**3. Results**

#### *3.1. Pattern of Humeral Biomechanical Asymmetry in Modern Humans*

The mean morphometric maps exhibiting SMA asymmetry values for each sub-group and pooled samples are presented in Figure 2. Hubei females and males are more asymmetrical in the near-anterolateral posteromedial aspect along the entire proximodistal diaphysis. The degree of asymmetry is transversely uniform around the mid-distal diaphysis for Hubei females, and around the midshaft for Hubei males. Hubei males have higher anteroposterior asymmetry from the proximal to mid-proximal diaphysis. Henan females have a restricted area of relatively higher anteroposterior asymmetry around the midproximal diaphysis, while Henan males are more asymmetrical in the near-anterolateral posteromedial aspect spanning the mid-proximal to distal diaphysis. Both Xinjiang females and males have reinforced anteroposterior asymmetrical areas around the proximal diaphysis, as well as the region between the proximal to mid-proximal diaphysis, mediolaterally. The region with a relatively higher asymmetry of Xinjiang males extends from the midshaft to the distal diaphysis in the near-anterolateral posteromedial aspect.

For the mean morphometric maps that are defined only by population, Hubei is more asymmetrical across the entire proximodistal diaphysis in the near-anterolateral posteromedial aspect, with a reinforcement of anteroposterior asymmetry along the proximal to mid-proximal diaphysis. The region with high asymmetry for Henan is located in the anterolateral posteromedial aspect between the mid-proximal to distal diaphysis. Xinjiang has higher anteroposterior asymmetry around the proximal diaphysis, connecting with another area with high mediolateral asymmetry around the mid-proximal diaphysis, which continuously extends to the midshaft in the anterolateral posteromedial aspect. Hubei and Xinjiang are more asymmetrical than Henan, according to their overall magnitude of SMA asymmetry values. For the mean morphometric maps that are defined only by sex, females

are more anteroposteriorly asymmetrical between the proximal and mid-distal diaphysis, with a reinforcement of asymmetry near the mid-proximal section. The distribution patterns of males resemble that of Xinjiang, but the regions with highest asymmetry at the proximal and mid-proximal diaphysis are not so prominent, and the region with relatively higher asymmetry along the distal half of the diaphysis in the anterolateral posteromedial aspect is more developed. Males are more asymmetrical than females in general. The mean morphometric map for pooled samples shows uniform areas of asymmetry spanning from the proximal diaphysis, anteroposteriorly, to the mid-proximal diaphysis, mediolaterally, and continuing distally in the anterolateral posteromedial aspect.

**Figure 2.** Mean morphometric maps exhibiting SMA asymmetry values for sub-groups and pooled samples (**P**). Sub-groups are defined by population, sex, and the pairwise combination of these two factors. Populations include Hubei (**HB**), Henan (**HN**), and Xinjiang (**XJ**); sexes include female (**F**) and male (**M**). All mean morphometric maps are under the same chromatic scale.

According to the results of MANOVA (Table 1), the differences sourced from sex (*P* = 0.11), population (*P* = 0.296), and the interaction of sex and population (*P* = 0.783) are not statistically significant. The R-squared values reveal that sex, population, and the interaction of sex and population accounted for 5.49%, 5.99%, and 2.74% of the total variation, respectively. Residuals accounted for 85.77% of the total variation.


**Table 1.** MANOVA results interpreting the differences between sexes and among populations.

Df: degree of freedom; SS: sums of squares; MS: mean squares; Rsq: R-squared values.

The CV morphometric maps show nearly identical distribution patterns across all the sub-groups and pooled samples (Figure 3). Relatively high CV values are concentrated in the region between the middle and mid-distal diaphysis, and at the distal extreme in the anteromedial posterolateral aspect. Similarly high CV values appear at the proximal section, mediolaterally, but to a smaller extent compared to the distal section. Henan has localized regions of higher CV values at the proximal extreme, mediolaterally, and at the mid-distal diaphysis in the anteromedial posterolateral aspect, but displays no other differences compared to Hebei and Xinjiang. Females present higher overall CV values than males.

**Figure 3.** Morphometric maps exhibiting the coefficient of variation (CV) for SMA asymmetry values in sub-groups and pooled samples (**P**). Sub-groups are defined by population and sex. Populations include Hubei (**HB**), Henan (**HN**), and Xinjiang (XJ); sexes include female (**F**) and male (**M**). All CV morphometric maps are under the same chromatic scale.

## *3.2. Representativeness of J35 and J50 Bilateral Asymmetry*

Table 2 and Figure 4 show the result of a multivariate regression fitting all the SMA asymmetry values on the J35 or J50 asymmetry value using pooled samples. The results of J35 and J50 asymmetry are highly significant (*P* < 0.001), indicating that the multivariate regression model is effective. According to the R-squared values, J35 asymmetry accounts for 48.66% of the total variation, whereas J50 asymmetry accounts for 50.93%. The remaining variations are explained by the residuals, which is 51.34% in the J35 asymmetry model and 49.07% in the J50 asymmetry model.

**Table 2.** Multivariate regression of all SMA asymmetry values on J asymmetry value.


Df: degree of freedom; SS: sums of squares; MS: mean squares; Rsq: R-squared values; \*\*: statistically highly significant.

**Figure 4.** Multivariate regression of all SMA asymmetry values on J asymmetry value at the 35% or 50% cross-section using pooled samples.

The CC morphometric maps of the sub-groups and pooled samples are shown in Figure 5. Across all the CC morphometric maps, the SMA asymmetry values and the J35 or J50 asymmetry value are positively correlated among the entire humeral diaphysis, except for some areas of Henan. When specific to the morphometric maps of CC35, high CC35 values are detected primarily among the distal half of the diaphysis, particularly around the mid-distal to distal section, while lower CC35 values are more inclined to distribute anteroposteriorly over the proximal half of the diaphysis. Henan differs from the other sub-groups in that its SMA asymmetry values are negatively correlated with the J35 asymmetry value in the region between the mid-proximal and middle diaphysis, anteroposteriorly. For the morphometric maps of CC50, high CC50 values are found between the proximal and middle diaphysis, anteroposteriorly, which gradually shift in the anterolateral posteromedial aspect, from the middle to distal diaphysis. Comparatively, low CC50 values tend to follow the approximately anterolateral posteromedial aspect between the mid-distal and distal diaphysis. In comparison to other sub-groups, Henan exhibits a distinct distribution pattern of CC50 values at the distal humeral section, mediolaterally, with the SMA asymmetry values being negatively correlated with the J50 asymmetry value.

**Figure 5.** Morphometric maps exhibiting the correlation coefficient (CC) between SMA asymmetry values and J asymmetry value at the 35% or 50% cross-section in sub-groups and pooled samples (**P**). Sub-groups are defined by population and sex. Populations include Hubei (**HB**), Henan (**HN**), and Xinjiang (**XJ**); sexes include female (**F**) and male (**M**). All CC morphometric maps are under the same chromatic scale.
