The genetic basis of neurocranial size and shape across varied lab mouse populations

Abstract

Brain and skull tissues interact through molecular signalling and mechanical forces during head development, leading to a strong correlation between the neurocranium and the external brain surface. Therefore, when brain tissue is unavailable, neurocranial endocasts are often used to approximate brain size and shape. Evolutionary changes in brain morphology may have resulted in secondary changes to neurocranial morphology, but the developmental and genetic processes underlying this relationship are not well understood. Using automated phenotyping methods, we quantified the genetic basis of endocast variation across large genetically varied populations of laboratory mice in two ways: (1) to determine the contributions of various genetic factors to neurocranial form and (2) to help clarify whether a neurocranial variation is based on genetic variation that primarily impacts bone development or on genetic variation that primarily impacts brain development, leading to secondary changes in bone morphology. Our results indicate that endocast size is highly heritable and is primarily determined by additive genetic factors. In addition, a non‐additive inbreeding effect led to founder strains with lower neurocranial size, but relatively large brains compared to skull size; suggesting stronger canalization of brain size and/or a general allometric effect. Within an outbred sample of mice, we identified a locus on mouse chromosome 1 that is significantly associated with variation in several positively correlated endocast size measures. Because the protein‐coding genes at this locus have been previously associated with brain development and not with bone development, we propose that genetic variation at this locus leads primarily to variation in brain volume that secondarily leads to changes in neurocranial globularity. We identify a strain‐specific missense mutation within Akt3 that is a strong causal candidate for this genetic effect. Whilst it is not appropriate to generalize our hypothesis for this single locus to all other loci that also contribute to the complex trait of neurocranial skull morphology, our results further reveal the genetic basis of neurocranial variation and highlight the importance of the mechanical influence of brain growth in determining skull morphology.

The genetic basis neurocranial size variation was analyzed in inbred and outbred mouse populations, indicating high heritability, with strong additive genetic contributions, as well as significant non‐additive contributions. A chromosome 1 locus encompassing protein‐coding genes of brain development is associated with several size measures, suggesting that genetic variation at this locus leads primarily to variation in brain volume that secondarily leads to changes in skull form.

1. INTRODUCTION

The skull develops as an integrated structure within the context of other head tissues, including external muscles and the growing brain. When mechanical forces imposed by adjacent soft tissue are modified, changes in skull morphology may result. For example, the lack of an eye results in changes to the adjacent bone morphology (Dufton et al., 2012; Dufton & Franz‐Odendaal, 2015; Kish et al., 2011; Smith et al., 2014). Similarly, growth of the brain is necessary for normal cranial vault shape, and the cranial vault will adapt to accommodate increases in brain size (Adameyko & Fried, 2016; Moss & Young, 1960; Richtsmeier et al., 2006; Richtsmeier & Flaherty, 2013).

This close developmental relationship produces morphological covariation between the interior surface of the neurocranium and the exterior surface of a mammal's brain. Because skeletal materials are more common within the fossil record and museum collections, the internal surface of the neurocranium has frequently been used to approximate brain size and shape for comparative studies of brain evolution (see citations within Balanoff et al., 2016). Casts of the internal neurocranial surface called endocasts come in the form of (1) naturally occurring fossilized sediment, (2) artificial casts made with a moulding material and (3) digital surfaces generated from three‐dimensional (3D) images of bone (e.g. computed tomography) (Holloway, 2018).

Although the brain occupies more than 80% of the endocranial volume within mammals (Watanabe et al., 2019; Zollikofer & Ponce de León, 2013) and approximately 97% of the endocranial volume within mice (Nieman et al., 2012), endocasts are not direct casts of the brain. In life, the neurocranial space is filled with the brain, the meningeal connective tissues that protect the brain, and the blood vessels found external to the brain. However, there is a strong correspondence between endocast measures and brain measures within the context of comparative mammalian anatomy, as supported by a comparison of endocast volume and brain weight amongst marsupials (Haight & Nelson, 1987), the correspondence of endocast and brain surface features (Dumoncel et al., 2021; Nieman et al., 2012), and by many unpublished anatomical observations.

There is also a strong allometric relationship between brain size and body size across a broad range of taxa. Indices of encephalization, such as the encephalization quotient (originally proposed by Jerison, 1973), represent the size of an animal's brain relative to its overall body size. These encephalization measures have been widely associated with behavioural and cognitive complexity (de Miguel & Henneberg, 1998; Jerison, 1973; Marino, 1998; Zollikofer & Ponce de León, 2013). In addition, recent analyses of variation in the allometric relationship between brain and body size across a variety of mammalian and avian clades have illuminated the macroevolutionary history of encephalization (Ksepka et al., 2020; Smaers et al., 2012; Weisbecker et al., 2021). Regardless of the comparative method used, choosing appropriate measures of both brain size and organismal size is critical for producing valid and interpretable encephalization measures (Hallgrímsson et al., 2019).

It has long been proposed that evolutionary changes in brain size across primate and human evolution resulted in secondary changes to skull morphology (e.g. De Beer, 1937). However, it is not clear whether known evolutionary changes in primate skull shape are primarily based on a plastic developmental response of the skull to mechanical forces during ontogeny or if they are instead based on natural selective pressures for modified skull morphology (reviewed by Lesciotto & Richtsmeier, 2019). For this reason, it is important to (1) identify the types of genetic factors that contribute most strongly to variation in neurocranial morphology and (2) to determine whether these factors play a primary role in skeletal development, brain development, or both via pleiotropy.

If neurocranial morphology is associated with variation in genes that significantly influence bone development, this would support the hypothesis that skull morphology is the direct result of evolution acting on genes with major effects on skull growth and skull shape. If neurocranial morphology is associated with genes that have major roles in brain development, this supports the hypothesis that secondary mechanical forces imposed by the growing brain contribute substantially to evolutionary changes in skull morphology. Whilst past evolutionary pressures and active phenotypic plasticity likely both play a role in determining adult neurocranial morphology, the underlying genetic factors remain poorly understood. Some genes may also have parallel pleiotropic effects on bone and brain development, so it is critical to consider all functions of identified genes when testing these predictions.

We perform a large‐scale analysis to identify the genetic and developmental factors underlying evolutionary changes in neurocranial form. We use an automated image registration method (Percival et al., 2019) to extract and quantify endocasts for a genetically diverse sample of laboratory mice. We then complete a diallel analysis on eight inbred founder strains of the Collaborative Cross (CC) mice (Chesler et al., 2008; Churchill et al., 2004; Collborative Cross Consortium, 2012) and their reciprocal F1 crosses to estimate the types of additive and non‐additive (e.g. maternal and inbreeding effects) genetic factors that underlie variation in endocast size and encephalization indices, as well as the heritability of those measures. Given that endocasts are an accurate estimate of brain size derived from neurocranial skull features in mice and are highly correlated with brain size, we anticipate that the heritability and the proportional importance of genetic factor types in determining endocast measures will be similar to values reported for other skull measurements in this sample (Percival et al., 2016a).

Finally, we perform genome‐wide association studies (GWAS) of the genetically heterogeneous Diversity Outbred (DO) mice to identify genomic regions where the eight original CC founder strain haplotypes are associated with endocast size variation. After identifying a single significant association, we investigated whether protein‐coding genes in this genomic region were previously linked to processes of bone development or brain development. We anticipated that any GWAS identified chromosomal regions would be enriched for genes that are important for brain growth rather than bone formation and growth. This result would match our expectation that processes of brain growth play a significant role in determining the shape of the skeletal neurocranium and that a substantial proportion of neurocranial size variation across our experimental sample is based on the plastic responses of developing skull bones to variation in the speed and intensity of brain growth.

2. METHODS

2.1. Sample and image acquisition

Our sample of 1204 mouse skull micro‐computed tomography (μCT) images of the eight inbred founder strains of the Collaborative Cross (CC) (Chesler et al., 2008; Churchill et al., 2004; Collborative Cross Consortium, 2012) and 54 (of 56 possible) reciprocal F1 crosses was previously used to elucidate the genetic structure of ‘normal’ laboratory mouse skull morphology (Pavličev et al., 2017; Percival et al., 2016a). Each cross is identified first by the maternal founder strain and second by the paternal founder strain (Collborative Cross Consortium, 2012). Because all founder strains are inbred, specimens within each founder strain and F1 cross are isogenic. Strain identity is referred to as specimen genotype throughout the analysis. These mice were bred as part of the Collaborative Cross breeding project at the University of North Carolina under the approval of the University of North Carolina Animal Care and Use Committee. These mice were housed at UNC for 8–12 weeks with standard chow and housing.

Our original sample of 1071 Diversity Outbred (DO) mice are a subset of a sample whose skull morphology was previously analyzed (Aponte et al., 2021; Devine et al., 2020; Katz et al., 2020; Percival et al., 2018). DO mice (J:DO, JAX stock #009376) are derived from the eight CC founder strains (Churchill et al., 2012; Svenson et al., 2012). As a result of outcrossing, the DO population has relatively high genetic diversity and increasingly fine‐mapping resolution with each generation. Therefore, this sample was used to (1) identify QTL associated with endocast measurement variation and their corresponding confidence intervals and (2) determine which CC founder strain haplotypes are associated with that endocast variation. Specimens were originally raised in several labs for unrelated experiments under the approval and conducted in accordance with the guidelines set forth by the Institutional Animal Care and Use Committees (IACUC) of the University of North Carolina (protocol #11–299), Jackson Laboratories (protocols #99066 and #15026), and The Scripps Research Institute (protocol #08–0150‐3).

Tissue specimens were received and imaged at the University of Calgary in accordance with IACUC protocols #AC13‐0268 and AC18‐0026. μCT images of mouse skulls were obtained in the 3D Morphometrics Centre at the University of Calgary with a Scanco vivaCT40 scanner (Scanco Medical, Brüttisellen, Switzerland) at 0.035–0.038 mm voxel dimensions at 55 kV and 72–145 μA. Our CC founder/F1, DO mouse samples, and relevant image analysis pipelines are available as part of the MusMorph public mouse dataset (Devine et al., 2021) and associated github repository (https://github.com/jaydevine/MusMorph).

2.2. Manual endocast estimation.

Endocasts were previously manually extracted from μCT images of specimens from 36 out of 54 available CC founder and F1 cross genotypes (Percival et al., 2016b). This manual extraction process included rough reorientation of CT skull images to a standard orientation, digital removal of all non‐skull bones, and the use of Endex software (Subsol et al., 2010) to fill the neurocranial space of the CT scan with an iteratively expanding endocast surface. This procedure was manual in the sense that a researcher preprocessed each CT image and made decisions about when to stop the Endex endocast expansion algorithm. More than 1 hour was required to generate an endocast from each specimen using this method. Most of this time was spent manually segmenting and removing non‐skull bones from the CT images.

2.3. Nonlinear image registration and automated endocast estimation

Using the Symmetric Normalization (SyN) algorithm (Avants et al., 2011) in the MINC toolkit (Vincent et al., 2016), the CC founder and F1 cross skull μCT images were all previously registered to a single common skull image average (atlas) during the process of automated landmark identification (Percival et al., 2019). As the basis for automated endocast estimation of the CC sample, Endex software was used to segment an endocast from the CC sample atlas image using the manual endocast estimation method. This CC atlas endocast was modified so that it did not overlap with skull bone in the atlas image and so that it represented a single continuous volume. It was then inverse transformed back onto the original skull μCT images of each individual CC founder/F1 specimen using previously calculated nonlinear volumetric image registrations (Percival et al., 2019). Measurements of each specimen's endocast were calculated from the resulting automated segmentations.

Following the non‐linear registration pipeline described above, we transformed all available DO mouse skull μCT images to a DO sample average image (atlas). Like the CC founder and F1 cross mice, a DO sample atlas endocast was produced and used to automatically extract an endocast for each μCT DO specimen. We repeated the process of (1) producing an endocast segmentation of the DO sample atlas and (2) automatically segmenting all DO specimens twice more to quantify the repeatability of endocast size measurement methods. This led to a total of three sets of endocast measurements for each DO mouse specimen in our sample. All variation between replicate measurements of DO specimens reflects differences between the three endocast segmentations of a single DO skull atlas image. After a replication analysis comparing these three measurement sets, the first set of DO endocast measurements were used as the basis for further analysis.

2.4. Endocast size measures and measurement validation

Five endocast measurements were estimated for each CC founder/F1 specimen automatically generated endocast, for each manually created CC founder/F1 specimen endocast, and all three automatically generated endocasts for each DO specimen. First, endocast volume and surface area were estimated. STL format meshes were generated from volumetric image endocast estimates with the marching cubes algorithm within the VTK library (Schroeder et al., 2006) in Python (version 3.7). These 3D surfaces were post‐processed by filling holes, checking for consistency, adjusting the surface normals to project from a single surface, and smoothing to remove duplicate surfaces. The surface area and volume of these 3D mesh representations were estimated using the vtkMassProperties subroutine. Total processing time for STL surface creation and measurement was approximately 1 min for each specimen. A custom Python script was written to automate this process (File S2).

Dimensions of endocast length, width, and height were automatically estimated from the previously produced STL mesh surfaces after rotating each surface to its principal axes with the Python Trimesh package (https://github.com/mikedh/trimesh). A 4 × 4 transformation matrix included rotation of the surface principal inertia vectors to a standard orientation and translation of the surface’s centre of mass to a standard position. After the standard orientation of each surface to align with principal axes, the dimensions of an endocast surface's rectangular bounding box approximate the length, width, and height of that endocast (Figure 1). Whilst the described Python‐based methods were used to estimate measures for all automatically generated endocasts, equivalent measurements were collected in MeshLab (Cignoni et al., 2008) for manually generated endocasts after orientation of endocast surfaces to their principal axes.

FIGURE 1.

Endocast length, width and height measures are collected from the surface bounding box after the surface has been reoriented along principal axes

The accuracy of endocast measures estimated from automatically generated endocasts was verified by comparing automatically and manually generated endocast measures of the 688 CC founder/F1 specimens for which we have both automated and manual measurements (Table S1). Differences between automated and manual measures of each specimen were calculated, as were correlations of those measures across our sample. To directly compare endocast overlap in the Endex and MINC image spaces, a random subsample of ten CC images with both automated and manual endocasts were aligned using manual landmark defined 3D transformations. Dice similarity scores (Dice, 1945) were calculated as the ratio of the intersection of two endocast volumes to the union of the same volumes. Landmark‐based transformations were needed to align manual and automated endocasts because of major differences in software pipelines and resulting coordinate systems, so our Dice score estimates are likely an underestimation of true volume overlap.

To identify specimens with automated endocast segmentation errors, we implemented two strategies, both of which can be used for samples without manual measurements. First, we computed a ratio of endocast length to volume, as an inappropriate posterior extension of the endocast via registration error can lead to a major increase in endocast length whilst having a minor effect on overall endocast volume. Second, we quantified placement errors in the foramen magnum landmarks (Devine et al., 2020; Percival et al., 2019). If the automated placement was inaccurate, it is likely that the position of the foramen magnum was misidentified, which may also lead to an error in identifying the posterior end of the endocast. We visually inspected these outliers manually to confirm this error.

2.5. Relative size (encephalization) measures

Measures of relative endocast size (encephalization indices) were estimated for all CC founder/F1 and DO specimens to determine whether the genetic structure of raw neurocranial size is similar to the genetic structure of relative neurocranial size. First, the index of relative encephalization (IRE) was calculated as the cube root of endocast volume divided by cranial base length (Lieberman et al., 2008). Cranial base length is the sum of midline linear distance from the basion to the presphenoid/sphenoid synchondrosis and the linear distance between the presphenoid/sphenoid synchondrosis to the crista galli. These linear distances were measured from anatomical landmarks previously collected manually on the founder/F1 (Percival et al., 2016a) and automatically on DO mice prior to neural network optimization (Devine et al., 2020).

Because the length of the cranial base is likely influenced by some of the same genetic factors that influence the overall neurocranial size, we also calculated a measure of encephalization for the founder/F1 sample that is standardized by tibia length, a postcranial proxy for body size. The ‘Vol/Tib’ measure was calculated as the cube root of endocast volume divided by tibia length. Tibia length was measured between a landmark placed on the anterior midline tibial tuberosity and a landmark placed on the inferior posterior point on the long bony prominence lateral to the malleolar groove (Figure S1). Body weight was not chosen as the proxy for postcranial body size in the founder/F1 sample because the NZO/HlLtJ mice and associated crosses tend to have large fat deposits. Instead, we preferred tibia length as a measure of postcranial skeletal size, because we wanted to standardize endocast size by a size measure that should be impacted by the same general systemic growth factors (not factors specifically associated with fat deposition). Because tibias were not available for all CC founder/F1 specimens, we estimated Vol/Tib measures for only 1089 specimens. Given a lack of postcranial data for our DO mouse sample, our only encephalization measure for DO mice is IRE.

2.6. Diallel analysis of CC founder/F1 strain measures

After removing specimens with substantial errors in automated endocast extraction and a few with unknown sex, we completed a diallel analysis of CC founder/F1 specimens to identify the contribution of various genetic factors to mouse endocast size and encephalization. We followed the procedures used for a previous diallel analysis of skull dimensions for the same sample (Percival et al., 2016a). A separate diallel analysis was carried out for four measures of endocast size (volume, length, height, and width) and two measures of encephalization (IRE and Vol/Tib) using BayesDiallel v0.982 package (Lenarcic et al., 2012) within R v3.2.5 (R Developmental Core Team, 2008). The results indicated which additive and nonadditive factors make a significant contribution to endocast variation. Additionally, estimates of heritability indicate the proportion of phenotypic variation that is associated with each type of additive and nonadditive genetic factor.

2.7. Genome‐wide association mapping of DO measures

After removing specimens with substantial errors in automated endocast extraction and those with potential errors in matching μCT images to genotype data, 884 DO specimens were available as the sample for our association analyses. Association mapping was performed to identify quantitative trait loci (QTL) that contribute to endocast size and encephalization variation. DO mice from generations 9, 10 and 15 were genotyped with the MegaMUGA genotyping array (77,808 markers), whilst the GigaMUGA genotyping array (143,259 markers) was used to genotype DO mice from generations 19, 21, 23 and 27 (Morgan et al., 2016). To prepare the genetic data for QTL analysis, we selected 58,907 markers found in both the MegaMUGA and GigaMUGA arrays. Next, we eliminated 2022 markers from the centre of Chromosome 2 (40–140 Mb) because genetic diversity in early DO generations is highly skewed in this region because of female meiotic drive favouring WSB/EiJ at the R2d2 locus (Chesler et al., 2016; Morgan et al., 2016). Finally, we used the qtl2 package (Broman et al., 2019) within R v3.6.1 statistical software (R Developmental Core Team, 2008) to insert pseudomarkers in sparsely typed genomic regions, such that no two markers in the dataset were separated by more than 1 kilobase, resulting in a final genotype array of 57,658 markers for QTL analysis. Genome locations are based on Mus musculus genome assembly GRCm38 (mm10).

A genome scan for QTL was completed for endocast volume, surface area, length, width, height and IRE. At each marker, we fit a mixed model with fixed effect coefficients for sex and the additive effect of each CC founder haplotype, a random effect of kinship, and an error term (Gatti et al., 2014). A predictor of DO generation number was also included in this model. Statistical significance of marker‐phenotype association was identified when the LOD score exceeded the 95% quantile of genome‐wide maximum LOD scores computed from 1000 random permutations of genotype‐phenotype associations (Churchill & Doerge, 1994). Genome‐wide heritability for endocast measures was estimated based on the results of this analysis within the qtl2 package. R‐squared (R ²) values were estimated from the peak LOD scores of phenotypes with significant associations using the following formula: R ² = 1–10^ [−LOD*(2/n)] (Broman & Sen, 2009).

We used a 1.5 LOD‐drop rule to define the boundaries of QTL support intervals (Manichaikul et al., 2006). Genome scans and QTL support intervals were estimated for each endocast measurement. We then inspected the support intervals for genes that had been previously linked to skeletal, craniofacial or neural tissue development or morphological variation.

3. RESULTS

3.1. Automated measurement validation

Comparing measurements derived from manually defined endocasts and automatically defined endocasts indicated that the automated endocast measures are accurate for most specimens. High correlations (r = 0.938 to 0.995) were noted for all measurements (Table 1). Nevertheless, there were some systematic differences in manual and automated measures. Automated volumes are, on average, 2.2% smaller than manual volumes, whilst automated surface area measures are 4.5% larger than manual surface areas (Table 1).

TABLE 1.

Comparison of manual and automated endocast measurements

Endocast measurement	Volume	Surface area	Length	Width	Height
Manual vs automated correlation	0.99	0.97	0.93	0.98	0.98
Mean % difference of automated from manual	−2.2	4.5	1.3	0.3	0.1

Dice scores comparing automated and manual endocast volumes for ten randomly chosen CC specimens range from 0.92 to 0.96, with a mean of 0.95, a standard deviation of 0.01, and a 1% coefficient of variation. A Dice score of 1 indicates complete correspondence of identified volumes, whilst 0 indicates no correspondence. Our measured scores are high, indicating a very strong correspondence of the manually and automatically identified endocast volumes.

Direct visual comparison of the automated and manual endocast surfaces indicated that the automated endocasts typically include more precise contours that closely match the edges of bone surfaces. Whilst this precision is important, more precise contours result in less smooth surfaces. Differences in smoothness largely explain the increased endocast surface area and the decreased endocast volume for automated measures. Although automated endocast contours are generally more precise, the non‐linear image registration algorithm artifactually produces a wavier automated endocast surface (Figure 2), so subtle endocast surface features may not be consistently visible.

FIGURE 2.

Surface images of manual method (Endex) and automated method endocast surfaces of the same specimen, from a lateral view (a&c) and a superior view (b&d). Asterisks indicate examples of common manual Endex endocast segmentation errors where thin portions of the skull bone are included in the endocast segmentations. Compared to other specimens, this specimen shows a moderate to low level of this type of manual endocast segmentation error

The weakest correlation between automated and manual measures was noted for endocast length (Table 1). Specimens with the largest difference between manual and automated endocast length tended to have either (1) automated endocasts that extended posteriorly through the foramen magnum or (2) manual endocasts where the olfactory bulb was shorter than it should have been due to an incomplete manual endocast expansion. Incomplete olfactory bulb expansion of some manual endocasts will not impact the results of our genetic analyses, which are based on automatic endocast measurements. However, errors in automated endocast estimation can have an impact on our results. The inappropriate posterior extension of some automatically estimated endocasts is the result of image registration errors where a vertebra is accidentally identified as the foramen magnum of the occipital bone. This same issue previously led to errors in automated landmark placement on the occipital bone (Percival et al., 2019). We successfully identified specimens with automated measurement errors in our samples and removed them as outliers prior to statistical analysis.

For the CC founder/F1 genotype sample, we identified 27 outlier specimens out of an original sample of 1204 specimens. Two specimens had incorrectly cropped original CT images, three specimens had major failures in nonlinear image registration, 20 specimens were identified based on extreme length to volume ratios, and two additional specimens were identified by looking at specimens with high foramen magnum landmark placement error. After removing outliers, a sample of 1177 CC Founder/F1 mice remained for all subsequent analyses (Table 2).

TABLE 2.

Sample sizes for all CC founder strains and F1 crosses, after removing specimens with high automated endocast segmentation error. A = A/J; B = C57BL/6J; C = 129S1/SvlmJ; D = NOD/ShiLtJ; E = NZO/HlLtJ; F = CAST/EiJ; G = PWK/PhJ; H = WSB/EiJ

		Paternal strain
		A	B	C	D	E	F	G	H
Maternal strain	A	18	18	19	18	18	20	20	20
	B	20	19	20	18	18	20	16	18
	C	21	17	19	17	13	19	19	22
	D	19	21	19	13	22	24	21	17
	E	19	18	22	20	7	0	0	19
	F	20	26	19	17	21	17	22	18
	G	19	20	20	17	19	17	18	17
	H	19	19	20	20	19	28	20	17

The repeatability of our automated endocast estimation method was quantified by comparing the measurements of each DO specimen produced using three independently generated segmentations of the DO sample atlas. The correlations between endocast size measures are close to maximum (rounded up to r = 1.00) for all measures except endocast length, where length estimates of replicate 1 diverge somewhat from the original length estimates and from replicate 2 length estimates (Table 3). A comparison of the independently produced atlas endocasts for each replicate indicates that the replicate 1 endocast has a greater expansion of the olfactory bulb area and a more posterior extent at the foramen magnum. It is likely that the Endex endocast expansion algorithm ran longer during atlas image endocast creation for replicate 1 than for the other replicates. This deviation of atlas endocast segmentation between replicates led to a systematic shift in specimen endocast length estimates, highlighting the importance of verifying the accuracy and consistency of atlas endocast segmentations across studies before combining measurements collected based on different atlases or using different segmentations of the same atlas image. The original DO endocast measurements were used as the basis for all subsequent analyses.

TABLE 3.

Correlations between DO replicate endocast measurements

		Replicate measurement correlations
Data 1	Data 2	Volume	Surf. area	Length	Width	Height
Original	Replicate 1	1.00	1.00	0.96	1.00	1.00
Original	Replicate 2	1.00	1.00	1.00	1.00	1.00
Replicate 1	Replicate 2	1.00	1.00	0.98	1.00	1.00

Using the methods of outlier identification tested on the CC founder/F1 sample, we identified 23 outlier specimens out of a total of 1071 DO specimens. Twenty‐one specimens were identified based on extreme length to volume ratios and two specimens were identified based on high foramen magnum landmark error. In addition, because of potential errors in matching μCT images of DO mice to genotype data, a subset of 884 specimens was available as the sample for our association analyses (File S4).

3.2. CC founder/F1 genotype variation

Many of the most extreme endocast size values belong to inbred founder strain specimens (Figure 3; Table 4; File S3). However, F1 cross specimens tend to be larger across all size measures (but not encephalization indices) than the average of their associated founder strains, which indicates a consistent non‐additive effect on overall size. This increase is likely explained by the inbreeding effect in our diallel models (see below). It also means that the largest endocast volumes belong to F1 cross specimens. The three wild‐derived inbred strains (CAST/EiJ, PWK/PhJ and WSB/EiJ) tend to be smallest, with intermediate values for A/J and 129S1/SvlmJ. Amongst founder strains, the New Zealand obese mice (NZO/HlLtJ) have the longest endocast length and overall skull size (i.e. centroid size of skull landmarks from Percival et al., 2019), whilst NOD/ShiLtJ and C57BL/6J have the tallest endocast heights. In fact, the correlation between endocast height and length (Figure 3a; r = 0.639) is weaker than the correlations between height and width (r = 0.751) and between length and width (Figure 3c; r = 0.800). In this way, height appears to vary under the influence of forces that do not similarly affect the other two endocast distance measures.

FIGURE 3.

Plots of endocast and skull size measurements for inbred founder strains (triangles) and F1 hybrid mice (dots). Comparisons of (a) endocast height versus length, (b) endocast volume versus surface area, (c) endocast width versus length, and (d) endocast volume versus skull centroid size. The correlation coefficients (r) of each pair of variables are listed. A comparison of IRE versus Vol/Tib is found in Figure S2

TABLE 4.

Endocast measurement mean (SD) values for whole CC founder/F1 strain sample and each founder strain

	Volume (mm3)	Surface area (mm2)	Length (mm)	Width (mm)	Height (mm)	IRE	Vol/Tib
Whole sample	461.71 (40.96)	365.11 (22.90)	15.40 (0.54)	10.16 (0.32)	6.87 (0.28)	0.55 (0.01)	0.47 (0.01)
A/J	402.33 (14.72)	333.36 (9.79)	14.71 (0.29)	9.73 (0.15)	6.48 (0.12)	0.54 (0.01)	0.46 (0.01)
C57BL/6J	470.06 (9.48)	363.22 (4.79)	15.19 (0.16)	10.20 (0.10)	7.13 (0.09)	0.57 (0.01)	0.47 (0.01)
129S1/SvlmJ	458.68 (21.16)	357.97 (11.72)	15.01 (0.28)	10.06 (0.12)	6.92 (0.16)	0.56 (0.01)	0.47 (0.01)
NOD/ShiLtJ	521.26 (7.95)	388.50 (4.22)	15.39 (0.16)	10.45 (0.10)	7.48 (0.10)	0.57 (0.01)	0.47 (0.01)
NZO/HlLtJ	461.25 (12.21)	375.70 (7.18)	15.89 (0.28)	10.47 (0.21)	6.64 (0.12)	0.52 (0.01)	0.46 (0.00)
CAST/EiJ	349.94 (6.87)	298.11 (4.17)	13.71 (0.14)	9.34 (0.13)	6.13 (0.10)	0.56 (0.01)	0.48 (0.01)
PWK/PhJ	359.84 (12.00)	306.66 (7.75)	14.25 (0.21)	9.18 (0.15)	6.43 (0.07)	0.54 (0.00)	0.50 (0.01)
WSB/EiJ	394.51 (13.37)	318.69 (7.27)	14.04 (0.22)	9.60 (0.14)	6.70 (0.14)	0.58 (0.01)	0.50 (0.01)

Similar distributions of founder strains are noted when comparing endocast volume to endocast surface area (Figure 3b) and overall skull size (Figure 3d; i.e. skull centroid size). Based on these comparisons and estimates of IRE, the founder strains with the highest encephalization measures include NOD/ShiLtJ, WSB/EiJ, 129S1/SvlmJ and C57BL/6J, whilst those with the lowest encephalization are PWK/PhJ and NZO/HlLtJ (Figure 3; Table 4). However, when looking at the Vol/Tib encephalization measure, the relative brain size of PWK/PhJ is estimated to be high compared to the other founder strains (Table 4; Figure S2).

3.3. Diallel analysis

Diallel analysis indicates similar sex, inbreeding, and strain‐specific additive effects for four raw endocast size measurements (length, height, width, volume) (Figure 4). Both female sex and inbreeding (i.e. having two parents of the same founder strain genotype) are associated with smaller endocast dimensions. The interaction of inbreeding and sex leads to a significant increase in endocast length but has no effect on other raw size measures. This means that female founder strain mice tend to have longer endocasts than expected based on the additive combination of overall inbreeding and sex effects, which are both individually associated with a reduced length. Almost all strain‐specific additive effects on endocast size are significant. C57BL/6J, 129S1/SvlmJ, NOD/ShiLtJ and NZO/HlLtJ typically lead to a larger endocast, whereas A/J, CAST/EiJ, PWK/PhJ and WSB/EiJ typically lead to a smaller endocast (Figures 4 and 5). These strain‐specific additive effects generally make sense, with strains of more extreme size having stronger estimated additive effects on each size measurement. One major exception to this is the endocast height of NZO/HlLtJ. This is the largest of the inbred founder strains and its strain‐specific additive effect is strongly positive for length, width and volume. But the additive effect of NZO/HlLtJ genotype on endocast height is not significantly different than zero.

FIGURE 4.

Diallel estimated mean effects of a subset of major additive and non‐additive genetic factors (circles) on endocast measurements, with 95% confidence intervals (horizontal lines). Genetic factors with a significant effect on an endocast measurement are those with a confidence interval that does not include zero (vertical dashed line)

FIGURE 5.

Visual representation of significant positive (+) and negative (−) additive strain‐specific effects on endocast measurements, as estimated using Diallel analysis

The diallel results for the index of relative encephalization (IRE) and the cube root of volume over tibia length (Vol/Tib) indicate a significant positive effect of female sex and inbreeding on encephalization (Figures 4 and 5). However, opposite to raw size measures, the positive inbreeding effect leads to higher encephalization index measures. Half of the strain‐specific additive effects are significant for IRE and Vol/Tib. The NOD/ShiLtJ effect is positive for IRE as it is for raw volume. The A/J Vol/Tib effect is negative as it is for raw volume. PWK/PhJ is negative for IRE as it is for raw volume, but (surprisingly) is positive for Vol/Tib. The WSB/EiJ genotype, which leads to a smaller endocast size, is associated with relatively high encephalization for both measures. The NZO/HlLtJ genotype, which is associated with large endocast size, exhibits relatively low encephalization.

Although a minority of non‐additive factors and their interactions have a significant effect on endocast measures, there are some non‐additive genetic factors that frequently show significant effects (Table 5). For example, 50% of strain‐specific maternal factors have a significant effect on endocast length, whilst 62.5% have a significant effect on IRE. Between 10% and 22% of the cross‐specific symmetric effects are significant for each of the six endocast measures.

TABLE 5.

The number and percentage (in parentheses) of additive and non‐additive factors with a significant effect on endocast measurements

	# of factors	Length	Height	Width	Volume	IRE	Vol/Tib
Female sex factor	1	1 (100%)	1 (100%)	1 (100%)	1 (100%)	1 (100%)	1 (100%)
Inbreeding factor	1	1 (100%)	1 (100%)	1 (100%)	1 (100%)	1 (100%)	1 (100%)
Inbreeding/sex interaction	1	1 (100%)	0 (0%)	0 (0%)	0 (0%)	1 (100%)	0 (0%)
Strain‐specific additive	8	7 (87.5%)	7 (87.5%)	8 (100%)	8 (100%)	4 (50%)	4 (50%)
Strain‐specific additive/sex	8	0 (0%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	2 (25%)
Strain‐specific maternal	8	4 (50%)	0 (0%)	0 (0%)	1 (12.5%)	5 (62.5%)	3 (37.5%)
Strain‐specific maternal/sex	8	0 (0%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)
Strain‐specific inbreeding	8	2 (25%)	1 (12.5%)	2 (25%)	0 (0%)	2 (25%)	4 (50%)
Strain‐specific inbreeding/sex	8	0 (0%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)
Cross‐specific symmetric	28	5 (17.9%)	5 (17.9%)	3 (10.7%)	6 (21.4%)	6 (21.4%)	5 (17.9%)
Cross‐specific symmetric/sex	28	4 (14.3%)	1 (3.6%)	0 (0%)	3 (10.7%)	0 (0%)	0 (0%)
Cross‐specific asymmetric	28	1 (3.6%)	3 (10.7%)	1 (3.6%)	2 (7.1%)	2 (7.1%)	2 (7.1%)
Cross‐specific asymmetric/sex	28	0 (0%)	1 (3.6%)	0 (0%)	1 (3.6%)	0 (0%)	0 (0%)

Whilst each significant non‐additive genetic factor typically explains a small amount of phenotypic variation, the combined effect of all non‐additive factors explains a sizable proportion of phenotypic variation. Strain‐specific additive factors explain between 32% and 78% of phenotypic variation, whereas the combined influence of non‐additive effects explains between 10% and 35% of phenotypic variation (Table 6). Generally, additive genetic factors explain much more of the total variation for the raw size measures and IRE. In contrast, non‐additive genetic factors explain approximately as much phenotypic variation as additive genetic factors for the Vol/Tib encephalization measure, which has a heritability (narrow‐sense) estimate of 32% and non‐additive factors explaining 35% of the variation.

TABLE 6.

Heritability estimates for each endocast measurement, broken down to indicate the amount of phenotypic variation explained by every category of additive and non‐additive genetic factors

	Length	Height	Width	Volume	IRE	Vol/Tib
Sum additive	0.64	0.76	0.71	0.78	0.68	0.32
Strain‐specific additive	0.63	0.76	0.71	0.78	0.68	0.30
Strain‐specific additive/sex	0.00	0.00	0.00	0.00	0.00	0.02
Sum non additive	0.19	0.12	0.14	0.10	0.16	0.35
Strain‐specific maternal	0.03	0.00	0.01	0.01	0.04	0.04
Strain‐specific maternal/sex	0.01	0.01	0.00	0.01	0.01	0.01
Strain‐specific inbreeding	0.03	0.02	0.03	0.01	0.02	0.09
Strain‐specific inbreeding/sex	0.00	0.00	0.00	0.00	0.00	0.00
Cross‐specific symmetric	0.09	0.07	0.09	0.06	0.09	0.17
Cross‐specific symmetric/sex	0.02	0.01	0.00	0.01	0.00	0.02
Cross‐specific asymmetric	0.00	0.00	0.01	0.00	0.01	0.01
Cross‐specific asymmetric/sex	0.00	0.00	0.00	0.00	0.00	0.00
Sum all	0.83	0.87	0.85	0.88	0.84	0.67
% additive	0.77	0.87	0.84	0.89	0.81	0.48

3.4. Significant DO QTL peaks

Genome scans for the endocast measurements (Figure 6) identified a shared QTL for endocast volume, surface area, width and height at approximately 177.04 Mb on Chromosome 1 (Figure 5; α = 0.05 LOD thresholds between 7.307 and 7.487). An R ² value was calculated from the LOD score at this QTL, separately for each of the measurements with a significant association. A 0.08 value for endocast volume indicates that 8% of endocast volume phenotypic variance is explained by genetic variation under this QTL. The R ² value is 0.07 for surface area, 0.06 for width, and 0.07 for height. Within the DO mouse sample, the genome‐wide heritability of these measures was estimated as 0.71 for volume, 0.66 for surface area, 0.76 for width and 0.71 for height.

FIGURE 6.

The results of genome‐wide scan using an additive haplotype model to identify genomic regions significantly associated with six endocast measurements

A 1.5 LOD score drop interval around the significant peak includes the Chromosome 1 region between 176.0610 and 177.4748 Mb (GRCm38 [mm10]; Table 7). The five protein‐coding genes found under this peak are Pld5, Cep170, Sdccag8, Akt3 and Zbtb18 (Figure 7). Variation in some of these genes has been previously associated with brain size phenotypes.

TABLE 7.

Chromosome peak locations associated with significant LOD scores, with 1.5 LOD drop confidence intervals defined

Measurement	Peak position (Mb)	LOD score	1.5 LOD interval (Mb)
Volume	Chr1: 177.0402	16.36296	176.0744–177.3097
Surface area	Chr1: 177.0402	13.83357	176.0744–177.3097
Width	Chr1: 177.0402	12.56471	176.4709–177.4748
Height	Chr1: 176.5670	14.42699	176.0610–177.4748

FIGURE 7.

Map of the protein‐coding genes found under our interval of interest on mouse Chromosome 1

No mutations in human PLD5 have been associated with disease. A mouse knockout of Pld5 displayed abnormal vertebral arch thoracic process morphology, but no other significant abnormalities (www.mousephenotype.org; Dickinson et al., 2016). CEP170 is a centrosome protein that is downstream of WDR62 in a pathway important for brain development. Mutations of WDR62 within cerebral organoids disrupt this pathway, leading to a depletion of CEP170, which may contribute to autosomal recessive primary microcephaly (Zhang et al., 2019). However, no specific mutations within CEP170 are known to contribute to microcephaly.

SDCCAG8 is a centrosome protein that is important for neuron differentiation and radial migration to the cortical plate of the brain (Insolera et al., 2014). Mutations in SDCCG8 have been previously associated with ciliopathy, cystic kidney and retinal disorder and syndromic patients that suffer from intellectual disability, seizures and schizophrenia (Flynn et al., 2020; Hamshere et al., 2013). Mice deficient in SDCCAG8 have the retinal‐renal phenotype, but also rib cage abnormalities and polydactyly with triphalangeal thumbs (Airik et al., 2016).

Akt family genes encode protein kinase enzymes that are important for growth and metabolism. Akt3 is most highly expressed in the developing brain and testes. Akt3 null mutant mice display normal body size, normal glucose levels and 20–25% smaller brains by weight when compared to controls (Easton et al., 2005; Tschopp et al., 2005). These mutant mice are healthy with normal brain structural organization, suggesting an overall scaled decrease in brain size rather than a specific reduction in a particular brain region. Brain cell size reduction and cell number reduction contribute to producing a smaller brain (Easton et al., 2005; Tschopp et al., 2005). Mice with increased AKT3 signalling activity in the developing brain had a larger brain and an increased frequency of seizures. These brains also display normal anatomical organization, although there may be a relatively large hippocampus (Tokuda et al., 2011). Humans with microdeletions that include AKT3 display microcephaly, agenesis of the corpus callosum, and epilepsy. However, it is likely that loss of AKT3 is primarily responsible for microcephaly whilst loss of other genes is responsible for the other phenotypes (Depienne et al., 2017).

ZBTB18 plays an important role in neurogenesis and normal cortical growth within the brain. Mice with ZBTB18 loss of function mutations die at birth with neocortical defects. Central nervous system specific loss of function leads to reduced neuronal differentiation and increased glial differentiation, in turn producing a serious postnatal phenotype with microencephaly, agenesis of the corpus callosum, and cerebellar hypoplasia (Xiang et al., 2012). Patients with microdeletions that include ZBTB18 (and often AKT3), display microcephaly, agenesis of the corpus callosum, and epilepsy. It is likely that loss of ZKTB18 is the primary cause of agenesis of the corpus callosum, although it may contribute secondarily to microcephaly phenotypes (Depienne et al., 2017).

3.5. DO QTL haplotype effects

The estimated effect of each CC founder strain haplotype indicates that a major negative effect of the NZO/HlLtJ haplotype drives the significant QTL on Chromosome 1 (Figure 8; Figure S3). On average, the NZO/HlLtJ haplotype in this genomic region leads to a decrease in endocast height, width, surface area and volume. No other founder strain haplotype has a notable effect on endocast phenotype in this region. This implies that one or more genetic variants found in the NZO/HlLtJ genome, but not in the other founder strain genomes, leads to significantly smaller endocast size across this region.

FIGURE 8.

CC founder strain‐specific phenotype coefficients (above) and LOD scores from the genome‐wide scan (below) for the significant association between founder strain haplotype and endocast volume. Coefficient plots for other significant association phenotypes are found in Figure S3

To identify candidate variants that might be functionally responsible for this endocast association, a search for variants was completed using the Wellcome Sanger Institute Mouse Genomes Project online query tool (https://www.sanger.ac.uk/sanger/Mouse_SnpViewer), which identifies SNPs and other variants that differ between the aligned genomes of many inbred mouse strains (Keane et al., 2011; Yalcin et al., 2011). We searched for missense mutations, frameshift variants, stop codon mutations, indels and structural variants within our region of interest on Chromosome 1 (1:176061000–177474800) across the eight CC founder strains because these variant types are most likely to lead to a change in protein expression and function.

Twenty missense mutations were identified across the eight CC founder strains, with 13 of them being CAST/EiJ specific variants, one being a WSB/EiJ specific variant, one a C57BL/6J specific variant, and one being an NZO/HlLtJ variant. Because our haplotype coefficient plots (Figure 8; Figure S3) indicate that the genetic variant(s) of interest are likely to be NZO/HlLtJ specific, we suggest SNP rs247597104 at 1:177050102 within Akt3 as the most promising causal mutation candidate within the QTL interval.

Amongst 59 structural variants identified in this region across the eight CC founder strains, three of them are NZO/HlLtJ specific insertions (176,406,258‐176,406,284; 176,441,538‐176,463,577; 176,867,926‐176,867,928). These insertions may also be interesting candidates to explore further.

4. DISCUSSION

The skull is a complex skeletal structure that supports many critical organismal functions. Simultaneous growth and development of multiple interacting tissues, including skull, brain and muscles, is required to produce a fully functional head. Molecular interactions are known to help regulate synchronous brain and face formation processes early in development, but physical‐mechanical interactions between tissues are also necessary for the development of typical adult head morphology (reviewed by Marcucio et al., 2011; Richtsmeier & Flaherty, 2013; Adameyko & Fried, 2016). Variation in skull morphology between populations or species may be based on some combination of (1) direct changes to bone developmental processes and (2) plastic responses of the developing bone to variation in the size of nearby soft tissue structures like the brain. Here, we quantified the importance of genetic factors in determining overall neurocranial form to help determine the mechanistic basis of neurocranial variation.

We investigated the genetic basis of total endocast size and relative brain size (i.e. encephalization) across a range of morphologically ‘normal’ adult mouse skulls. Our diallel analysis of eight inbred strains and their F1 crosses indicated that endocast size measures are highly heritable and are primarily determined by additive genetic factors, although some non‐additive genetic factors have a significant impact on phenotype. Our association study of an outbred population derived from the same founder strains identified a significant association between several endocast size measures and haplotype variation within a short interval on mouse Chromosome 1. The list of protein‐coding genes within this genomic interval supports the hypothesis that genes primarily driving brain growth to contribute secondarily to determining neurocranial size and shape. In this case, it appears that increased mouse endocast size relative to overall skull size is accommodated by increased neurocranial height.

4.1. Automated method validation

Our automated endocast segmentation method produced measurements that closely matched those collected using a time‐consuming process of manual μCT image preparation and Endex software application on the same specimens. However, a few sources of error were noted. Most important for our genetic analysis, the incorrect identification of the foramen magnum by our nonlinear registration process led to inaccurate endocast length measurements in some of the specimens. However, specimens with high automated endocast length error were successfully identified as outliers based on residuals of an endocast volume to endocast length regression. This is because errors in foramen magnum identification cause proportionally greater errors in endocast length estimates compared to endocast volume estimates. These outlier specimens were removed from the sample before other analyses were performed. Other notable differences between automated and manual endocast segmentations were based primarily on manual endocast identification error and had no impact on the quality of our diallel analysis or GWAS. A more detailed discussion/comparison of segmentation methods can be found in the Supporting Methods, Figures and Tables document (File S1).

4.2. Normal mouse endocast variation

Across our sample of CC founder strains and F1 crosses, raw endocast measurements were positively correlated with each other and with overall skull size (Figure 3). Founder strains can be differentiated by mean endocast size values, with wild‐derived strains being the smallest for most measures. The NZO/HlLtJ strain pops out as unusual because it has the largest overall skull size, but an intermediate endocast volume. This strain was bred for increased obesity (Bielschowsky & Bielschowsky, 1956), resulting in a mouse with both higher fat and lean body mass (Ackert‐Bicknell et al., 2008). This strain also displays a longer body length (Center for Genome Dynamics, 2009) and a large but flat skull compared to the other CC founder strains (Percival et al., 2016a). The NZO/HlLtJ strain has a high endocast surface area relative to endocast volume (Figure 3b), which likely reflects a relatively elongated and disproportionately flat neurocranium.

Pairwise correlations suggest that endocast height can vary somewhat independently from volume, width, and length. From a genotype‐specific perspective, the additive effect of the NZO/HlLtJ genotype is associated with the increased size of most measures, but there is no significant additive effect for the NZO/HlLtJ genotype on endocast height. More broadly, we argue that variation in endocast length and width are driven more by the growth of the endochondrally ossified cranial base bones whilst endocast height depends more on the growth of intramembranously ossified bones of the cranial vault. The longitudinal growth of the cranial base is limited by the speed of cellular proliferation and hypertrophy in cartilaginous synchondroses between ossified centres. On the contrary, intramembranous ossification at cranial vault sutures is possible in multiple directions at once as these bones continue to expand towards each other dorsally and medially. Additionally, mechanical forces are important for maintaining open cranial vault sutures with viable precursor cell populations at the suture margins (Herring, 2008). Therefore, cranial vault shape and size may be more directly affected by the mechanical forces (or lack of forces) imposed during postnatal brain growth. In other words, vault bone sutures are likely to remain patent and growing as long as there is a tensile force caused by brain growth, and they are likely to meet and fuse when this force decreases below a certain threshold (or even with the appearance of compressive forces across the suture as bone fronts touch).

If an adult brain is small in proportion to overall skull size, we expect the size of the early ossifying cranial base to be roughly proportional to overall skull size whilst the cranial vault will more closely match brain size. We expect low encephalization organisms to have flatter neurocrania based on the argument that cranial vault height has a more plastic response to variation in brain size. Similarly, we expect organisms with high encephalization to have taller and rounder cranial vaults that accommodate their proportionally larger brains. Previous analysis of the CC founder/F1 skull dataset identified a pattern where specimens with larger overall skull size showed proportionally smaller and less globular neurocrania with greater basicranial flexion (Pavličev et al., 2017). We assume that this result is largely driven by the presence of the NZO/HlLtJ genotype in F1 crosses leading to relatively small brain to skull size ratios. Our expectations are also supported by the fact that increased endocranial pressure and intracranial fluid volume in rodent models of hydrocephaly tend to have more domed or globular cranial vaults rather than proportionally longer cranial bases (Holdener et al., 2019; Ibañez‐Tallon et al., 2002; Moss & Young, 1960).

If the cranial vault is more developmentally plastic than length or width, it might easily accommodate evolutionary changes in brain size and encephalization, potentially leading it to covary strongly with encephalization across species. However, multiple regression analysis indicates that (out of length, width and height) maximum brain width contributes most to variation in endocast volume across avian species and has increased relative to brain endocast volume over the course of evolutionary history in birds and mammals (Kawabe et al., 2009). A subsequent analysis of mammalian endocast width and volume indicated a strong linear relationship, although mammalian brains tend to be more slender than avian brains (Kawabe et al., 2013). Neurocranial globularity and endocast length were also identified as a major axis of endocast shape variation across marsupials (Weisbecker et al., 2021). So, although variation in vault height might be a major basis for the intraspecies neurocranial shape differences across mice, evolution has produced inter‐species differences that vary strongly along other axes of neurocranial shape variation.

4.3. Mouse endocast quantitative genetics

Our results indicate a high heritability of endocast size and encephalization measures, with a low proportion of variance explained by non‐additive factors; except in the case of endocast volume relative to tibia length (Vol/Tib). Endocast heritability values (0.32–0.78) are higher or similar to those previously reported for measures of relative skull length (0.46) in the same sample of mice (Percival et al., 2016a) and those estimated for principal components of DO mouse facial shape (generally between 0.42 and 0.57) (Katz et al., 2020). Although it is tempting to think that these higher heritability values indicate a greater potential for heritable change in morphology, lower values in the previous analyses might be expected based on scaling of linear skull measures (Percival et al., 2016a), differences in the type of measurement and the list of covariates (Katz et al., 2020). Either way, our results confirm a high heritability for endocast size measures.

Although strain‐specific additive factors explain three to four times more endocast variation than non‐additive factors, there is a substantial nonadditive inbreeding effect for each measure. As with previous analyses of these and other mouse populations, inbred mice tend to be smaller than expected based on additive genotypic predictions (Ingram et al., 1982; Kurnianto et al., 1999; Leamy, 1982; Pavličev et al., 2017; Percival et al., 2016a), although the inbreeding effect on encephalization measures is reversed. So, inbred mice tend to have reduced total body and neurocranial size, but large brains relative to skull size and body size. This may indicate stronger canalization of brain size, in the sense that brain size varies less than skull size or body size within an intraspecies context. Studies of encephalization indices across species covering a much wider range of body sizes indicate an allometric relationship where larger organisms tend to have proportionally smaller brains (Marugán‐Lobón et al., 2016) and proportionally larger faces (Cardini, 2019) than small organisms. Strong brain size canalization or this broad allometric pattern may partially explain why artificial selection for increased body size in the NZO/HlLtJ strain has produced mice with a large body and skull size, but brain volumes equivalent to mice with moderate body sizes (e.g. C57BL/6J) (Figure 3).

The Vol/Tib encephalization measure has a lower heritability, where an equal proportion of phenotypic variance is associated with additive and non‐additive genetic factors. This lower heritability might be expected if there are fewer genetic factors that pleiotropically influence neurocranial and tibia variation than those that pleiotropically influence neurocranial and cranial base variation. A lower number of shared additive genetic factors is expected to lead to a lower proportional additive heritability component.

Cross‐specific symmetric genetic effects explain about half of the non‐additive factor contributions to Vol/Tib variance. This indicates that specific founder strain combinations in first‐generation crosses produce Vol/Tib values that consistently diverge from the additive genetic expectations, regardless of which strain is the mother (because it is a ‘symmetric’ effect). The second highest non‐additive contribution to Vol/Tib variance is from strain‐specific inbreeding factors. Fifty percent of the founder strains display a statistically significant inbreeding effect that diverges from the overall mouse inbreeding effect for this encephalization measurement.

Differences between the direction and strength of additive genotypic effects on the IRE and Vol/Tib encephalization indices are mathematically based on the choice of size standardization measurements. Tibia length is an aspect of hind limb length, whilst cranial base length measures an aspect of neurocranial size that we believe is more strongly representative of body size than other skull measures. However, because cranial base length is a skull measurement, we anticipate that it will covary more strongly than overall body size with neurocranial measurements. Tibia length was chosen as a proxy for the overall skeletal size of the body because we were concerned that body size measures like weight would be inappropriately skewed by variation in body fat between mouse strains. Unfortunately, both of our proxies for body size are imperfect and we cannot currently determine which of these measures is a better basis for encephalization estimation at this time. A post hoc comparison indicated that NZO/HlLtJ and PWK/PhJ have an unusually high overall skull size (i.e. centroid size) compared to tibia length, whilst the other founder strain specimens fall close to a single regression line. This difference between skull and tibia size measures partially explains the divergent interpretations of additive strain encephalization effects within our results. It also confirms that different body size measures can lead to notably different conclusions (see also Hallgrímsson et al., 2019).

4.4. Chromosome 1 QTL for neurocranial size

We identified a significant QTL on mouse Chromosome 1 for measures of endocast width, height, volume and surface area (Figure 6). In each case, the QTL effect at this locus is entirely driven by the contrast between the NZO/HlLtJ strain and remaining strain haplotypes. Mice carrying the NZO/HlLtJ haplotype tend to have smaller endocasts (Figure 8; Figure S3) in all measured dimensions except length. This failure to discover a neurocranial length QTL may mean that neurocranial length is determined by different genetic loci. It is also possible that a relatively high level of endocast length measurement error serves to obscure a true causal effect of this locus, despite the successful removal of major endocast measurement error outlier specimens prior to analysis. Whether or not endocast length should display a significant association with haplotype variation in this region, we interpret this QTL as being associated with the overall neurocranial size.

Given that our endocast size measurements have a high heritability for both CC Founder/F1 and DO samples and most strain‐specific additive genetic effects on endocast size are significant, it is surprising that only one QTL was identified in our analysis and that only one of the founder strains displays a significant haplotype effect at this QTL. Other portions of the additive variance in endocast size measures may be distributed across many loci, making them difficult to identify as QTL. Given our relatively high sample size, it is disappointing that so much of the endocast size heritability remains unexplained by our association study. The clear presence of this missing heritability suggests that seemingly simple strain‐specific additive genetic effects are usually the result of allelic variation at many loci.

A variety of QTL related to skull size, organ size and overall body size have been previously identified in mice, although none of them appears to overlap our Chromosome 1 QTL. For example, multiple QTL associated with a skeletal size and organ weights in a mouse intercross of SM/J and LG/J inbred strains have been identified, but do not overlap with our QTL (Kenney‐Hunt et al., 2006, 2008; Norgard et al., 2009; Wolf et al., 2005). QTL associated with skull morphological variation for recombinant congenic strains of Mus spretus (SEG/Pas) and Mus musculus (C57BL/6) (Burgio et al., 2009; Burgio et al., 2012a, 2012b), hybrids of wild Mus musculus domesticus and Mus musculus (Pallares et al., 2014), a backcross of C57BL/6J and A/J (Maga et al., 2015), and a different outbred population of mice (Carworth Farms White) (Pallares et al., 2015) also do not overlap with our region of interest.

Given that neurocranial size is a major contributor to overall skull size and there are systemic growth factors that impact many aspects of organismal growth, it is surprising that our QTL for general neurocranial size was not identified in previous mouse studies of size variation, especially since we estimate it explains 8% of endocast volume variation in our sample. This may mean the QTL contributes specifically to endocast size and/or brain size. Alternatively, this might be an important locus for determining overall organismal size, but for which most mouse strains are genetically fixed. In this case, the QTL might only be identifiable when a mouse strain with an otherwise rare allele is included in the analysis (hypothetically, the NZO/HlLtJ strain in this case).

The fact that all protein‐coding genes under the region of interest have been previously associated with brain growth and/or brain pathology supports the idea that genetic variation at this QTL primarily impacts brain developmental processes rather than bone developmental processes. One alternative explanation for this result is that the identified ‘brain’ factor also has undocumented pleiotropic effects on bone development. Although we are unable to systematically reject this hypothesis, we believe it is unlikely, particularly if the causal mutation falls within Akt3. AKT3 is reported to be strongly expressed within the developing brain and testes, but not within developing bone.

Of particular interest as a candidate for the measured QTL effect is an NZO/HlLtJ specific missense mutation within Akt3. Decreased AKT3 expression during early development leads to significant reductions in brain size without notable abnormalities in brain structure or body size (Easton et al., 2005; Tschopp et al., 2005). Similarly, mice with increased AKT3 expression have larger brains with largely normal anatomical organization and higher seizure risk (Tokuda et al., 2011). A human genome‐wide significant locus for brain shape is also found centred on AKT3 (Naqvi et al., 2021), reinforcing the importance of this locus for determining gross brain phenotype in other mammalian species. However, it is one of the hundreds of genome‐wide significant loci for human brain shape, reinforcing the fact that a very large number of genetic factors contribute to brain development and adult phenotype.

If the identified missense mutation reduces AKT3 expression, activity or downstream signalling, this might explain why the NZO/HlLtJ haplotype within our candidate region leads to reduced endocast dimensions. Since the total loss of AKT3 does not appear to modify brain structural organization, we do not anticipate that this mutation will influence brain structure or mouse behaviour. Further investigation of various candidate mutations and the study of brain growth processes in the CC inbred strains will help to determine the true causal mutation underlying the identified phenotype‐genotype association. However, a single Akt3 missense mutation is quite appealing as a candidate. If this or another single NZO/HlLtJ specific mutation is responsible for reduced adult brain and neurocranial size, inserting this mutation into other inbred mouse backgrounds could provide a great way to test how a major non‐pathogenic change in brain size is accommodated by the normal developmental processes of the growing skull. In this case, we would anticipate a reduction in early brain growth and adult brain size when compared to the inbred background strain without the mutation. Based on our current results, we would expect mutant mouse neurocrania to be relatively flat compared to control specimens from the associated inbred backgrounds.

4.5. Concluding statement

Endocast size variation across mouse strains is highly heritable and explained largely by additive genetic factors. Our results suggest that variation in brain volume leads to secondary variation in neurocranial shape, with a particular impact on the degree of neurocranial globularity. We propose that a mutation found under the identified Chromosome 1 peak within the NZO/HlLtJ haplotype primarily modifies brain developmental processes, leading to a smaller brain, a notably reduced encephalization index, and a relatively flat neurocranium. If a single mutation in a gene that regulates brain growth is responsible for this phenotypic shift, it is evidence that substantial evolutionary change in brain size can happen quite abruptly after a simple mutation event. Furthermore, it may lead to major secondary changes in neurocranial shape based on developmental plasticity of bone growth processes without any subsequent mutations in genes that directly regulate changes in bone cell activity. Although increased brain volume in mice may be accommodated largely by increased neurocranial globularity, other aspects of shape may be more developmentally plastic in other species. Of course, both skull shape and brain size are complex traits that are driven by variation within many genetic loci, some of which may influence both phenotypes pleiotropically. The fact that so much additive endocast size variation remains unexplained by our association analysis suggests that most relevant mutations have small effects on neurocranial size and encephalization, with our QTL being an outlier. This analysis does not prove that the close covariation of neurocranial and brain size and shape is driven primarily by variation in genes of brain growth. Instead, our results highlight the importance of accounting for the mechanical influence of nearby soft tissues on the development and the evolution of skull shape, where some small subset of simple mutations might lead to substantial evolutionary changes in both brain size and skull shape.

AUTHOR CONTRIBUTIONS

CJP – concept/design, acquisition of data, data analysis/interpretation, drafting of the manuscript, critical revision of the manuscript, approval of the article. JD – concept/design, acquisition of data, critical revision of the manuscript, approval of the article. CRH – concept/design, acquisition of data, drafting of the manuscript, approval of the article. MV – data analysis/interpretation, critical revision of the manuscript, approval of the article. CJOC – acquisition of data, data analysis/interpretation, approval of the article. EZ – data analysis/interpretation, critical revision of the manuscript, approval of the article. CR – concept/design, critical revision of the manuscript, approval of the article. DK – concept/design, data analysis/interpretation, critical revision of the manuscript, approval of the article. BH – concept/design, critical revision of the manuscript, approval of the article.

OPEN RESEARCH BADGES

This article has been awarded Open Data Badge for making publicly available the digitally‐shareable data necessary to reproduce the reported results. Data is available at Open Science Framework

Supporting information

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Percival, C.J. , Devine, J. , Hassan, C.R. , Vidal‐Garcia, M. , O’Connor‐Coates, C.J. & Zaffarini, E. et al. (2022) The genetic basis of neurocranial size and shape across varied lab mouse populations. Journal of Anatomy, 241, 211–229. Available from: 10.1111/joa.13657

DATA AVAILABILITY STATEMENT

All data included as the basis for our analysis are publicly available. Endocast measurements and covariates of analyzed specimens are included as supporting files for this manuscript. μCT images of the CC Founder/F1 specimens can be found on FaceBase (https://www.facebase.org/chaise/record/#1/isa:dataset/RID=1‐43F6). μCT images and genotype data of the DO specimens can be found on FaceBase (https://www.facebase.org/chaise/record/#1/isa:dataset/RID=1‐731C). Further details on the MusMorph public mouse dataset are found in a recent publication (Devine et al., 2021) and associated github repository (https://github.com/jaydevine/MusMorph), which contain all the information, links, and code necessary for automated image registration, atlas creation, and automated segmentation. The code and files used as the basis for our GWAS analysis are found in a different github repository (https://github.com/martavidalgarcia/endocast_qtl).