An active area of research interest is the inference of ecological models of complex microbial communities. Inferring such ecological models entails understanding the interactions between microbes and how they affect each other's growth. This dissertation employs a statistical perspective to contribute further to the knowledge currently addressing this problem. Part I explains how high-throughput droplet-based microfluidics technology can be used to screen for microbial interactions. An explicit, statistical framework is motivated and developed that can guide the analysis of data from such experiments. Part II explains how it might be possible to predict, based on the experimental setup, how much data will be produced to infer given microbial interactions. Running the experiment once without incubating the droplets turns out to be necessary to make such predictions. Part III demonstrates the feasibility of inferring microbial interactions from the data produced by these experiments. Relevant ideas from the microbiological and ecological literature are recast into an explicit, statistical framework.
High throughput sequencing (HTS) continues to expand our understanding of microbial communities, despite insufficient sequencing depths to detect all rare taxa. These low abundance taxa are not accounted for in existing methods for detecting changes in species richness. We address this with a new hierarchical model that permits rigorous testing for both heterogeneity and biodiversity changes, and simultaneously improves Type I & II error rates compared to existing methods.
High throughput sequencing (HTS)-based technology enables identifying and quantifying non-culturable microbial organisms in all environments. Microbial sequences have enhanced our understanding of the human microbiome, the soil and plant environment, and the marine environment. All molecular microbial data pose statistical challenges due to contamination sequences from reagents, batch effects, unequal sampling, and undetected taxa. Technical biases and heteroscedasticity have the strongest effects, but different strains across subjects and environments also make direct differential abundance t…
In microbial studies, samples are often treated under different experimental conditions and then tested for microbial survival. A technique, dating back to the 1880's, consists of diluting the samples several times and incubating each dilution to verify the existence of microbial Colony Forming Units or CFU's, seen by the naked eye. The main problem in the dilution series data analysis is the uncertainty quantification of the simple point estimate of the original number of CFU's in the sample (i.e., at dilution zero). Common approaches such as log-normal or Poisson models do not seem to handle…
16S-ribosomal sequencing and other metagonomic techniques provide snapshots of microbial communities, revealing phylogeny and the abundances of microbial populations across diverse ecosystems. While changes in microbial community structure are demonstrably associated with certain environmental conditions, identification of underlying mechanisms requires new statistical tools, as these datasets present several technical challenges. First, the abundances of microbial operational taxonomic units (OTUs) from 16S datasets are compositional, and thus, microbial abundances are not independent. Second…
By creating networks of biochemical pathways, communities of micro-organisms are able to modulate the properties of their environment and even the metabolic processes within their hosts. Next-generation high-throughput sequencing has led to a new frontier in microbial ecology, promising the ability to leverage the microbiome to make crucial advancements in the environmental and biomedical sciences. However, this is challenging, as genomic data are high-dimensional, sparse, and noisy. Much of this noise reflects the exact conditions under which sequencing took place, and is so significant that …
Microbes can affect processes from food production to human health. Such microbes are not isolated, but rather interact with each other and establish connections with their living environments. Understanding these interactions is essential to an understanding of the organization and complex interplay of microbial communities, as well as the structure and dynamics of various ecosystems. A common and essential approach toward this objective involves the inference of microbiome interaction networks. Although network inference methods in other fields have been studied before, applying these method…
Microbial ecology serves as a foundation for a wide range of scientific and biomedical studies. Rapidly-evolving high-throughput sequencing technology enables the comprehensive search for microbial biomarkers using longitudinal experiments. Such experiments consist of repeated biological observations from each subject over time and are essential in accounting for the high between-subject and within-subject variability. Unfortunately, many of the statistical tests based on parametric models rely on correctly specifying temporal dependence structure which is unavailable in most microbiome data. …
Microbiome data analyses require statistical tools that can simultaneously decode microbes' reactions to the environment and interactions among microbes. We introduce CARlasso, the first user-friendly open-source and publicly available R package to fit a chain graph model for the inference of sparse microbial networks that represent both interactions among nodes and effects of a set of predictors. Unlike in standard regression approaches, the edges represent the correct conditional structure among responses and predictors that allows the incorporation of prior knowledge from controlled experim…
Microbiome data require statistical models that can simultaneously decode microbes' reaction to the environment and interactions among microbes. While a multiresponse linear regression model seems like a straight-forward solution, we argue that treating it as a graphical model is flawed given that the regression coefficient matrix does not encode the conditional dependence structure between response and predictor nodes as it does not represent the adjacency matrix. This observation is especially important in biological settings when we have prior knowledge on the edges from specific experiment…
Many biological high-throughput data sets, such as targeted amplicon-based and metagenomic sequencing data, are compositional in nature. A common exploratory data analysis task is to infer statistical associations between the high-dimensional microbial compositions and habitat- or host-related covariates. We propose a general robust statistical regression framework, RobRegCC (Robust Regression with Compositional Covariates), which extends the linear log-contrast model by a mean shift formulation for capturing outliers. RobRegCC includes sparsity-promoting convex and non-convex penalties for pa…
Monod's model describes the growth of microorganisms using a hyperbolic function of extracellular resource concentration. Under fluctuating or limited resource concentrations this model performs poorly against experimental data, motivating the more complex Droop model with a time-varying internal storage pool. We extend the Monod model to incorporate memory of past conditions, adding a single parameter motivated by a fractional calculus analysis. We show how to interpret the memory element in a biological context and describe its connection to a resource storage pool. Under nitrogen starvation…
Microbiota contribute to many dimensions of host phenotype, including disease. To link specific microbes to specific phenotypes, microbiome-wide association studies compare microbial abundances between two groups of samples. Abundance differences, however, reflect not only direct associations with the phenotype, but also indirect effects due to microbial interactions. We found that microbial interactions could easily generate a large number of spurious associations that provide no mechanistic insight. Using techniques from statistical physics, we developed a method to remove indirect associati…
Identifying genetic interactions for a given microorganism such as yeast is difficult. Quantitative Fitness Analysis (QFA) is a high-throughput experimental and computational methodology for quantifying the fitness of microbial cultures. QFA can be used to compare between fitness observations for different genotypes and thereby infer genetic interaction strengths. Current "naive" frequentist statistical approaches used in QFA do not model between-genotype variation or difference in genotype variation under different conditions. In this thesis, a Bayesian approach is introduced to evaluate hier…
Testing Microbiome Community Differences in High Dimensions: A Bootstrap Approach for Compositional Data
Indian Institute of Technology Bombay（印度理工学院孟买分校）；Missouri University of Science and Technology（密苏里科技大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；University of Missouri（密苏里大学）；University of Michigan（密歇根大学）
Quantitative Fitness Analysis (QFA) is a high-throughput experimental and computational methodology for measuring the growth of microbial populations. QFA screens can be used to compare the health of cell populations with and without a mutation in a query gene in order to infer genetic interaction strengths genome-wide, examining thousands of separate genotypes. We introduce Bayesian, hierarchical models of population growth rates and genetic interactions that better reflect QFA experimental design than current approaches. Our new approach models population dynamics and genetic interaction sim…
Quantifying the relation between gut microbiome and body weight can provide insights into personalized strategies for improving digestive health. In this paper, we present an algorithm that predicts weight fluctuations using gut microbiome in a healthy cohort of newborns from a previously published dataset. Microbial data has been known to present unique statistical challenges that defy most conventional models. We propose a mixed effect Dirichlet-tree multinomial (DTM) model to untangle these difficulties as well as incorporate covariate information and account for species relatedness. The DT…
We report new statistical time-series analysis tools providing significant improvements in the rapid, precision extraction of discrete state dynamics from large databases of experimental observations of molecular machines. By building physical knowledge and statistical innovations into analysis tools, we demonstrate new techniques for recovering discrete state transitions buried in highly correlated molecular noise. We demonstrate the effectiveness of our approach on simulated and real examples of step-like rotation of the bacterial flagellar motor and the F1-ATPase enzyme. We show that our me…
High-throughput screening (HTS) is a large-scale hierarchical process in which a large number of chemicals are tested in multiple stages. Conventional statistical analyses of HTS studies often suffer from high testing error rates and soaring costs in large-scale settings. This article develops new methodologies for false discovery rate control and optimal design in HTS studies. We propose a two-stage procedure that determines the optimal numbers of replicates at different screening stages while simultaneously controlling the false discovery rate in the confirmatory stage subject to a constrain…
Background: We study the statistical properties of fragment coverage in genome sequencing experiments. In an extension of the classic Lander-Waterman model, we consider the effect of the length distribution of fragments. We also introduce the notion of the shape of a coverage function, which can be used to detect abberations in coverage. The probability theory underlying these problems is essential for constructing models of current high-throughput sequencing experiments, where both sample preparation protocols and sequencing technology particulars can affect fragment length distributions. Res…
