Traditional studies exploring the interrelationships between growth and development traits have lacked the data necessary to fully describe the multivariate growth and development phenotype and the statistical methodology to quantify the complex interrelationships between varied trait types. Subsequently, human growth and development are often defined by a series of contrasts via the juxtaposition of seemingly disjoint processes in skeletal diaphyseal growth, skeletal ossification and fusion, and development of the dentition. In conjunction with robust data sources from the Subadult Virtual Anthropology Databases (SVAD), this work introduces a Mixed Discrete-Continuous Gaussian copula to explore the multivariate human growth and development phenotype. A copula is a probabilistic function that explicitly models the interrelationships between traits and describes the joint structure of the multivariate relationships.Fifty-four growth traits are collected from the United States sample in SVAD (n = 1,316). These traits include 18 measurements associated with diaphyseal dimensions collected from six long bones, 20 scores of both epiphyseal fusion and primary ossification centers, and 16 scores of dental development across the left-sided mandibular and maxillary dentition. All data are collected from computed tomography (CT) images and includes demographic information such as an individual’s chronological age and biological sex. The joint probability distribution of the 54 growth traits and the underlying dependency structure are fit to a Mixed Discrete-Continuous Gaussian copula using the gradient-based Markov Chain Monte Carlo algorithm known as Hamiltonian Monte Carlo within the Stan probabilistic programming environment. Six total copula models are fit: the first model utilizes the full dataset, the next three models use subsets of the full dataset representing the individual developmental stages of infancy, childhood, and juvenile/adolescence, and the last two models use subset of the full dataset representing biological males and females.Results from the full model show that relationships are strongest within each growth module. Further, traits that develop across similar developmental windows show stronger positive correlations as compared to traits that grow and develop during separate periods. These relationships are similar between males and females suggesting that, independent of age, multivariate growth and development processes are the same across the sexes. When considering developmental stages, the results show that the multivariate phenotype presents with different relationships between variables across ontogeny with the strongest relationships between growth and development modules tied to active growth and development periods. Importantly, the skeletal growth, skeletal development, and dental development modules can be further divided into additional units that themselves have various levels of dependence.The copula demonstrates that the relationships between broad growth modules cannot be summarized via a few pairwise correlations taken at one point during ontogeny. Instead, analyses should be conducted with as much trait information as possible and at various points throughout ontogeny. In the future, copulas could also be extended to additional applications in biological anthropology including research in bioarchaeology and paleoanthropology, method formation in forensic anthropology, and the estimation and imputation of missing data. In sum, the Mixed Discrete-Continuous Gaussian copula provides the most comprehensive analysis to date of the multivariate human growth and development phenotype and lays the groundwork for future research into the growing, developing, multivariate human
