Purkait’s Triangle Revisited: Role in Sex and Ancestry Estimation
Authors: Attia MennattAllah Hassan , Attia Mohamed Hassan , Farghaly Yasmin Tarek , Abulnoor Bassam Ahmed El-Sayed , Manolis Sotiris K. , Purkait Ruma , Ubelaker Douglas H. 
Published: February 2022

Identification of unknown remains recovered from marine and terrestrial locations is a significant humanitarian problem. This investigation proposes a simple method applicable to fragmentary femora for a more refined level of ancestry and/or sex estimation. To that end, we re-examined Purkait’s triangle which involves three inter-landmark distances between the traction epiphyses and the articular rim of femoral head. A large sample (n = 584) from geographically diverse (Egyptian, Indian and Greek) populations was compiled. Additionally, shape (n = 3) and trigonometrically derived variables and ratios (n = 9 variables) were employed to detect any geographically-clustered morphological differences between these populations. Random forest modelling (RFM) and linear discriminant function analysis (LDA) were employed to create classification models in instances where sex was known or unknown. The sample was apportioned into training and test sets with a ratio 70/30. The classification accuracies were evaluated by means of k fold cross-validation procedure. In sex estimation, RFM showed similar performance to LDA. However, RFM outperformed LDA in ancestry estimation. Ancestry estimation was satisfactory in the Indian and Egyptian samples albeit the Greek sample was problematic. The Greek samples presented greater morphological overlap with the Indian sample due to high within-group variation. Test samples were accurately assigned to their ancestral category when sex was known. Generally, higher classification accuracies in the validation sample were obtained in the sex-specific model of females than in males. Using RFM and the linear variables, the overall accuracy reached 83% which is distributed as 95%, 71% and 86% for the Egyptian, Indian and Greek females, respectively; whereas in males, the overall accuracy is 72% and is distributed as 58%, 87% and 50% for the Egyptian, Indian and Greek males, respectively. Classification accuracies were also calculated per group in the test data using the 12 derived variables. For the females, the accuracies using the medians model was comparable to the linear model whereas in males the angles model outperformed the linear model for each group but with similar overall accuracy. The classification rates of male specific ancestry were 82%, 78% and 56% for the Egyptian, Indian and Greek males, respectively. In conclusion, Purkait’s triangle has potential utility in ancestry and sex estimation albeit it is not possible to separate all groups successfully with the same efficiency. Intrapopulation variation may impact the accuracy of assigned group membership in forensic contexts. Key PointsPurkait’s method is a possible ancestry group indicator applicable to fragmentary femora.Random forest model surpassed linear discriminant function analysis in multi-group ancestry classification.Ancestry is more accurately assessed in females than males.The intertrochanteric distance is the most important feature in discrimination of sex whereas in ancestry it was the head to lesser trochanter distance.Sex differences override ancestry due to the tendency of misclassification into same sex but different group rather than the opposite sex of the same ancestry.