Quantitative trait locus analysis of stage-specific inbreeding depression in the Pacific oyster Crassostrea gigas

Inbreeding depression and genetic load have been widely observed, but their genetic basis and effects on fitness during the life cycle remain poorly understood, especially for marine animals with high fecundity and high, early mortality (type-III survivorship). A high load of recessive mutations was previously inferred for the Pacific oyster Crassostrea gigas, from massive distortions of zygotic, marker segregation ratios in F(2) families. However, the number, genomic location, and stage-specific onset of mutations affecting viability have not been thoroughly investigated. Here, we again report massive distortions of microsatellite-marker segregation ratios in two F(2) hybrid families, but we now locate the causative deleterious mutations, using a quantitative trait locus (QTL) interval-mapping model, and we characterize their mode of gene action. We find 14-15 viability QTL (vQTL) in the two families. Genotypic frequencies at vQTL generally suggest selection against recessive or partially recessive alleles, supporting the dominance theory of inbreeding depression. No epistasis was detected among vQTL, so unlinked vQTL presumably have independent effects on survival. For the first time, we track segregation ratios of vQTL-linked markers through the life cycle, to determine their stage-specific expression. Almost all vQTL are absent in the earliest life stages examined, confirming zygotic viability selection; vQTL are predominantly expressed before the juvenile stage (90%), mostly at metamorphosis (50%). We estimate that, altogether, selection on vQTL caused 96% mortality in these families, accounting for nearly all of the actual mortality. Thus, genetic load causes substantial mortality in inbred Pacific oysters, particularly during metamorphosis, a critical developmental transition warranting further investigation.     

Mapping quantitative trait loci with censored observations

The existing statistical methods for mapping quantitative trait loci (QTL) assume that the phenotype follows a normal distribution and is fully observed. These assumptions may not be satisfied when the phenotype pertains to the survival time or failure time, which has a skewed distribution and is usually subject to censoring due to random loss of follow-up or limited duration of the experiment. In this article, we propose an interval-mapping approach for censored failure time phenotypes. We formulate the effects of QTL on the failure time through parametric proportional hazards models and develop efficient likelihood-based inference procedures. In addition, we show how to assess genome-wide statistical significance. The performance of the proposed methods is evaluated through extensive simulation studies. An application to a mouse cross is provided.     

Quantitative trait locus mapping using human pedigrees

In the past decade phenomenal progress has been made in molecular and statistical genetic methods for localizing quantitative trait loci. Because of these advances, we can anticipate a long period of active genetic research in which the genes influencing human quantitative variability will be mapped and their effects accurately evaluated. Here, we review the current state of the science in statistical genetic methods for quantitative trait linkage analysis. In particular, we detail a variance component-based framework for localizing quantitative trait loci and for accurately estimating their relative effect sizes. Attention is paid to the optimal design of human family studies for localizing genes of small to moderate effect. In addition, methods and strategies are described for dealing with the most important complications of quantitative variation, including the assessment of genotype x environment interaction and epistasis.     

A Novel Targeted Learning Method for Quantitative Trait Loci Mapping

We present a novel semiparametric method for quantitative trait loci (QTL) mapping in experimental crosses. Conventional genetic mapping methods typically assume parametric models with Gaussian errors and obtain parameter estimates through maximum-likelihood estimation. In contrast with univariate regression and interval-mapping methods, our model requires fewer assumptions and also accommodates various machine-learning algorithms. Estimation is performed with targeted maximum-likelihood learning methods. We demonstrate our semiparametric targeted learning approach in a simulation study and a well-studied barley data set.     

Evidence for a novel late-onset Alzheimer disease locus on chromosome 19p13.2

Late-onset familial Alzheimer disease (LOFAD) is a genetically heterogeneous and complex disease for which only one locus, APOE, has been definitively identified. Difficulties in identifying additional loci are likely to stem from inadequate linkage analysis methods. Nonparametric methods suffer from low power because of limited use of the data, and traditional parametric methods suffer from limitations in the complexity of the genetic model that can be feasibly used in analysis. Alternative methods that have recently been developed include Bayesian Markov chain-Monte Carlo methods. These methods allow multipoint linkage analysis under oligogenic trait models in pedigrees of arbitrary size; at the same time, they allow for inclusion of covariates in the analysis. We applied this approach to an analysis of LOFAD on five chromosomes with previous reports of linkage. We identified strong evidence of a second LOFAD gene on chromosome 19p13.2, which is distinct from APOE on 19q. We also obtained weak evidence of linkage to chromosome 10 at the same location as a previous report of linkage but found no evidence for linkage of LOFAD age-at-onset loci to chromosomes 9, 12, or 21.     

Model choice in gene mapping: what and why

The choice of an appropriate genetic model describing the genetic architecture underlying a character of interest is an inherent part of the gene mapping studies of human and other living organisms. The genetic model specifies the statistical parameters for the number of genes, their positions, and the types and magnitudes of their contributions to the phenotype. There are many considerations involved in model formulation (choice) ranging from the assumptions concerning the data, the role of environment, and the number of oligogenes (or quantitative trait loci) influencing the trait behavior. There are several model selection procedures and criteria under specific sampling designs in the genetic literature. These approaches often have their origin in computer science or in general statistical theory. Our aim here is to give an overview of the most popular statistical criteria and to present principles behind them. Bayesian model averaging is suggested as a robust alternative for such methods.     

Polygenic score accuracy in ancient samples: Quantifying the effects of allelic turnover

Polygenic scores link the genotypes of ancient individuals to their phenotypes, which are often unobservable, offering a tantalizing opportunity to reconstruct complex trait evolution. In practice, however, interpretation of ancient polygenic scores is subject to numerous assumptions. For one, the genome-wide association (GWA) studies from which polygenic scores are derived, can only estimate effect sizes for loci segregating in contemporary populations. Therefore, a GWA study may not correctly identify all loci relevant to trait variation in the ancient population. In addition, the frequencies of trait-associated loci may have changed in the intervening years. Here, we devise a theoretical framework to quantify the effect of this allelic turnover on the statistical properties of polygenic scores as functions of population genetic dynamics, trait architecture, power to detect significant loci, and the age of the ancient sample. We model the allele frequencies of loci underlying trait variation using the Wright-Fisher diffusion, and employ the spectral representation of its transition density to find analytical expressions for several error metrics, including the expected sample correlation between the polygenic scores of ancient individuals and their true phenotypes, referred to as polygenic score accuracy. Our theory also applies to a two-population scenario and demonstrates that allelic turnover alone may explain a substantial percentage of the reduced accuracy observed in cross-population predictions, akin to those performed in human genetics. Finally, we use simulations to explore the effects of recent directional selection, a bias-inducing process, on the statistics of interest. We find that even in the presence of bias, weak selection induces minimal deviations from our neutral expectations for the decay of polygenic score accuracy. By quantifying the limitations of polygenic scores in an explicit evolutionary context, our work lays the foundation for the development of more sophisticated statistical procedures to analyze both temporally and geographically resolved polygenic scores.     

Statistical optimization of parametric accelerated failure time model for mapping survival trait loci

Most existing statistical methods for mapping quantitative trait loci (QTL) are not suitable for analyzing survival traits with a skewed distribution and censoring mechanism. As a result, researchers incorporate parametric and semi-parametric models of survival analysis into the framework of the interval mapping for QTL controlling survival traits. In survival analysis, accelerated failure time (AFT) model is considered as a de facto standard and fundamental model for data analysis. Based on AFT model, we propose a parametric approach for mapping survival traits using the EM algorithm to obtain the maximum likelihood estimates of the parameters. Also, with Bayesian information criterion (BIC) as a model selection criterion, an optimal mapping model is constructed by choosing specific error distributions with maximum likelihood and parsimonious parameters. Two real datasets were analyzed by our proposed method for illustration. The results show that among the five commonly used survival distributions, Weibull distribution is the optimal survival function for mapping of heading time in rice, while Log-logistic distribution is the optimal one for hyperoxic acute lung injury.     

How to model a complex trait. 1. General considerations and suggestions

Usually, when complex traits are at issue, not only are the loci of the responsible genes a priori unknown; the same also holds for the mode of inheritance of the trait, and sometimes even for the phenotype definition. The term mode of inheritance relates to both the genetic mechanism, i.e., the number of loci implicated in the etiology of the disease, and the genotype-phenotype relation, which describes the influence of these loci on the trait. Having an idea of the genetic model can crucially facilitate the mapping process. This holds especially in the context of linkage analysis, where an appropriate parametric model or a suitable nonparametric allele sharing statistic may accordingly be selected. Here, we review the difficulties with parametric and nonparametric linkage analysis when applied to multifactorial diseases. We address the question why it is necessary to adequately model a genetically complex trait in a linkage study, and elucidate the steps to do so. Furthermore, we discuss the value of including unaffected individuals into the analysis, as well as of looking at larger pedigrees, both with parametric and nonparametric methods. Our considerations and suggestions aim at guiding researchers to genotyping individuals at a trait locus as accurately as possible.     

Methods for genetic linkage analysis using trisomies.

Certain genetic disorders are rare in the general population, but more common in individuals with specific trisomies. Examples of this include leukemia and duodenal atresia in trisomy 21. This paper presents a linkage analysis method for using trisomic individuals to map genes for such traits. It is based on a very general gene-specific dosage model that posits that the trait is caused by specific effects of different alleles at one or a few loci and that duplicate copies of "susceptibility" alleles inherited from the nondisjoining parent give increased likelihood of having the trait. Our mapping method is similar to identity-by-descent-based mapping methods using affected relative pairs and also to methods for mapping recessive traits using inbred individuals by looking for markers with greater than expected homozygosity by descent. In the trisomy case, one would take trisomic individuals and look for markers with greater than expected homozygosity in the chromosomes inherited from the nondisjoining parent. We present statistical methods for performing such a linkage analysis, including a test for linkage to a marker, a method for estimating the distance from the marker to the trait gene, a confidence interval for that distance, and methods for computing power and sample sizes. We also resolve some practical issues involved in implementing the methods, including how to use partially informative markers and how to test candidate genes.     

A Multi-Marker Model for Detecting Chromosomal Segments Displaying Qtl Activity

A statistical method is presented for detecting quantitative trait loci (QTLs), based on the linear model. Unlike methods able to detect a few well separated QTLs and to estimate their effects and positions, this method considers the genome as a whole and enables the detection of chromosomal segments involved in the differences between two homozygous lines, and their backcross, doubled haploid, or F(2) progenies, for a quantitative trait. Genetic markers must be codominant, but missing markers are accepted, provided they are missing independently from the experiment. Asymptotic properties, which are of practical use, are developed. This method does not rely on strong genetic hypotheses, and thus does not permit any precise genetic analysis of the trait under study, but it does assess which regions of the genome are involved, whatever the complexity of the genetic determinism (number, effects and interactions among QTLs). Simultaneous use of several methods, including this one, should lead to better efficiency in QTL detection.     

Environmental stress increases selection against and dominance of deleterious mutations in inbred families of the Pacific oyster Crassostrea gigas

The deleterious effects of inbreeding are well documented and of major concern in conservation biology. Stressful environments have generally been shown to increase inbreeding depression; however, little is known about the underlying genetic mechanisms of the inbreeding-by-stress interaction and to what extent the fitness of individual deleterious mutations is altered under stress. Using microsatellite marker segregation data and quantitative trait locus (QTL) mapping methods, I performed a genome scan for deleterious mutations affecting viability (viability or vQTL) in two inbred families of the Pacific oyster Crassostrea gigas, reared in a stressful, nutrient-poor diet and a favourable, nutrient-rich diet, which had significant effects on growth and survival. Twice as many vQTL were detected in the stressful diet compared with the favourable diet, resulting primarily from substantially greater mortality of homozygous genotypes. At vQTL, estimates of selection (s) and dominance (h) were greater in the stressful environment (= 0.86 vs. 0.54 and = 0.35 vs. 0.18, in stressful and nonstressful diets, respectively). There was no evidence of interaction between vQTL. Individual vQTL differed across diets in selection only, or in both selection and dominance, and some vQTL were not affected by diet. These results suggest that stress-associated increases in selection against individual deleterious alleles underlie greater inbreeding depression with stress. Furthermore, the finding that inbreeding-by-environment interaction appears, to some extent, to be locus specific, helps to explain previous observations of lineage-specific expression of inbreeding depression and environment-specific purging, which have important implications for conservation and evolutionary biology.     

Varying coefficient models for mapping quantitative trait loci using recombinant inbred intercrosses

There has been a great deal of interest in the development of methodologies to map quantitative trait loci (QTL) using experimental crosses in the last 2 decades. Experimental crosses in animal and plant sciences provide important data sources for mapping QTL through linkage analysis. The Collaborative Cross (CC) is a renewable mouse resource that is generated from eight genetically diverse founder strains to mimic the genetic diversity in humans. The recombinant inbred intercrosses (RIX) generated from CC recombinant inbred (RI) lines share similar genetic structures of F(2) individuals but with up to eight alleles segregating at any one locus. In contrast to F(2) mice, genotypes of RIX can be inferred from the genotypes of their RI parents and can be produced repeatedly. Also, RIX mice typically do not share the same degree of relatedness. This unbalanced genetic relatedness requires careful statistical modeling to avoid false-positive findings. Many quantitative traits are inherently complex with genetic effects varying with other covariates, such as age. For such complex traits, if phenotype data can be collected over a wide range of ages across study subjects, their dynamic genetic patterns can be investigated. Parametric functions, such as sigmoidal or logistic functions, have been used for such purpose. In this article, we propose a flexible nonparametric time-varying coefficient QTL mapping method for RIX data. Our method allows the QTL effects to evolve with time and naturally extends classical parametric QTL mapping methods. We model the varying genetic effects nonparametrically with the B-spline bases. Our model investigates gene-by-time interactions for RIX data in a very flexible nonparametric fashion. Simulation results indicate that the varying coefficient QTL mapping has higher power and mapping precision compared to parametric models when the assumption of constant genetic effects fails. We also apply a modified permutation procedure to control overall significance level.     

Assessment of Multiple Ordinal Endpoints

Ranking multivariate ordinal data and applying a non‐parametric test is an analytical approach commonly employed to compare treatments. We study three types of ranking and demonstrate how to combine them. The ranking methods rest upon partial orders of the multidimensional measurements or upon the sum of ranks. Since their usage is simple as regards statistical assumptions and technical realization, they are also adapted for health professionals without deep statistical knowledge. Our goal is discussing differences between the approaches and disclosing possible statistical consequences of their usage (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Species selection and random drift in macroevolution

Species selection resulting from trait‐dependent speciation and extinction is increasingly recognized as an important mechanism of phenotypic macroevolution. However, the recent bloom in statistical methods quantifying this process faces a scarcity of dynamical theory for their interpretation, notably regarding the relative contributions of deterministic versus stochastic evolutionary forces. I use simple diffusion approximations of birth‐death processes to investigate how the expected and random components of macroevolutionary change depend on phenotype‐dependent speciation and extinction rates, as can be estimated empirically. I show that the species selection coefficient for a binary trait, and selection differential for a quantitative trait, depend not only on differences in net diversification rates (speciation minus extinction), but also on differences in species turnover rates (speciation plus extinction), especially in small clades. The randomness in speciation and extinction events also produces a species‐level equivalent to random genetic drift, which is stronger for higher turnover rates. I then show how microevolutionary processes including mutation, organismic selection, and random genetic drift cause state transitions at the species level, allowing comparison of evolutionary forces across levels. A key parameter that would be needed to apply this theory is the distribution and rate of origination of new optimum phenotypes along a phylogeny.     

Simultaneous Statistical Inference for Epigenetic Data

Epigenetic research leads to complex data structures. Since parametric model assumptions for the distribution of epigenetic data are hard to verify we introduce in the present work a nonparametric statistical framework for two-group comparisons. Furthermore, epigenetic analyses are often performed at various genetic loci simultaneously. Hence, in order to be able to draw valid conclusions for specific loci, an appropriate multiple testing correction is necessary. Finally, with technologies available for the simultaneous assessment of many interrelated biological parameters (such as gene arrays), statistical approaches also need to deal with a possibly unknown dependency structure in the data. Our statistical approach to the nonparametric comparison of two samples with independent multivariate observables is based on recently developed multivariate multiple permutation tests. We adapt their theory in order to cope with families of hypotheses regarding relative effects. Our results indicate that the multivariate multiple permutation test keeps the pre-assigned type I error level for the global null hypothesis. In combination with the closure principle, the family-wise error rate for the simultaneous test of the corresponding locus/parameter-specific null hypotheses can be controlled. In applications we demonstrate that group differences in epigenetic data can be detected reliably with our methodology.     

R/qtl: QTL mapping in experimental crosses

SUMMARY: R/qtl is an extensible, interactive environment for mapping quantitative trait loci (QTLs) in experimental populations derived from inbred lines. It is implemented as an add-on package for the freely-available statistical software, R, and includes functions for estimating genetic maps, identifying genotyping errors, and performing single-QTL and two-dimensional, two-QTL genome scans by multiple methods, with the possible inclusion of covariates. AVAILABILITY: The package is freely available at http://www.biostat.jhsph.edu/~kbroman/qtl.     

Complexity of the simplest species tree problem

The multispecies coalescent model provides a natural framework for species tree estimation accounting for gene-tree conflicts. Although a number of species tree methods under the multispecies coalescent have been suggested and evaluated using simulation, their statistical properties remain poorly understood. Here, we use mathematical analysis aided by computer simulation to examine the identifiability, consistency, and efficiency of different species tree methods in the case of three species and three sequences under the molecular clock. We consider four major species-tree methods including concatenation, two-step, independent-sites maximum likelihood, and maximum likelihood. We develop approximations that predict that the probit transform of the species tree estimation error decreases linearly with the square root of the number of loci. Even in this simplest case, major differences exist among the methods. Full-likelihood methods are considerably more efficient than summary methods such as concatenation and two-step. They also provide estimates of important parameters such as species divergence times and ancestral population sizes,whereas these parameters are not identifiable by summary methods. Our results highlight the need to improve the statistical efficiency of summary methods and the computational efficiency of full likelihood methods of species tree estimation.     

Congruent population structure across paralogous and nonparalogous loci in Salish Sea chum salmon (Oncorhynchus keta)

Whole‐genome duplications are major evolutionary events with a lasting impact on genome structure. Duplication events complicate genetic analyses as paralogous sequences are difficult to distinguish; consequently, paralogs are often excluded from studies. The effects of an ancient whole‐genome duplication (approximately 88 MYA) are still evident in salmonids through the persistence of numerous paralogous gene sequences and partial tetrasomic inheritance. We use restriction site‐associated DNA sequencing on 10 collections of chum salmon from the Salish Sea in the USA and Canada to investigate genetic diversity and population structure in both tetrasomic and rediploidized regions of the genome. We use a pedigree and high‐density linkage map to identify paralogous loci and to investigate genetic variation across the genome. By applying multivariate statistical methods, we show that it is possible to characterize paralogous loci and that they display similar patterns of population structure as the diploidized portion of the genome. We find genetic associations with the adaptively important trait of run‐timing in both sets of loci. By including paralogous loci in genome scans, we can observe evolutionary signals in genomic regions that have routinely been excluded from population genetic studies in other polyploid‐derived species.