Introduction

The anatomy and circuitry of the cerebellum is largely conserved across jawed vertebrates (Voogd and Glickstein 1998), but cerebellar size and shape vary considerably across clades (Larsell 1967; Yopak et al. 2017). For example, while non-avian reptiles and amphibians have relatively small cerebella with few folds (i.e., low degree of foliation), mammals and birds have relatively large cerebella that are highly folded (Yopak et al. 2017). Even within vertebrate classes, such as birds, cerebellar morphology varies greatly across species (Iwaniuk et al. 2006, 2007; Sultan and Glickstein 2007). Some of this variation is thought to reflect differences in neuron number and/or neuron size (Herculano-Houzel et al. 2014), and thus neural processing related to, for example, cognitive processing (Hall et al. 2013; Iwaniuk et al. 2009; Smaers et al. 2018) and locomotion (Iwaniuk et al. 2007; Larsell 1967). However, the extent to which interspecific variation in cerebellum size and morphology arises from neuron sizes and numbers remains uncertain. Recent studies on total neuron numbers in the cerebellum indicate that the allometric relationship between the number of neurons and cerebellar mass is largely conserved across species (Herculano-Houzel et al. 2015a; Jardim-Messeder et al. 2017; Olkowicz et al. 2016), with only a couple of clades deviating from this general “scaling rule” (Herculano-Houzel et al. 2014, 2015a).

Of the mammal species studied thus far, two clades diverge from a general allometric relationship between cerebellar mass and total number of neurons such that they have higher neuronal densities in the cerebellum: primates and eulipotyphlans (shrews, moles, and hedgehogs) (Herculano-Houzel et al. 2014, 2015a). This increased neuronal density accompanies a highly folded cerebellum and an expansion of the cerebellar hemispheres in primates (MacLeod et al. 2003; Smaers et al. 2018), but no comparable changes in eulipotyphlan cerebella. In birds, songbirds and parrots also have higher neuronal densities in the cerebellum compared with other avian clades (Olkowicz et al. 2016), but both songbirds and parrots also tend to have relatively smaller and more foliated cerebella (Iwaniuk et al. 2005, 2006). Thus, an increase in neuronal density in the cerebellum is associated with larger or smaller cerebella, a more folded cerebellar cortex or no discernible gross anatomical changes at all. These mixed results across mammals and birds means that the relationship between neuron numbers and cerebellar size and shape remains unclear.

All of the neuron-volume scaling relationships described above were obtained through the use of the isotropic fractionator (Herculano-Houzel and Lent 2005), which provides accurate estimates of total neuron numbers in dissectible brain regions (Herculano-Houzel et al. 2015c; Ngwenya et al. 2017), but does not yet allow for the separation of different neuronal populations within the cerebellum. Further, the isotropic fractionator method does not include Purkinje cells because they do not express NeuN (Apps and Hawkes 2009; Mullen et al. 1992). Like any larger brain region, the cerebellum is comprised of different types of neurons connected to each other in different ways (Yopak et al. 2017). For example, while granule cells receive input from mossy fibers and project to Purkinje cells through parallel fibers, Purkinje cells also receive input from climbing fibers and are the sole source of output to the cerebellar and vestibular nuclei (Apps and Hawkes 2009). The numbers of these different neuronal populations could vary at a different rate relative to total cerebellar size. Determining whether different neuronal populations increase with cerebellum size at different rates would provide novel and more specific insights into the functional consequences of a relatively larger and/or more folded cerebellum. For example, if some clades or cerebellar morphologies have more Purkinje cells, this could indicate enhanced output processing from the cerebellar cortex.

Another caveat of the isotropic fractionator method is that neuron size is not measured directly, but rather is inferred as inversely proportional to neuronal density (Herculano-Houzel et al. 2014). This is because the method relies on rupturing cell membranes to stain nuclei. Scaling of neuron size with cerebellum size, or for that matter most brain regions, across species, therefore, remains largely unexplored (but see Stevens 1969; Teeter and Stevens 2011). Just as different neuronal populations might vary in neuron number–region volume relationships, the scaling of cell size could also vary among different types of neurons. This is especially true for the cerebellum, which contains both the largest neurons (Purkinje cells) and the smallest neurons (granule cells) in the brain (Lange 1982). In fact, across galliform birds (e.g., quail, partridge, pheasant), Purkinje cell size is positively correlated with the size of the cerebellum, while granule cell size is not (Cunha et al. 2020). Thus, instead of inferring the average size of total cerebellar neurons from neuronal density (Herculano-Houzel et al. 2014), actual measurements of neuron size are needed to determine to what extent species differences in cerebellum size are driven by neuron numbers and/or sizes.

As noted above, the cerebellum not only varies in overall size, but also morphology. More specifically, the degree of folding, referred to as foliation, varies greatly across and within clades (Cunha et al. 2020; Iwaniuk et al. 2006; Yopak et al. 2007). Such variation is thought to reflect behavioural differences across species. For example, fast-swimming sharks performing complex manoeuvres tend to have a more foliated cerebellum than slow-moving sharks (Yopak et al. 2007) and birds that build more complex nests (Hall et al. 2013) or use tools (Iwaniuk et al. 2009) have relatively more folded cerebella than other species. An assumption that underlies these studies is that a higher degree of foliation reflects an increase in the surface area of the cerebellum relative to cerebellar volume, therefore, allowing more cells within a given volume and an increase in processing capacity (Hall et al. 2013; Iwaniuk et al. 2009). Within galliform birds, the degree of foliation is positively correlated with the number of cerebellar neurons, but neuronal populations differ in their allometric relationships with the degree of foliation (Cunha et al. 2020). Whether these same patterns can be generalized across other clades remains to be determined, but is critical to understand the functional implications of cerebellar foliation. For example, if a more foliated cerebellum has more Purkinje cells, which would reflect greater output from the cerebellar cortex to the cerebellar and vestibular nuclei. Thus, a detailed investigation on the cellular scaling of the cerebellum, combined with what is known of cerebellar circuitry, would provide novel insights into the functional consequences of species differences in not only cerebellar size, but also morphology.

To address these key issues in cerebellar evolution, we provide the most detailed quantitative analysis of cerebellar anatomy conducted in a comparative context so far. We quantified the volumes of different layers of the cerebellar cortex, surface area of the Purkinje cell layer, cerebellar foliation and the sizes and numbers of Purkinje cells, granule cells, and cerebellar nuclei neurons across 54 avian species. Using this data set, we calculated allometric relationships among all variables to test whether: (i) cerebellar layers increase in volume at a same rate across species; (ii) different neuronal populations scale with cerebellar size at the same rate; (iii) a higher degree of cerebellar foliation is associated with an increase in the surface area of the Purkinje cell layer and thus number of cerebellar neurons (e.g., Purkinje cells); and (iv) if there are quantitative differences in the cerebellar anatomy among clades.

Methods

Specimens

We obtained measurements of the cerebella from 54 species representing 18 orders of birds (Fig. 1; Tables 1, 2, 3). With the exception of some galliform species (Bonasa umbellus, Coturnix japonica, and Perdix perdix; Cunha et al. 2020), a single individual was sampled per species. As described elsewhere, our brain collection is derived from specimens obtained from wildlife sanctuaries, veterinary clinics in Australia and hunters in Canada and New Zealand (Corfield et al. 2013, 2015) and the methods of collection of the specimens adhered to the guidelines of the Canada Council for Animal Care. The heads of these specimens were immersion fixed in 4% buffered paraformaldehyde for at least 2 weeks. The brains were extracted, weighed, and stored in paraformaldehyde. The brains then were place in 30% sucrose in 0.1 M phosphate buffer until they sank (for cryoprotection), embedded in gelatin, sectioned on a freezing stage microtome in the sagittal plane at a thickness of 40 μm and every section collected in 0.1 M phosphate buffered saline. For some specimens, the cerebella were first dissected from the brain by cutting through the cerebellar peduncles and processed in the same way as the intact brains. For all species, every other section (1:2 series) was mounted onto gelatinized slides, stained with thionin acetate, dehydrated through a graded ethanol series, cleared in Hemo-De (Thermo Fisher Scientific, #HD-150) and coverslipped with Permount (Thermo Fisher Scientific, #SP15-150).

Fig. 1
figure 1

Phylogeny of the species analyzed in this study. The orders Passeriformes (songbirds), Psittaciformes (parrots), Anseriformes (waterfowls), and Galliformes (chicken-like birds) are indicated on the branches

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Table 1 A list of the avian species analyzed and their respective brain volumes, cerebellum volumes, molecular layer volumes, granule cell layer volumes, white matter volumes, surface area of the Purkinje cell layer, and cerebellar foliation index (CFI)
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Table 2 Numbers (#) of Purkinje cells, granule cells, and cerebellar nuclei neurons across species analyzed
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Table 3 Soma sizes (μm2) of Purkinje cells, granule cells, and cerebellar nuclei neurons across species analyzed (± SD)
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Volumetric measurements

We measured the volumes of molecular cell layer (ml), granule cell layer (gl), white matter layer including the cerebellar nuclei (wm + cn) and total cerebellum volume (cb) using the Cavalieri method, as implemented in Stereo Investigator software (Microbrightfield Inc., VT, USA), with a 2.5 × objective (n.a. = 0.075) on a Zeiss Axio Imager 2 microscope. The Cavalieri method consists of counting grid points that are inside a region of interest (e.g., molecular layer). Each point has a specific area, and the sum of those areas can be multiplied by the thickness of the tissue and sampling interval (i.e., inverse of the proportion of sections analyzed) to accurately estimate the volume of the entire region (Gundersen et al. 1999; Table S1). Each of the cerebellar layers measured are easily distinguishable from one another (Fig. 2), but the cerebellar nuclei were included with the white matter volume because of the indistinct borders of the cerebellar nuclei in sagittal sections. We, therefore, refer to this as the white matter plus cerebellar nuclei (wm + cn). The Purkinje cell layer is typically a thick, mono-cell layer with some discontinuous gaps between cells in sagittal sections. Hence, calculating the volume of this layer could lead to significant measurement errors. As an alternative, we measured the surface area of Purkinje cell layer, and size and number of Purkinje cells (see below) rather than the volume of the layer. Estimated volumes of all regions of interest are provided in Table 1. The distance between the grid points (grid size), and the sampling interval, varied according to overall cerebellum size (Table S1). The coefficients of error for all volumes ranged from 0.002 to 0.014.

Fig. 2
figure 2

Midsagittal sections of Nissl-stained cerebella of: a peaceful dove (Geopelia placida), b grey partridge (Perdix perdix), c lesser scaup (Aythya affinis), d brown thornbill (Acanthiza pusilla), e sulphur-crested cockatoo (Cacatua galerita), and f Australian bustard (Ardeotis australis). Note the difference in cerebellar size and shape across avian species. For example, while the sulphur-crested cockatoo has a CFI of 5.56, the peaceful dove has a CFI of 2.97. For the peaceful dove (A), cerebellar folia are represented as roman numerals, from I (anterior) to X (posterior), as suggested by Larsell (1967). The black continuous line follows the Purkinje cell layer. The ratio between the length of the Purkinje cell layer (continuous black line) and the envelope length of this same layer (dotted black line) is referred to as the cerebellar foliation index (CFI). ml molecular layer, gr granule cell layer, and “wm + cn” white matter layer and cerebellar nuclei. Scale-bars: A–C = 1 mm, D = 0.5 mm, E–F = 2 mm

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Surface area of the Purkinje cell layer

The surface area of the Purkinje cell layer was calculated by measuring the total length of the Purkinje cell layer through the sagittal axis of the cerebellum, and multiplying it by the thickness of the Sects. (40 μm) and sampling interval (Table 1). The sampling interval was the same one used for the volumetric measurements (see Table S1).

Cerebellar foliation index (CFI)

We used the same approach as in Iwaniuk et al. (2006, 2009) to calculate the degree of foliation (i.e., folding) in the cerebellum (Table 1). First, we measured (a) the total length of the Purkinje cell layer of the midsagittal section and then (b) the length of the “envelope” enclosing the Purkinje cell layer (see Fig. 2a). The ratio (a/b) between these two measurements serves as a metric to calculate the degree of foliation, referred to as the cerebellar foliation index (CFI), and is comparable to gyrification indices calculated in mammals (Hofman 1985; Pillay and Manger 2007; Zilles et al. 1989). Thus, a higher number reflects a greater degree of foliation.

Cell counts

We estimated the number of three types of cerebellar neurons: Purkinje cells, granule cells, and cerebellar nuclei neurons (Table 2; Fig. S1). Purkinje cells are found exclusively within the Purkinje cell layer and are readily identifiable from other cerebellar cell types based on size, shape, and location. We only counted Purkinje cells with intact continuous cell membranes, typical “teardrop” shape, and clearly visible nuclei. The numbers of Purkinje cells were estimated using the optical fractionator method implemented in Stereo Investigator software (Microbrightfield Inc., VT, USA), with a 20 × objective (n.a. = 0.5) on a Zeiss Axio Imager 2 microscope. Frame size remained constant across all species, but grid size varied according to cerebellum size (Table S1). The coefficients of error (CE) of the Purkinje cell counts, defined as the standard error of the mean of repeated estimates divided by the mean (Microbrightfield Inc., VT; USA), were all equal to or below 0.05, indicating that our measurements were precise (Gundersen et al. 1999).

Granule cells are densely packed within the granule cell layer and it is possible to distinguish them from other neuron types within this layer by cellular morphology and spatial distribution (Fig. S1). Granule cells, however, cannot be necessarily discerned from non-neuronal cells (e.g., glia) in Nissl-stained tissue; thus, our granule cell counts likely represent an overestimation of granule cell numbers (Cunha et al. 2020). The fact that specimens in our lab collection were fixed, prepared and mounted previously, at different times, prevented us from using NeuN as a neuron-specific marker in the cerebellum (Mullen et al. 1992). Still, given that specimens were processed consistently by the same method, neuronal counts likely yield comparable numbers across species within our study.

We counted granule cells with continuous, round shaped, and intact cell membranes and darkly stained nuclei (Table 2), which distinguishes them from Lugaro, Golgi, and unipolar brush cells. Lugaro cells are either globular or spindle-like in shape, are mostly clustered just below the Purkinje cell layer (Craciun et al. 2019; Fox 1959). Golgi cells have an irregular shape, are much larger than granule cells and typically have pale cytoplasmic staining (Andersen et al. 1992; Dieudonné 1998). Last, unipolar brush cells have circular-ovoid somata and are intermediate in size between granule cells and Golgi cells (Mugnaini and Floris 1994). Therefore, based on our morphological selection criteria, and given the low density of these other neuronal types, the potential inclusion of some is unlikely to affect our estimates of the total number of granule cells. The optical fractionator method was also used to quantify the numbers of granule cells under the same microscope with a 100 × objective (n.a. = 1.4). Frame size remained constant across species, but grid size varied (Table S1). Because granule cells are relatively small (< 20 μm2) and densely packed (Fig. S1), they could be damaged or sectioned at the top and bottom surfaces of the tissue. Thus, guard zones of 4–7 μm were used to protect against lost caps (Gardella et al. 2003). All granule cell counts had CEs that were equal to or below 0.07.

Cerebellar nuclei neurons are distributed in two paired nuclei within the white matter layer (Arends and Zeigler 1991). Here, we counted all of them as a single population (Table 2) because it was not possible to define clear anatomical borders between the cerebellar nuclei in sagittal sections (see also above). We only counted cerebellar nuclei neurons with intact cell membranes. The shape and size of the soma of cerebellar nuclei neurons was highly variable, ranging from globular to fusiform-like shape (Fig. S1). As with other cells, we used the optical fractionator probe with the same microscope, and a 40 × objective (n.a. = 0.95), to estimate the numbers of cerebellar nuclei neurons. Frame size remained constant across species, but grid size varied (Table S1). To compensate and protect against lost caps, we used guard zones from 4 to 7 μm (Gardella et al. 2003). All cerebellar nuclei neuron counts had CEs that were equal to or below 0.07.

Cell sizes

We measured soma sizes of Purkinje cells, granule cells, and cerebellar nuclei neurons. All cell sizes were measured using the nucleator probe (4 rays), implemented in Stereo Investigator (Microbrightfield Inc., VT, USA). The nucleator probe estimates the average cross-sectional area of randomly selected neurons. For the current study, at least 100 size measurements were made of each neuronal type for each specimen (Table 3). The measurements for each cell size followed a typical normal distribution (see Fig. 3). For all neuron types, cell membranes were intact, and morphologies followed the descriptions provided above.

Fig. 3
figure 3

Distribution of cell soma sizes (μm2) of Purkinje cells (a, d, g, j, m), granule cells (b, e, h, k, n), and cerebellar nuclei neurons (c, f, i, l, o) within the following specimens: brown thornbill (Acanthiza pusilla, a–c), lesser scaup (Aythya affinis, d–f), galah (Cacatua roseicapilla, g–i), collared sparrowhawk (Accipiter cirrocephalus, j–l) and emu (Dromaius novaehollandiae, m–o). The depicted bars represent the summed-up counts of cells within the following ranges: 25–50 µm for Purkinje cells and cerebellar nuclei neurons, and 0.75–1.50 µm for granule cells. The distribution of cell soma sizes followed a normal distribution curve. Although the distribution of the granule cell sizes in the emu appears to be slightly different than a normal curve, most of the measurements were still restricted to a narrow range of sizes (e.g., 16–22 μm)

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Variation across orders

Due to common ancestry, closely related species are expected to have more traits in common (Garamszegi 2014). Therefore, to examine allometric relationships among all measurements, we performed phylogenetic generalized least squares (PGLS) of log-transformed data. The aim of PGLS is to test hypotheses about correlated evolution, assuming that the residuals from a linear model have a phylogenetic covariance. All statistical analyses were performed in R 4.0.3 (R Core Team 2020), using the pgls function in caper (Orme et al. 2013) and nlme (Pinheiro et al. 2006) with maximum likelihood estimations of Pagel’s λ (Pagel 1999). We extracted 1000 fully resolved trees from birdtree.org (Jetz et al. 2012), with Ericson et al. (2006) backbone phylogeny, and built a maximum clade credibility tree (consensus tree; Fig. 1) using phangorn (Schliep 2011). For all PGLS analyses, we used log-transformed data and the consensus phylogenetic tree. We ran phylogenetic analyses of covariance (pANCOVA) to test for significant differences across clades. We specifically tested for allometric differences across avian orders that have at least five species represented in our sample: Anseriformes (waterfowl), Galliformes (chicken-like birds), Passeriformes (songbirds), and Psittaciformes (parrots). Species from all other clades were lumped together as “other birds”. Because Galliformes and Anseriformes form a monophyletic group (“Galloanserae”) and Passeriformes and Psittaciformes form another monophyletic group (“Psittacopasserae”) (Hackett et al. 2008; Jarvis et al. 2014; Prum et al. 2015), we also ran separate statistical analyses for both of these clades against “other birds”. The percentage differences reported in the results (see below) are based on the differences between the intercepts and/or slopes for a given clade (e.g., Galliformes) and other birds.

Model selection and hypothesis testing

To test whether surface area of the Purkinje cell layer or cerebellar volume better explains the variation of the Purkinje cell number, we compared allometric models using Akaike information criterion (AIC) values to identify the most parsimonious model (Burnham and Anderson 2002, 2004).

Results

Allometric relationships of the cerebellum volume

The molecular, granule cell, and white matter plus cerebellar nuclei (wm + cn) layers increased with the rest of the cerebellum with slopes that approximated isometry (Table S2; Fig. 4). The scaling of the molecular layer did not differ significantly across clades (Fig. 4a), but galliforms had relatively smaller granule cell layer (− 38%; Fig. 4b; pANCOVA, p = 0.01; no differences in slopes) and wm + cn volumes compared with other birds (− 11%; Fig. 4c; pANCOVA, p < 0.01; no differences in slopes). In contrast, parrots had significantly larger wm + cn volumes than other birds (+ 10%; Fig. 4c; pANCOVA, p = 0.04; no differences in slopes). Note that despite these significant differences, there was quite a bit of overlap across clades (Fig. 4).

Fig. 4
figure 4

Scatterplots of the log-transformed volumes (mm3) of: a molecular layer (mm3) against rest of cerebellum and b granule cell layer against rest of the cerebellum, c white matter layer plus cerebellar nuclei neurons against rest of the cerebellum. Clades with significant differences from other birds are indicated in the graph. See allometric equations and statistical data in Table S2. The rest of the cerebellum refers to as total cerebellum size minus the size of the cerebellar layer in the y-axis

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The number of Purkinje cells increased with cerebellar volume with a slope less than 1 (slope = 0.703 ± 0.035 (standard error); PGLS, p < 0.01; Fig. 5a; Table S2). The only clade that differed significantly from this allometric relationship was Galliformes, which had relatively more Purkinje cells (+ 2.5%; Fig. 5a; pANCOVA, p = 0.01; no differences in slopes). Waterfowl did not differ significantly from other groups and, therefore, the difference between Galliformes and other clades also drove a significant, but marginal, difference in relative Purkinje cell numbers between Galloanserae and other birds (+ 1.6%, Fig. 5a; pANCOVA, p = 0.04; no differences in slopes). Granule cells increased in number with cerebellum volume with a steeper slope than that of Purkinje cells (0.867 ± 0.038, PGLS, p < 0.01; Fig. 5b; Table S2). Across clades, galliforms had significantly fewer granule cells relative to cerebellar volume (− 2.1%; Fig. 5b; pANCOVA, p < 0.01; no differences in slopes) and songbirds have significantly more granule cells (+ 2.4%, Fig. 5b; pANCOVA, p < 0.01). Last, the number of cerebellar nuclei neurons increases significantly with the cerebellum volume, but with the shallowest slope of the three neuron types (0.518 ± 0.027; Fig. 5c; PGLS, p < 0.01; Table S2) and no significant differences were detected across clades.

Fig. 5
figure 5

Scatterplots of the log-transformed of: a Purkinje cell number, b granule cell number, c cerebellar nuclei neuron number, d Purkinje cell size (mm2), e granule cell size (mm2), and f cerebellar nuclei neuron size (mm2) against the log-transformed volume (mm3) of the cerebellum. Clades with significant differences from other birds are indicated in the graph. See allometric equations and statistical data in Table S2. CbN cerebellar nuclei

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As shown in Fig. 3, cell sizes varied greatly within species (coefficients of variation = 20–30%). Average cell sizes scaled at different slopes relative to total cerebellar volume (Table S2) and the slopes were much shallower than that for cell numbers (Fig. 5). Across clades, Galliformes have significantly larger Purkinje cells relative to cerebellar volume than other birds (+ 4.7%, Fig. 5d; pANCOVA, p < 0.01; no differences in slopes). At the other end of the spectrum, songbirds have significantly smaller granule cells relative to cerebellum size than other birds, which also drove a significant difference between Psittacopasserae and other birds (− 9%; Fig. 5e; pANCOVA, p = 0.01; no slope differences). No significant differences were detected across orders or clades for the size of the cerebellar nuclei neurons relative to the volume of the cerebellum (Fig. 5f; Table S2).

Allometric relationships among neuronal populations

Among the three neuronal populations, allometric relationships varied in strength and slope. The number of granule cells increased with positive allometry relative to the number of Purkinje cells (1.125 ± 0.064; Fig. 6a; PGLS, p < 0.01; Table S2). Across clades, galliforms had significantly fewer granule cells relative to the number of Purkinje cells compared to other birds (− 11%, Fig. 6a; pANCOVA, p < 0.01) and drove a significant difference between Galloanserae and other birds (− 7%, Fig. 6a; pANCOVA, p = 0.01). Galliformes also had a steeper slope for the granule cell-Purkinje cell relationship compared to other birds (+ 36%, Fig. 6a; pANCOVA, p = 0.03). The number of cerebellar nuclei neurons increased with the number of Purkinje cells with a much shallower slope than the number of granule cells (0.690 ± 0.037; Fig. 6b; PGLS, p < 0.01; Table S2), and no significant differences were detected among clades. The number of cerebellar nuclei neurons increased with the number of granule cells with the shallowest slope (0.534 ± 0.041; Fig. 6c; PGLS, p < 0.01; Table S2). As shown in Fig. 6c, Galliformes had significantly more cerebellar nuclei neurons relative to granule cells than other birds (+ 41%; Fig. 6c; pANCOVA, p = 0.01) and this also drove significant differences between Galloanserae and other birds (+ 28%; Fig. 6c; pANCOVA, p < 0.01; no slope differences).

Fig. 6
figure 6

Scatterplots of the log-transformed of: a granule cell number against Purkinje cell number, b cerebellar nuclei neuron number against Purkinje cell number, c cerebellar nuclei neuron number against granule cell number, d granule cell size (μm2) against Purkinje cell size (μm2), e cerebellar nuclei neuron size (μm2) against Purkinje cell size, and f cerebellar nuclei neuron size against granule cell size. Clades with significant differences from other birds are indicated in the graph. See allometric equations and statistical data in Table S2. CbN cerebellar nuclei

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Allometric relationships among the sizes of the three neuronal populations also varied in strength and slope. The size of granule cells increased with the size of Purkinje cells with the shallowest slope (0.280 ± 0.073; Fig. 6d; PGLS, p < 0.01; Table S2). The size of cerebellar nuclei neurons increased with the size of Purkinje cells with a much steeper slope (0.452 ± 0.065; Fig. 6e; PGLS, p < 0.01; Table S2). Lastly, the size of cerebellar nuclei neurons increased significantly with the size of granule cells with a slope similar to that of the Purkinje cells (0.408 ± 0.116; Fig. 6f; PGLS, p < 0.01; Table S2). The only difference detected among clades is that the Psittacopasserae had a higher slope (+ 64%) for the relationship between cerebellar nuclei and granule cell sizes (Fig. 6f; pANCOVA, p = 0.04). This difference remains significant (pANCOVA, p < 0.05) when excluding an outlier (the brown thornbill (Acanthiza pusilla); Fig. 6f).

When plotting the numbers of each neuronal population against neuron size, no significant differences were detected across clades (Fig. 7). The number of Purkinje cells increased with the size of Purkinje cells with a slope close to isometry (1.105 ± 0.246; Fig. 7a; PGLS, p < 0.01; Table S2). Similarly, the number of cerebellar nuclei neurons increased with the size of cerebellar nuclei neurons with a slope close to 1 (0.983 ± 0.311; Fig. 7b; PGLS, p < 0.01; Table S2). However, for both of these relationships, the coefficients of correlation were no higher than 0.265 (see Table S2). For granule cells, the relationship between neuron number and neuron size was not significant (PGLS, p > 0.05; Fig. 7c; Table S2).

Fig. 7
figure 7

Scatterplots of the log-transformed of: a Purkinje cell number against Purkinje cell size (μm2), b granule cell number against granule cell size (μm2), and c cerebellar nuclei neuron number against cerebellar nuclei neuron size (μm2). See allometric equations and statistical data in Table S2

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Allometry of cerebellar foliation and surface area

As demonstrated in previous studies (Cunha et al. 2020; Iwaniuk et al. 2005), the avian cerebellum increased in volume relative to the rest of the brain with isometry (slope = 0.934 ± 0.046, PGLS, p < 0.01; Table S2; Fig. 8a), although parrots and songbirds (Psittacopasserae) had relatively smaller cerebella (− 18%; Fig. 8a; pANCOVA, p = 0.01; no differences in slopes). However, Iwaniuk et al. (2006) noted that the cerebellum is more foliated in these groups, as measured by the CFI, and suggested that the surface area of the cerebellum and the number of Purkinje cells would be higher in relation to cerebellar volume. When we plotted the surface area of the Purkinje cell layer against the rest of brain size (0.752 ± 0.044; Fig. 8b; PGLS, p < 0.01), and number of Purkinje cells against the rest of brain size (0.656 ± 0.048; Fig. 8c; PGLS, p < 0.01; Table S2), parrots and songbirds did not differ from other clades (Fig. 8b, c). These data support the inferences of Iwaniuk et al. (2006): despite having a relatively smaller cerebellum, parrots and songbirds do not have a smaller surface area or number of Purkinje cells relative to the rest of the brain.

Fig. 8
figure 8

Scatterplots of the log-transformed of: a cerebellum volume (mm3) against rest of the brain volume (mm3), b surface area of Purkinje cell layer (mm2) against rest of the brain volume, and c Purkinje cell number against rest of the brain volume. Clades with significant differences from other birds are indicated in the graph. See allometric equations and statistical data in Table S2

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However, the same data plotted relative to cerebellar volume yielded contradictory evidence. First, as shown above in Fig. 5a, the number of Purkinje cells relative to cerebellar volume is not higher for parrots and songbirds. Second, when the surface area of the Purkinje cell layer is plotted against cerebellar volume (Fig. 9a, Table S2) most of the parrots and songbirds lie above the regression line, but there were no significant differences across clades detected. Nonetheless, when we ran multiple allometric models to determine whether cerebellar volume or surface area of the Purkinje cell layer best explained the number of Purkinje cells (Figs. 5a, 9b; Table S3), Purkinje cell layer surface area was the best predictor of the number of Purkinje cells (dAIC > 2; Table S3).

Fig. 9
figure 9

Scatterplots of the log-transformed of: a surface area of the Purkinje cell layer (mm2) against cerebellum volume (mm3), b Purkinje cell number against surface area of the Purkinje cell layer, c cerebellar foliation index (CFI) against cerebellum volume, d cerebellar foliation index against surface area of the Purkinje cell layer, and e cerebellar foliation index against Purkinje cell number. Clades with significant differences from other birds are indicated in the graph. See allometric equations and statistical data in Table S2

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We then plotted CFI against cerebellar volume (Fig. 9c), Purkinje cell layer surface area (Fig. 9d) and number of Purkinje cells (Fig. 9e). In all three plots, parrots and songbirds are shifted to the left, indicating significantly higher CFI values relative to all three scaling variables. This grade shift indicates that the CFI is a poor proxy, specifically an overestimate, for both measures of cerebellar surface area and Purkinje cell numbers in parrots and songbirds.

Discussion

As found previously within galliform birds (Cunha et al. 2020), the expansion of the cerebellum across bird species is due to coordinated changes in volume across cerebellar layers such that no one layer increases in size more than another. Despite conservation of the proportional volumes of the layers, the numbers and sizes of different neuronal populations have different allometric relationships with cerebellar volume, and several differences among clades were detected (see Table 4).

Table 4 Summary of the clade differences for the measurements examined relative to brain volume (vol.) or cerebellum volume
Full size table

Despite these overall patterns, a few caveats should be considered in interpreting our data and analyses. First, some avian/clades are represented by more species than others. We, therefore, cannot negate the possibility that there are other differences among clades that we were unable to detect due to small sample sizes. Second, we sampled only one individual of most species. The morphology of the cerebellum can vary significantly within species (El-Andari et al. 2020; Escalona et al. 1991; Inouye and Oda 1980; Puzdrowski and Leonard 1992), but variation in brain or brain region size is usually higher across species than within species (Herculano-Houzel et al. 2014, 2015a, b) and the intraspecific coefficients of variation for the measurements on galliform species are typically lower than 15% (see Cunha et al. 2020; El-Andari et al. 2020). Although the specific slopes and intercepts of the various allometric relationships described herein might shift with the addition of more individuals per species and/or more species overall, the general patterns are unlikely to change. We also stress that it remains unclear to what extent fixation affects cell density or cell size. Given that our specimens were processed following the same procedure, this potential artifact is unlikely to affect our main findings, but could still affect direct comparisons between our data and future studies using different histological procedures. Last, our granule cell counts likely include non-neuronal cells (e.g., glia) and, therefore, represent an overestimation of total granule cell numbers. Because of that, our data cannot be compared directly with that of isotropic fractionation studies (Olkowicz et al. 2016) and the allometric equations that include granule cell numbers should be interpreted with caution. For example, when comparing the number of cerebellar neurons in the six species (Cacatua galerita, Columba livia, Dromaius novaehollandiae, Melopsittacus undulatus, Nymphicus hollandicus, Tyto alba) examined in this study and Olkowicz et al (2016), our study reports on average two times more cerebellar neurons than Olkowicz et al (2016). We also note that the brain sizes for the six species mentioned above were on average 1.2 times larger in our study than in Olkowicz et al. (2016). Nevertheless, our data are the most comprehensive to date for a comparative study and provides some novel insights into cerebellar evolution.

Allometric scaling within the cerebellum

The cerebellum has an anatomical organization that is highly conserved across most species, including the connectivity patterns across neuronal populations (Voogd and Glickstein 1998; Yopak et al. 2017). This pattern of connectivity is not only preserved across vertebrate species, but also across different functional units within the cerebellum itself (Apps et al. 2018; Voogd and Glickstein 1998; Yopak et al. 2017). It is, therefore, unsurprising that all three cerebellar layers change in volume in a concerted fashion, with little deviation across clades. As shown in Fig. 4, there is little scatter around the allometric lines and the correlation coefficients (r2 s in Table S2) are all above 0.95, indicating that interspecific variation in the absolute and relative size of the whole cerebellum largely arises from coordinated, volumetric increases across cell layers.

In contrast to the strong, nearly isometric relationships among layer volumes, larger cerebella have lower neuronal densities, a pattern that is typical of most brain regions and clades, regardless of whether the data are acquired through stereology (Cunha et al. 2020; Haug 1987; Lange 1975; Sherwood et al. 2020) or isotropic fractionation (Olkowicz et al. 2016; Herculano-Houzel et al. 2014, 2015a). There are, however, differences in the slope and strength of the neuron number-cerebellum volume relationship (i.e., r2) among the three neuronal populations (see Table S2). Relative to cerebellar volume, the number of granule cells increases faster than the number of Purkinje cells, which increases faster than the number of cerebellar nuclei neurons (Fig. 5; Cunha et al. 2020). Thus, different types of neurons vary in their scaling relationship with brain region size and, by extension, a constant scaling pattern (or neuronal scaling “rule” sensu Herculano-Houzel et al. 2014) does not apply uniformly to cerebellar neurons and is unlikely to apply to other brain regions. In much the same way that volumetric measurements have moved away from large, multifunctional brain regions to functionally specific regions and/or circuits (Corfield et al. 2015; Gutiérrez-Ibáñez et al. 2011, 2013; Moore and DeVoogd 2017; Smaers and Vanier 2019; Vanier et al. 2019), the quantification of neuron numbers should extend to different neuronal populations and the role they have in neural circuits, to better understand how the brain evolves.

In addition to neuron numbers, we also estimated neuron sizes by measuring soma areas. Relative to cerebellum volume, neuron sizes increase at a significantly slower rate (see Fig. 5), and with much lower correlation coefficients (r2 s = 0.08–0.37) than neuron numbers (r2 s = 0.87–0.90). Thus, our results suggest that neuron size, relative to cerebellum volume, is more likely to vary across species than relative neuron numbers. The fact that neuron sizes are highly variable within a single neuronal population (see Fig. 3) might also explain why neuron size is much more variable than neuron number across species. As shown with neuron numbers (see above), each neuron type also scaled at a different rate with cerebellar volume. Neuron size is not discussed as frequently as neuron numbers in comparative studies, but it is an important contributor to brain region volume and information processing capacity (Chang et al. 2020; de Sousa and Proulx 2014; Smith et al. 1997). Although soma size is only one metric of neuron size, it is often associated with the physiological properties of a neuron (Chang et al. 2020; Cooper and Stanford 2000; Meitzen and Thompson 2008). For example, variation in soma size of Purkinje cells can reflect firing type and input resistance (Chang et al. 2020), and larger cells tend to have larger or more organelles, such as the endoplasmic reticulum and mitochondria (Reber and Goehring 2015), which would potentially enable higher energetic capacity (Marshall 2015; Reber and Goehring 2015). Relatively larger (or smaller) neurons within a clade, therefore, might reflect physiological differences that are relevant to behaviour. However, what those differences might be is entirely speculative as little is known about differences in motor control and coordination across bird species. Regardless of the functional correlates and implications of neuron size, our data indicate neuron size cannot be inferred accurately from neuron numbers due to differences in the allometric scaling of neuron size and numbers across neuronal populations (see Figs. 6, 7). Moreover, as shown in Fig. 3, neuron size is highly variable within a single neuronal population, and for that reason estimations of neuron size from neuronal density (see Herculano-Houzel et al. 2014) are likely inaccurate.

One of the few exceptions to the general patterns observed across species is the order Galliformes. Galliforms have smaller granule cell and white matter layer-cerebellar nuclei (“wm + cn”) layers relative to the size of the rest of the cerebellum compared to other birds (Fig. 4), even though they do not have relatively small cerebella (Fig. 8a). The molecular layer in galliforms is not proportionally expanded (Fig. 4a), indicating that the relative decrease in the other layers is due to a change in Purkinje cells. Accurately measuring the volume of the Purkinje cell layer is not possible due to frequent gaps between Purkinje cells (see “Methods”), but galliforms do have more and larger Purkinje cells relative to the size of the cerebellum (Fig. 5), which would result in a larger Purkinje cell layer. Why galliforms differ from other clades in these scaling relationships is unclear, but some insights might be gleaned by examining the cerebella of behaviorally and ecologically similar clades, such as tinamous (Tinamiformes), bustards (Otidiformes), and/or buttonquail (Turnicidae).

Cerebellar volume, surface area of the Purkinje cell layer, and foliation

Parrots and songbirds have relatively smaller cerebellar volumes (Fig. 8a; Iwaniuk et al. 2006), but a greater degree of foliation, as measured by a higher midsagittal CFI (Fig. 9c–e). In previous studies, this measure was considered a proxy for surface area and Purkinje cell number (Hall et al. 2013; Iwaniuk et al. 2009). That is, parrots and songbirds may have a smaller cerebellum by volume, but an increase in the foliation provides a larger surface area and thus a greater processing capacity for the cerebellum. In the present study, we actually measured the surface area of the cerebellum and the number of Purkinje cells. On the one hand, we found that relative to the rest of the brain, the surface area of the cerebellum and the number of Purkinje cells is not reduced in parrots and songbirds despite smaller cerebellar volumes (see Fig. 8). This is further supported by the cerebellar surface area being a better predictor of Purkinje cell number than cerebellar volume (see Figs. 5a, 9b). Thus, the increase in cerebellar foliation in parrots and songbirds maintains the processing capacity of a smaller cerebellum, a functionality that might be required for their expanded telencephala (Boire and Baron 1994; Iwaniuk et al. 2005). On the other hand, parrots and songbirds did not significantly increase surface area or Purkinje cell number relative to cerebellar volume (see Figs. 5a, 9a). We must, therefore, conclude that any effects of foliation are weak and that the midsagittal CFI is not a good proxy for surface area or number of Purkinje cells. This is very apparent in Figs. 9d–e, where the CFI grossly overestimates the surface area and number of Purkinje cells in parrots and songbirds. Intuitively, this should not come as a surprise. In birds the cerebellum is folded only in the anterior–posterior dimension, which is not the case in sharks (Yopak et al. 2007, 2017), the cerebellar hemispheres in mammals (Smaers et al. 2018; Voogd and Glickstein 1998) or the cerebral cortex in mammals (Pillay and Manger 2007; Zilles et al. 1989). Thus, in birds the CFI is maximal in the midsagittal section, and progressively approaches 1.0 as one moves laterally to the flocculus and lateral unfoliated cortex. The result is that the midsagittal CFI overestimates total foliation, and by extension also overestimates surface area and Purkinje cell number.

Conclusions

Our results show that cerebellar layers increase in size proportionally and the numbers of cerebellar neurons explain more variation in cerebellar volume than the sizes of cerebellar neurons. Thus, despite all the species differences in cerebellar size and shape (Cunha et al. 2020; Macrì et al. 2019; Smaers et al. 2018), the conserved pattern of cerebellar connectivity across species is reflected in proportional increases in size of the cerebellar layers. Within this general framework, we also found that different neuronal populations have different allometric scaling rules relative to the size of the cerebellum, thus indicating that measuring total neuron numbers within larger brain regions (Herculano-Houzel et al. 2014; Olkowicz et al. 2016) might not provide a complete picture of the relationship between neuron numbers and brain region sizes. Given that patterns of cerebellar connectivity are relatively uniform across vertebrate species (Yopak et al. 2017), we expect to find similar changes across the volumes of cerebellar layers in other vertebrate clades, but also varying allometric scaling patterns across neuronal populations in the cerebellum. Testing the extent to which these patterns are conserved in the cerebellum across all vertebrates would provide insights into the putative mechanisms responsible for clade differences in relative cerebellum size and morphology.