### One for all and all for one: Linear regression from the mass of individual bones to assess human skeletal mass completeness

Complete and accurate human skeletal inventory is seldom possible in archaeological and forensic cases involving severe fragmentation. In such cases, skeletal mass comparisons with published references may be used as an alternative to assess skeletal completeness but they are too general for a case-by-case routine analysis. The objective is to solve this issue by creating linear regression equations to estimate the total mass of a skeleton based on the mass of isolated bones.

Total skeleton mass and individual mass of the clavicle, humerus, femur, patella, carpal, metacarpal, tarsal and metatarsal bones were recorded in a sample of 60 skeletons from the 21st Century Identified Skeletal Collection (University of Coimbra). The sample included 32 females and 28 males with ages ranging from 31 to 96 years old (mean = 76.4; sd = 14.8).

The mass of isolated bones could be used to predict the approximate total mass of the skeleton. The femur, humerus and second metacarpal were the best predictors of total skeletal mass with root mean squared errors ranging from 292.9 to 346.1 gm.

Although relatively successful, the non-normal distribution of the sample in terms of mass may have reduced the predictive power of the equations. Mass regression can be more adequately applied to forensic than to archaeological remains as the latter are generally more affected by post-depositional mass loss. The impact for bioanthropology, especially forensic anthropology, is important since this method may improve methodology to calculate the completeness of the skeleton or the minimum number of individuals.

Keywords: bioarchaeology; forensic anthropology; bone mass; scattered remains; funerary practice

#### Data exploration through heatmap

All variables are in columns representing type of bone, ex. CLV.L = clavicle (left side). All the individuals of the sample are represented as rows and organized by clusters of mass values. Blank (white) spaces are non available values that for some reason were not measured.

As a pre-analysis procedure, significant bilateral asymmetries in each bone were investigated. This was carried out to determine if both sides of the skeleton had to be treated separately during statistical analysis. If differences from both sides were not substantial, then it would be possible to overcome the absence of a bone by replacing it by its antimere, if available. Bilateral asymmetry was investigated through a Wilcoxon signed ranks test. Also, relative directional asymmetry (%DA), which has been often used previously (Auerbach and Ruff, 2006), was calculated for each individual so that a better notion of asymmetry in a case by case basis could be attained.

The formula used was the following:

$$\%DA=\frac{M_R-M_L}{\frac{M_R+M_L}{2}}*100$$

where every M is an individual bone mass, while L and R are left and right side, respectively

Current Value:

Total skeleton mass, based on your input value is:

## Authors

David Gonçalves, João d'Oliveira Coelho, Maria A. Acosta, Catarina Coelho, Francisco Curate, Maria Teresa Ferreira, Márcia Gouveia, Calil Makhoul, David Navega, Débora Pinto, Inês Oliveira-Santos, Ana R. Vassalo, Eugénia Cunha.

Laboratory of Forensic Anthropology Life Sciences Department, University of Coimbra

## Data Analysis, App Development and Hosting

Osteomics (Instituto Pedro Nunes, Portugal)

## References

Auerbach BM, and Ruff CB. 2006. Limb bone bilateral asymmetry: variability and commonality among modern humans. Journal of Human Evolution 50:203-218.

Ferreira MT, Vicente R, Navega D, Gonçalves D, Curate F, and Cunha E. 2014. A new forensic collection housed at the University of Coimbra, Portugal: The 21st century identified skeletal collection. Forensic Science International 245:202.e201-202.e205.