Computing the nonnull asymptotic variance and the asymptotic relative efficiency of Spearman's rank correlation

Correlation and association analyses in microbiome study integrating multiomics in health and disease

Correlation and association analyses are one of the most widely used statistical methods in research fields, including microbiome and integrative multiomics studies. Correlation and association have two implications: dependence and co-occurrence. Microbiome data are structured as phylogenetic tree and have several unique characteristics, including high dimensionality, compositionality, sparsity with excess zeros, and heterogeneity. These unique characteristics cause several statistical issues when analyzing microbiome data and integrating multiomics data, such as large p and small n, dependency, overdispersion, and zero-inflation. In microbiome research, on the one hand, classic correlation and association methods are still applied in real studies and used for the development of new methods; on the other hand, new methods have been developed to target statistical issues arising from unique characteristics of microbiome data. Here, we first provide a comprehensive view of classic and newly developed univariate correlation and association-based methods. We discuss the appropriateness and limitations of using classic methods and demonstrate how the newly developed methods mitigate the issues of microbiome data. Second, we emphasize that concepts of correlation and association analyses have been shifted by introducing network analysis, microbe-metabolite interactions, functional analysis, etc. Third, we introduce multivariate correlation and association-based methods, which are organized by the categories of exploratory, interpretive, and discriminatory analyses and classification methods. Fourth, we focus on the hypothesis testing of univariate and multivariate regression-based association methods, including alpha and beta diversities-based, count-based, and relative abundance (or compositional)-based association analyses. We demonstrate the characteristics and limitations of each approaches. Fifth, we introduce two specific microbiome-based methods: phylogenetic tree-based association analysis and testing for survival outcomes. Sixth, we provide an overall view of longitudinal methods in analysis of microbiome and omics data, which cover standard, static, regression-based time series methods, principal trend analysis, and newly developed univariate overdispersed and zero-inflated as well as multivariate distance/kernel-based longitudinal models. Finally, we comment on current association analysis and future direction of association analysis in microbiome and multiomics studies.

Population models and simulation methods: The case of the Spearman rank correlation

The purpose of this paper is to highlight the importance of a population model in guiding the design and interpretation of simulation studies used to investigate the Spearman rank correlation. The Spearman rank correlation has been known for over a hundred years to applied researchers and methodologists alike and is one of the most widely used non-parametric statistics. Still, certain misconceptions can be found, either explicitly or implicitly, in the published literature because a population definition for this statistic is rarely discussed within the social and behavioural sciences. By relying on copula distribution theory, a population model is presented for the Spearman rank correlation, and its properties are explored both theoretically and in a simulation study. Through the use of the Iman-Conover algorithm (which allows the user to specify the rank correlation as a population parameter), simulation studies from previously published articles are explored, and it is found that many of the conclusions purported in them regarding the nature of the Spearman correlation would change if the data-generation mechanism better matched the simulation design. More specifically, issues such as small sample bias and lack of power of the t-test and r-to-z Fisher transformation disappear when the rank correlation is calculated from data sampled where the rank correlation is the population parameter. A proof for the consistency of the sample estimate of the rank correlation is shown as well as the flexibility of the copula model to encompass results previously published in the mathematical literature.

Unraveling Core Functional Microbiota in Traditional Solid-State Fermentation by High-Throughput Amplicons and Metatranscriptomics Sequencing

Fermentation microbiota is specific microorganisms that generate different types of metabolites in many productions. In traditional solid-state fermentation, the structural composition and functional capacity of the core microbiota determine the quality and quantity of products. As a typical example of food fermentation, Chinese Maotai-flavor liquor production involves a complex of various microorganisms and a wide variety of metabolites. However, the microbial succession and functional shift of the core microbiota in this traditional food fermentation remain unclear. Here, high-throughput amplicons (16S rRNA gene amplicon sequencing and internal transcribed space amplicon sequencing) and metatranscriptomics sequencing technologies were combined to reveal the structure and function of the core microbiota in Chinese soy sauce aroma type liquor production. In addition, ultra-performance liquid chromatography and headspace-solid phase microextraction-gas chromatography-mass spectrometry were employed to provide qualitative and quantitative analysis of the major flavor metabolites. A total of 10 fungal and 11 bacterial genera were identified as the core microbiota. In addition, metatranscriptomic analysis revealed pyruvate metabolism in yeasts (genera Pichia, Schizosaccharomyces, Saccharomyces, and Zygosaccharomyces) and lactic acid bacteria (genus Lactobacillus) classified into two stages in the production of flavor components. Stage I involved high-level alcohol (ethanol) production, with the genus Schizosaccharomyces serving as the core functional microorganism. Stage II involved high-level acid (lactic acid and acetic acid) production, with the genus Lactobacillus serving as the core functional microorganism. The functional shift from the genus Schizosaccharomyces to the genus Lactobacillus drives flavor component conversion from alcohol (ethanol) to acid (lactic acid and acetic acid) in Chinese Maotai-flavor liquor production. Our findings provide insight into the effects of the core functional microbiota in soy sauce aroma type liquor production and the characteristics of the fermentation microbiota under different environmental conditions.

Coincidence of variation in potato yield and climate in northern China

Understanding the effects of climate change on crops is vital for food security. We aimed to characterise the coincidence of yield variations with weather variable for potato in northern China using long-term datasets. Daily climate variables obtained from 607 meteorological stations from 1961 to 2014, detailed field experimental data for the period of 1982 to 2012 in northern China, and multivariate linear statistical model were used in this study. In particular, the first difference method was used to disentangle the contributions of climate change to potato yield. We concluded that during the potato growing, the average daily, maximum and minimum temperatures significantly increased by 0.23°C per decade, 0.20°C per decade and 0.36°C per decade from 1961 to 2014 in northern China, respectively. However, average total radiation, total annual precipitation and potential evapotranspiration from April to September all exhibited downward trends, but the variation of evapotranspiration (-9.99mm per decade) was greater than that of precipitation (-2.65mm per decade). The key climatic factors limiting potato yields in northern China over the past 30years at a regional scale were diurnal temperature range, precipitation, radiation and ET₀. The potato yield in northern China was the most sensitive to variation of the diurnal temperature range followed by radiation, precipitation and reference crop evapotranspiration (ET₀). Specifically, when the diurnal temperature range decreased 1°C, the potato yield increased 543.9kg·ha^-1. When the total radiation decreased 1MJ·m², the potato yield increased 63.8kg·ha^-1. When the ET₀ decreased 1mm, the potato yield increased 62.7kg·ha^-1. When the precipitation increased 1mm, the potato yield increased 62.9kg·ha^-1. A regression model describing the combined effects of different climate variables on potato yield in northern China was established.

Building damage-resilient dominating sets in complex networks against random and targeted attacks

We study the vulnerability of dominating sets against random and targeted node removals in complex networks. While small, cost-efficient dominating sets play a significant role in controllability and observability of these networks, a fixed and intact network structure is always implicitly assumed. We find that cost-efficiency of dominating sets optimized for small size alone comes at a price of being vulnerable to damage; domination in the remaining network can be severely disrupted, even if a small fraction of dominator nodes are lost. We develop two new methods for finding flexible dominating sets, allowing either adjustable overall resilience, or dominating set size, while maximizing the dominated fraction of the remaining network after the attack. We analyze the efficiency of each method on synthetic scale-free networks, as well as real complex networks.

Uncovering disassortativity in large scale-free networks

Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, and social and biological networks, are often characterized by degree-degree dependencies between neighboring nodes. In this paper, we propose a new way of measuring degree-degree dependencies. One of the problems with the commonly used assortativity coefficient is that in disassortative networks its magnitude decreases with the network size. We mathematically explain this phenomenon and validate the results on synthetic graphs and real-world network data. As an alternative, we suggest to use rank correlation measures such as Spearman's ρ. Our experiments convincingly show that Spearman's ρ produces consistent values in graphs of different sizes but similar structure, and it is able to reveal strong (positive or negative) dependencies in large graphs. In particular, we discover much stronger negative degree-degree dependencies in Web graphs than was previously thought. Rank correlations allow us to compare the assortativity of networks of different sizes, which is impossible with the assortativity coefficient due to its genuine dependence on the network size. We conclude that rank correlations provide a suitable and informative method for uncovering network mixing patterns.