**3. Results**

Preliminary results from summary statistics (Table 2) detailing the differences between the left and right occipital lobes and the variation between height and width measurements.


**Table 2.** Summary statistics detailing mean, variance, standard deviations for the subsample (*n* = 15) with known hemisphere siding.

Canonical Correspondence Analysis (CCA) was used to determine the strength of the correlation between different occipital bridge types, and the left (L) and right (R) height or width of the occipital lobe. The presence or absence of bridging patterns requires assessment where the potential correlation between occipital lobe height and width could be assessed against the presence or absence of Left or Right bridging patterns, or whether those with Both patterns were associated more with Occipital lobe width or height. Consistent with CCA, the type of bridging patterns grouped specimens accordingly and the effect of

occipital lobe height or width determined. Results indicated that greater occipital width was associated with both Left and Right bridging patterns (Axis 1), while occipital lobe height (Axis 2) was associated more strongly with No Bridging pattern. The correlations between variables indicated by Axis 1 (89% variance) and Axis 2 (11% variance) were statistically significant (*p* < 0.002) with 1000 permutations (Table 3).

**Table 3.** Canonical Correspondence Analysis values of occipital lobe bridge patterns, with permutation (999 iterations). Statistically significant values are reported in italics.


Abbreviations: *p*-value is the permutated *p*-value from 1000 iterations.

There were four distinct groups based on the type of bridge patterns observed with a left bridge associated with marginally shorter L lobe height and greater R lobe width, a right bridge was associated with shorter R lobe height and slightly greater R lobe width, where both L and R bridges were present, these were weakly associated with smaller L height, and no bridges was associated with greater R lobe height and width (Figure 2).

**Figure 2.** Canonical Correspondence analysis showing the four distinct groups of bridge patterns and a biplot indicating the direction of correlations between variables where longer lines indicate a stronger correlation. Abbreviations: Green square = Right Bridge; Purple square = Left bridge; Blue Sphere = No bridge; Red Triangle = Both bridges; L Height = Left occipital lobe height; R Height = Right occipital lobe height; L Width = Left occipital lobe width; R Width = Right occipital lobe width.

Correlation analysis examined potential correlations between variables using Pearson's *r* correlation coefficient for significance and a Monte Carlo permutation (9999 iterations) with the probability of variables being uncorrelated using a two-tailed significance set to *p* < 0.01. Statistically significant correlations using Monte Carlo permutation are reported (Table 4) for R and L lobe height and width (*p* ≤ 0.0001), with slightly less robust correlations for R lobe width and right bridge (*p* = 0.0008), and L lobe height and L bridge (*p* = 0.0022). Correlations between bridging patterns are entirely due to the binary coding and do not reflect a true correlation.


**Table 4.** Correlation Analysis between occipital lobe metrics and bridging patterns, with Monte Carlo permutation (9999 iterations) and two-tailed significance. Statistically significant values are reported in italics (*p* < 0.01). Correlation values reported in the lower triangle with two-tailed significance that variables are uncorrelated are reported in the upper triangle.

Abbreviations: Correlation in lower triangle of matrix; probability of uncorrelated variables with two-tailed significance (*p* < 0.05) in upper triangle of matrix. L Height = Left occipital lobe height; R Height = Right occipital lobe height; L Width = Left occipital lobe width; R Width = Right occipital lobe width; R Bridge = Right Bridge; L Bridge = Left bridge; No Bridge = Nbridge; 1 = Included as binary values (present/absent scores).

Caution is warranted with these initial findings where uncertainty associated with correct hemisphere siding, and the low number of individuals who possessed a bridging pattern could be obscured by the higher number of those who possessed no bridging pattern and where known siding is uncertain. However, correlation results and those reported from the CCA sugges<sup>t</sup> a likely association between lobe width and bridging patterns.

Ordinary Least Squares (OLS) regression examined a subsample (*n* = 15) of individuals with known right and left hemisphere siding allowing a test of bridging and siding prediction and associated uncertainty. Metrics (in mm) for both right and left width and height were first transformed by natural logarithm (base *e*) maintaining linearity. Both height and width were predicted using Right from Left and then Left from Right to determine the potential effect of siding on prediction uncertainty. All predictions were made with a 95% confidence interval (CI) with strong correlations (*r* ≥ 0.86, *p* ≤ 0.0001). However, between the regression models, there was little observable difference whether the left or right hemisphere was used for the predictions (Table 5, Figure 3).


**Table 5.** Parameters for ordinary least-squares regression detailing the regression statistics for the four metrics both left and right side. Statistically significant results reported in italics.

Abbreviations: *a* = slope; *b* = intercept; s.e = standard error of the regression estimate; *r* = Correlation coefficient; *p* = *p*-value for significance; L Height = Left occipital lobe height; R Height = Right occipital lobe height; L Width = Left occipital lobe width; R Width = Right occipital lobe width.

All regression models showed a strong prediction overall, calculating the percentage of prediction uncertainty (PPE) allows a better comparison of the uncertainty within each model. Percentage of prediction error (PPE) was calculated for occipital height and width, respectively, and the difference between these left and right predictions compared with robust agreemen<sup>t</sup> between the observed and the predicted values (Table 5). Prediction reliability assessed the difference within the regression models and between left and right

lobes. Greater prediction uncertainty existed for lobe height, with a disparity of 17%, than for width where the disparity was only 6%. This sugges<sup>t</sup> that occipital lobe width might be a more stable variable with less prediction uncertainty than height, potentially making it more suitable for predicting occipital lobe side and hence, more reliable for assessing bridging pattern associations (Table 6).

**Figure 3.** Log-log Ordinary Least Squares (OLS) regression of Occipital lobe fitted with a 95% confidence interval for lobe (**A**) height and (**B**) width where black triangles are specimens with a bridging gyrus and black dashed line to emphasize symmetry and asymmetry (the departure from symmetry).

The predictions for both L and R occipital lobe width and height are provided for both known and unknown sample, with predicted values converted from log-units to metrics (in mm) by taking the inverse-log and the observed values reported in parentheses alongside the predicted values (Table 7, Figure 4). Considering there was no discernible difference in pattern of reliability between the hemispheres, only the prediction of R lobe height and width are provided.

**Table 6.** Percentage of prediction errors (PPE) for four occipital metrics calculated as the difference between observed and predicted height and width, and percentage of prediction reliability calculated as difference between observed and predicted height and width (in mm) divided by observed height and width. Negative and positive values indicate an increase or decrease, respectively, in the predicted value from the observed.



**Table 6.** *Cont.*

**Table 7.** Prediction of occipital lobe width and height (in mm) listed with the corresponding variable calculated from the bivariate ordinary least-squares equations. Observed values reported beside predicted in parentheses.




Abbreviations: 1 Measurements of left (L) and right (R) height and width (in mm), 2 The subsample with known hemisphere siding.

**Figure 4.** The predicted height and width (in mm) for the R occipital lobe in the known subsample with a confidence interval applied, calculated from the standard error of the regression.
