A statistical procedure to map high-order epistasis for complex traits

High-order interactions distort the functional landscape of microbial consortia

Understanding the link between community composition and function is a major challenge in microbial population biology, with implications for the management of natural microbiomes and the design of synthetic consortia. Specifically, it is poorly understood whether community functions can be quantitatively predicted from traits of species in monoculture. Inspired by the study of complex genetic interactions, we have examined how the amylolytic rate of combinatorial assemblages of six starch-degrading soil bacteria depend on the separate functional contributions from each species and their interactions. Filtering our results through the theory of biochemical kinetics, we show that this simple function is additive in the absence of interactions among community members. For about half of the combinatorially assembled consortia, the amylolytic function is dominated by pairwise and higher-order interactions. For the other half, the function is additive despite the presence of strong competitive interactions. We explain the mechanistic basis of these findings and propose a quantitative framework that allows us to separate the effect of behavioral and population dynamics interactions. Our results suggest that the functional robustness of a consortium to pairwise and higher-order interactions critically affects our ability to predict and bottom-up engineer ecosystem function in complex communities.

High-order interactions distort the functional landscape of microbial consortia

Understanding the link between community composition and function is a major challenge in microbial population biology, with implications for the management of natural microbiomes and the design of synthetic consortia. Specifically, it is poorly understood whether community functions can be quantitatively predicted from traits of species in monoculture. Inspired by the study of complex genetic interactions, we have examined how the amylolytic rate of combinatorial assemblages of six starch-degrading soil bacteria depend on the separate functional contributions from each species and their interactions. Filtering our results through the theory of biochemical kinetics, we show that this simple function is additive in the absence of interactions among community members. For about half of the combinatorially assembled consortia, the amylolytic function is dominated by pairwise and higher-order interactions. For the other half, the function is additive despite the presence of strong competitive interactions. We explain the mechanistic basis of these findings and propose a quantitative framework that allows us to separate the effect of behavioral and population dynamics interactions. Our results suggest that the functional robustness of a consortium to pairwise and higher-order interactions critically affects our ability to predict and bottom-up engineer ecosystem function in complex communities.

Mapping Covariation Quantitative Trait Loci That Control Organ Growth and Whole-Plant Biomass

Covariation between organ growth and biomass accumulation plays an important role in plants. Plant to capture optimal fitness in nature, which depend coordinate and interact for distinct organs such as leaves, stems, and roots. Although many studies have focused on plant growth or biomass allocation, detailed information on the genetic mechanism of coordinated variation is lacking. Here, we expand a new mapping model based on functional mapping to detect covariation quantitative trait loci (QTLs) that govern development of plant organs and whole biomass, which, via a series of hypothesis tests, allows quantification of how QTLs regulate covariation between organ growth and biomass accumulation. The model was implemented to analyze leaf number data and the whole dry weight of recombinant inbred lines (RILs) of Arabidopsis. Two key QTLs related to growth and biomass allocation that reside within biologically meaningful genes, CRA1 and HIPP25, are characterized. These two genes may control covariation between two traits. The new model will enable the elucidation of the genetic architecture underlying growth and biomass accumulation, which may enhance our understanding of fitness development in plants.

Evolutionary footprint of epistasis

Variation of an inherited trait across a population cannot be explained by additive contributions of relevant genes, due to epigenetic effects and biochemical interactions (epistasis). Detecting epistasis in genomic data still represents a significant challenge that requires a better understanding of epistasis from the mechanistic point of view. Using a standard Wright-Fisher model of bi-allelic asexual population, we study how compensatory epistasis affects the process of adaptation. The main result is a universal relationship between four haplotype frequencies of a single site pair in a genome, which depends only on the epistasis strength of the pair defined regarding Darwinian fitness. We demonstrate the existence, at any time point, of a quasi-equilibrium between epistasis and disorder (entropy) caused by random genetic drift and mutation. We verify the accuracy of these analytic results by Monte-Carlo simulation over a broad range of parameters, including the topology of the interacting network. Thus, epistasis assists the evolutionary transit through evolutionary hurdles leaving marks at the level of haplotype disequilibrium. The method allows determining selection coefficient for each site and the epistasis strength of each pair from a sequence set. The resulting ability to detect clusters of deleterious mutation close to full compensation is essential for biomedical applications. These findings help to understand the role of epistasis in multiple compensatory mutations in viral resistance to antivirals and immune response.

An Ultrahigh-Dimensional Mapping Model of High-order Epistatic Networks for Complex Traits

BACKGROUND

Genetic interactions involving more than two loci have been thought to affect quantitatively inherited traits and diseases more pervasively than previously appreciated. However, the detection of such high-order interactions to chart a complete portrait of genetic architecture has not been well explored.

METHODS

We present an ultrahigh-dimensional model to systematically characterize genetic main effects and interaction effects of various orders among all possible markers in a genetic mapping or association study. The model was built on the extension of a variable selection procedure, called iFORM, derived from forward selection. The model shows its unique power to estimate the magnitudes and signs of high-order epistatic effects, in addition to those of main effects and pairwise epistatic effects.

RESULTS

The statistical properties of the model were tested and validated through simulation studies. By analyzing a real data for shoot growth in a mapping population of woody plant, mei (Prunus mume), we demonstrated the usefulness and utility of the model in practical genetic studies. The model has identified important high-order interactions that contribute to shoot growth for mei.

CONCLUSION

The model provides a tool to precisely construct genotype-phenotype maps for quantitative traits by identifying any possible high-order epistasis which is often ignored in the current genetic literature.

iFORM/eQTL: an ultrahigh-dimensional platform for inferring the global genetic architecture of gene transcripts

Knowledge about how changes in gene expression are encoded by expression quantitative trait loci (eQTLs) is a key to construct the genotype-phenotype map for complex traits or diseases. Traditional eQTL mapping is to associate one transcript with a single marker at a time, thereby limiting our inference about a complete picture of the genetic architecture of gene expression. Here, we implemented an ultrahigh-dimensional variable selection model to build a computing platform that can systematically scan main effects and interaction effects among all possible loci and identify a set of significant eQTLs modulating differentiation and function of gene expression. This platform, named iFORM/eQTL, was assembled by forward-selection-based procedures to tackle complex covariance structures of gene-gene interactions. iFORM/eQTL can particularly discern the role of cis-QTLs, trans-QTLs and their epistatic interactions in gene expression. Results from the reanalysis of a published genetic and genomic data set through iFORM/eQTL gain new discoveries on the genetic origin of gene expression differentiation in Caenorhabditis elegans, which could not be detected by a traditional one-locus/one-transcript analysis approach.

Evo-Devo-EpiR: a genome-wide search platform for epistatic control on the evolution of development

Evo-devo is a theory proposed to study how phenotypes evolve by comparing the developmental processes of different organisms or the same organism experiencing changing environments. It has been recognized that nonallelic interactions at different genes or quantitative trait loci, known as epistasis, may play a pivotal role in the evolution of development, but it has proven difficult to quantify and elucidate this role into a coherent picture. We implement a high-dimensional genome-wide association study model into the evo-devo paradigm and pack it into the R-based Evo-Devo-EpiR, aimed at facilitating the genome-wide landscaping of epistasis for the diversification of phenotypic development. By analyzing a high-throughput assay of DNA markers and their pairs simultaneously, Evo-Devo-EpiR is equipped with a capacity to systematically characterize various epistatic interactions that impact on the pattern and timing of development and its evolution. Enabling a global search for all possible genetic interactions for developmental processes throughout the whole genome, Evo-Devo-EpiR provides a computational tool to illustrate a precise genotype-phenotype map at interface between epistasis, development and evolution.

Detecting epistasis in human complex traits

Genome-wide association studies (GWASs) have become the focus of the statistical analysis of complex traits in humans, successfully shedding light on several aspects of genetic architecture and biological aetiology. Single-nucleotide polymorphisms (SNPs) are usually modelled as having additive, cumulative and independent effects on the phenotype. Although evidently a useful approach, it is often argued that this is not a realistic biological model and that epistasis (that is, the statistical interaction between SNPs) should be included. The purpose of this Review is to summarize recent directions in methodology for detecting epistasis and to discuss evidence of the role of epistasis in human complex trait variation. We also discuss the relevance of epistasis in the context of GWASs and potential hazards in the interpretation of statistical interaction terms.

Structural mapping: how to study the genetic architecture of a phenotypic trait through its formation mechanism

Traditional approaches for genetic mapping are to simply associate the genotypes of a quantitative trait locus (QTL) with the phenotypic variation of a complex trait. A more mechanistic strategy has emerged to dissect the trait phenotype into its structural components and map specific QTLs that control the mechanistic and structural formation of a complex trait. We describe and assess such a strategy, called structural mapping, by integrating the internal structural basis of trait formation into a QTL mapping framework. Electrical impedance spectroscopy (EIS) has been instrumental for describing the structural components of a phenotypic trait and their interactions. By building robust mathematical models on circuit EIS data and embedding these models within a mixture model-based likelihood for QTL mapping, structural mapping implements the EM algorithm to obtain maximum likelihood estimates of QTL genotype-specific EIS parameters. The uniqueness of structural mapping is to make it possible to test a number of hypotheses about the pattern of the genetic control of structural components. We validated structural mapping by analyzing an EIS data collected for QTL mapping of frost hardiness in a controlled cross of jujube trees. The statistical properties of parameter estimates were examined by simulation studies. Structural mapping can be a powerful alternative for genetic mapping of complex traits by taking account into the biological and physical mechanisms underlying their formation.