# Correlation Measures in Metagenomic Data: The Blessing of Dimensionality
###### Abstract  
Microbiome analysis has revolutionized our understanding of various biological processes, spanning human health and epidemiology (including antimicrobial resistance and horizontal gene transfer), as well as environmental and agricultural studies. At the heart of microbiome analysis lies the characterization of microbial communities through the quantification of microbial taxa and their dynamics. In the study of bacterial abundances, it is becoming more relevant to consider their relationship, to embed these data in the framework of network theory, allowing characterization of features like node relevance, pathways, and community structure. In this study, we address the primary biases encountered in reconstructing networks through correlation measures, particularly in light of the compositional nature of the data, within-sample diversity, and the presence of a high number of unobserved species. These factors can lead to inaccurate correlation estimates. To tackle these challenges, we employ simulated data to demonstrate how many of these issues can be mitigated by applying typical transformations designed for compositional data. These transformations enable the use of straightforward measures like Pearson's correlation to correctly identify positive and negative relationships among relative abundances, especially in high-dimensional data, without having any need for further corrections. However, some challenges persist, such as addressing data sparsity, as neglecting this aspect can result in an underestimation of negative correlations. microbiome analysis; metagenomics; correlation; compositional data; data sparsity; second order statistics 20251586022025158602 by the relationships among the observed species. Network theory provides many essential tools to characterize collective properties of the ecology of a natural environment by defining central elements or communities in the system and allowing visualization of these results by exploiting network structural properties [4]. Consequently, the initial step in reconstructing any network involves the identification and quantification of relationships between species, often achieved by assessing correlations or conditional dependencies among each pairwise combination of variables. In this study, we specifically focus on marginal correlations rather than partial correlations. Although partial correlations are a powerful tool for network reconstruction, by explicitly removing indirect associations, they complicate the direct assessment and interpretation of the biases introduced by compositionality and sparsity. Marginal correlations, being simpler and more straightforward, allow a clearer analysis of these biases, which are expected to similarly affect partial correlations. Independent from the NGS techniques used like RNA-seq, 16s, or whole-genome shotgun, the underlying data are similar, composed of counts of sequencing reads mapped to a large number of references (taxa), and the unifying theoretical framework is their compositional nature [5; 6]. Taxa abundance is determined by the number of read counts, which is affected by sequencing depth and varies from sample to sample. Typically, a sum constraint is imposed over all the samples (1 for probability, 100 for percentage, or \(10^{6}\) for part per million) called L1 normalization, to remove the effect of sample depth. In this way, data are described as proportions and referred to as compositional data [7]. However, as noted by [PERSON] at the end of the 19 th century, compositional data can generate spurious correlations between measurements [8]. From a mathematical point of view, the data lie on a simplex [9]; thus, it can be extremely dangerous to use Euclidean metrics for proximity and correlation estimations in a non-Euclidean context. These biases on correlation between relative abundances can be significant in some datasets but mild in others [Figure 1], and the diversity within each sample, called \(\alpha\)-diversity, concurs to enforce this bias [10].