules identified previously, and that the updated power functions for the extended sample are similar to those determined earlier. Accounting for phylogenetic relatedness in the combined dataset does not affect the scaling slopes that apply to the cerebral cortex and cerebellum, but alters the slope for the remaining brain structures to a value that is similar to that observed in rodents, which raises the possibility that the neuronal scaling rules for these structures are shared among rodents and primates. The conformity of the new set of primate species to the previous rules strongly suggests that the cellular scaling rules we have identified apply to primates in general, including humans, and not only to particular subgroups of primate species. In contrast, the allometric rules relating body and brain size are highly sensitive to the particular species sampled, suggesting that brain size is neither determined by body size nor together with it, but is rather only loosely correlated with body size.

Fig. 1

Phylogenetic relationships between the 12 primate species examined. Average brain mass and body mass for the species are shown in parentheses. Data from Herculano-Houzel et al. [2007], Azevedo et al. [2009] and this study.

Fig. 2

The current primate species deviate from the expected in their cellular composition by as much as the primate species studied earlier. Y-axis, percent deviation from the neuronal and non-neuronal composition expected from cerebral cortex, cerebellum and RoB mass according to the cellular scaling rules determined earlier for 6 primate species [Herculano-Houzel et al., 2007] (a) and 6 rodent species [Herculano-Houzel et al., 2006] (b). For each species, the median deviation, 25th percentile and 75th percentiles, 10th and 90th percentiles, and maximal and minimal deviations are indicated. Dots indicate maximal and minimal variation from the expected cellular composition. Deviations for the 6 primate species studied earlier and for the human brain are shown in the light and dark grey areas, respectively; the 5 new species are shown in the unshaded area. Comparison of a and b shows that the cellular composition of the primate brains studied here conforms to the primate scaling rules, but not to the rodent scaling rules, identified previously.

Fig. 3

Scaling of brain structure mass in the combined dataset as a function of numbers of neurons and non-neuronal cells. Each point represents the average mass and number of neurons (left) or other cells (right) in the cerebral cortex (circles), cerebellum (squares) or RoB (triangles) of a primate species. Filled symbols = Current dataset; unfilled symbols = previous datasets [Herculano-Houzel et al., 2007; Azevedo et al., 2009]. The power and linear fits that can describe the individual relationships for each structure are shown in table 3.

Fig. 4

The percentage of neurons in each structure does not vary significantly with structure mass in the combined dataset. Each point represents the average percentage of neurons among all cells found in the cerebral cortex (circles), cerebellum (squares) or RoB (triangles) of a species. Filled symbols = current dataset; unfilled symbols = previous datasets [Herculano-Houzel et al., 2007; Azevedo et al., 2009].

Fig. 5

Neuronal and non-neuronal densities do not co-vary with structure mass. Variation in density of neuronal cells (a) and other cells (b) in cerebral cortex, cerebellum and remaining areas plotted against the mass of each structure. Spearman correlation p values are indicated for each structure. The correlation between cerebral cortex and RoB neuronal densities and structure mass reach significance in the combined dataset, but are not significantly related by a power law (see text). Filled symbols = present species; unfilled symbols = previous datasets [Herculano-Houzel et al., 2007; Azevedo et al., 2009].

Fig. 6

Relative size of the cerebral cortex and cerebellum does not reflect relative number of neurons in these structures. Each point represents the average relative mass or average relative number of neurons, compared to the whole brain, of the cerebral cortex (circles), cerebellum (squares) or RoB (triangles) of a species. Filled symbols = current dataset; unfilled symbols = previous datasets [Herculano-Houzel et al., 2007; Azevedo et al., 2009]. a Variations in relative mass (% of brain mass) of the cerebral cortex and RoB are significantly correlated to variations in the absolute mass of these structures. b The relative number of brain neurons (% brain neurons) in a structure is only significantly correlated with variations in structure mass in the RoB. c The relative number of brain neurons (% brain neurons) found in the cerebral cortex or cerebellum is not correlated with the relative mass of these structures; only the relative size of the RoB reflects significantly the relative number of neurons in the structure. Spearman correlation p values are indicated for each structure.

Fig. 7

Variation in brain mass and body mass across species. Each point represents the average brain and body mass of a primate species. Filled symbols = current dataset; unfilled circles = previous non-human dataset (Herculano-Houzel et al., 2007); cross = human data (Azevedo et al., 2009). The plotted function, brain mass ∼ body mass^0.903, applies to the entire dataset, but the slope of the power law that best fits the relationship is highly dependent on the species compared (see Results).

Fig. 8

Brain mass is better correlated than body mass with total number of brain neurons. Variation in brain mass (a) and body mass (b) are shown plotted against the total number of brain neurons in each species. Filled symbols = present species; unfilled symbols = previous datasets [Herculano-Houzel et al., 2007; Azevedo et al., 2009]. Power laws plotted are brain mass = 7.134 × 10⁻¹⁰ brain neurons^1.130 and body mass = 3.088 × 10⁻⁸ brain neurons^1.144.

Fig. 9

Residuals of brain and body mass regressed onto total number of neurons in the brain. Each point represents the residual of the regression of brain mass (M_br, filled symbols) or body mass (M_body, unfilled symbols) onto the total number of neurons in the brain of each species (N_br) using the power laws that applies to the combined primate dataset, including humans, shown in figure 8.