A class of cumulant plots for assessing mode and asymmetry of transmission of a quantitative trait

A class of cumulant plot statistics of use in assessing mode and asymmetry of transmission of a quantitative trait within a nuclear family is introduced. Various models for transmission modes involving continuous parameterization are described. Behavior of the cumulant plots under the differing transmission modes is delineated with use made of results from theoretical and simulation studies. Application to the analysis of specific data sets is given.     

Generation of bilateral symmetry in Anthozoa: a model

Polyps of Anthozoa usually display bilateral symmetry with respect to their mouth opening, to their pharynx, and in particular to the arrangement of their mesenteries. Mesenteries, which are endodermal folds running from the apical to the basal end of the body, subdivide the gastric cavity into pouches. They form in a bilateral symmetric sequence. In this article I propose that early in polyp development the endoderm subdivides successively into three different types of compartments. A mesentery forms at the border between compartments. Two of the compartments are homologous to those of Scyphozoa. They form by mutual activation of cell states that locally exclude each other. The third compartment leads to siphonoglyph formation and is an evolutionary innovation of the Anthozoa. The mechanism that controls the number and spatial arrangement of the third type of compartment changes the radial symmetry into a bilateral one and occasionally into a different one. The dynamics of its formation indicate an activator-inhibitor mechanism. Computer models are provided that reproduce decision steps in the generation of the mesenteries.     

Ontogenetic symmetry and asymmetry in energetics

Body size ( $\equiv $ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as “ontogenetic symmetry”. Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.     

Heritability and tissue specificity of expression quantitative trait loci

Variation in gene expression is heritable and has been mapped to the genome in humans and model organisms as expression quantitative trait loci (eQTLs). We applied integrated genome-wide expression profiling and linkage analysis to the regulation of gene expression in fat, kidney, adrenal, and heart tissues using the BXH/HXB panel of rat recombinant inbred strains. Here, we report the influence of heritability and allelic effect of the quantitative trait locus on detection of cis- and trans-acting eQTLs and discuss how these factors operate in a tissue-specific context. We identified several hundred major eQTLs in each tissue and found that cis-acting eQTLs are highly heritable and easier to detect than trans-eQTLs. The proportion of heritable expression traits was similar in all tissues; however, heritability alone was not a reliable predictor of whether an eQTL will be detected. We empirically show how the use of heritability as a filter reduces the ability to discover trans-eQTLs, particularly for eQTLs with small effects. Only 3% of cis- and trans-eQTLs exhibited large allelic effects, explaining more than 40% of the phenotypic variance, suggestive of a highly polygenic control of gene expression. Power calculations indicated that, across tissues, minor differences in genetic effects are expected to have a significant impact on detection of trans-eQTLs. Trans-eQTLs generally show smaller effects than cis-eQTLs and have a higher false discovery rate, particularly in more heterogeneous tissues, suggesting that small biological variability, likely relating to tissue composition, may influence detection of trans-eQTLs in this system. We delineate the effects of genetic architecture on variation in gene expression and show the sensitivity of this experimental design to tissue sampling variability in large-scale eQTL studies.     

Determining causality and consequence of expression quantitative trait loci

Expression quantitative trait loci (eQTLs) are currently the most abundant and systematically-surveyed class of functional consequence for genetic variation. Recent genetic studies of gene expression have identified thousands of eQTLs in diverse tissue types for the majority of human genes. Application of this large eQTL catalog provides an important resource for understanding the molecular basis of common genetic diseases. However, only now has both the availability of individuals with full genomes and corresponding advances in functional genomics provided the opportunity to dissect eQTLs to identify causal regulatory variants. Resolving the properties of such causal regulatory variants is improving understanding of the molecular mechanisms that influence traits and guiding the development of new genome-scale approaches to variant interpretation. In this review, we provide an overview of current computational and experimental methods for identifying causal regulatory variants and predicting their phenotypic consequences.     

Accommodating pathway information in expression quantitative trait locus analysis

The availability of high-throughput genotyping technologies and microarray assays has allowed researchers to consider pursuing investigations whose ultimate goal is the identification of genetic variations that influence levels of gene expression, e.g., "expression quantitative trait locus" or "eQTL" mapping studies. However, the large number of genes whose expression levels can be tested for association with genetic variations in such studies can create both statistical and biological interpretive problems. We consider the integrated analysis of eQTL mapping data that incorporates pathway, function, and disease process information. The goal of this analysis is to determine if compelling patterns emerge from the data that are consistent with the notion that perturbations in the molecular physiologic environment induced by genetic variations implicate the expression patterns of multiple genes via genetic network relationships or feedback mechanisms. We apply available genetic network and pathway analysis software, as well as a novel regression analysis technique, to carry out the proposed studies. We also consider extensions of the proposed strategies and areas of future research.     

Birth-death symmetry in the evolution of a social trait

Studies of the evolution of a social trait often make ecological assumptions (of population structure, life history), and thus a trait can be studied many different times with different assumptions. Here, I consider a Moran model of continuous reproduction and use an inclusive fitness analysis to investigate the relationships between fecundity or survival selection and birth-death (BD) or death-birth (DB) demography on the evolution of a social trait. A simple symmetry obtains: fecundity (respectively survival) effects under BD behave the same as survival (respectively fecundity) effects under DB. When these results are specialized to a homogeneous population, greatly simplified conditions for a positive inclusive fitness effect are obtained in both a finite and an infinite population. The results are established using the elegant formalism of mathematical group theory and are illustrated with an example of a finite population arranged in a cycle with asymmetric offspring dispersal.     

Otx-dependent expression of proneural bHLH genes establishes a neuronal bilateral asymmetry in C. elegans

Bilateral asymmetry in Caenorhabditis elegans arises in part from cell lineages that differ on the left and right sides of the animal. The unpaired MI neuron descends from the right side of an otherwise left-right symmetric cell lineage that generates the MI neuron on the right and the e3D epithelial cell on the left. We isolated mutations in three genes that caused left-right symmetry in this normally asymmetric cell lineage by transforming MI into an e3D-like cell. These genes encode the proneural bHLH proteins NGN-1 and HLH-2 and the Otx homeodomain protein CEH-36. We identified the precise precursor cells in which ceh-36 and ngn-1 act, and showed that CEH-36 protein is asymmetrically expressed and is present in an MI progenitor cell on the right but not in its bilateral counterpart. This asymmetric CEH-36 expression promotes asymmetric ngn-1 and hlh-2 expression, which in turn induces asymmetric MI neurogenesis. Our results indicate that this left-right asymmetry is specified within the two sister cells that first separate the left and right branches of the cell lineage. We conclude that the components of an evolutionarily conserved Otx/bHLH pathway act sequentially through multiple rounds of cell division on the right to relay an initial apparently cryptic asymmetry to the presumptive post-mitotic MI neuron, thereby creating an anatomical bilateral asymmetry in the C. elegans nervous system.     

Aroma in rice: genetic analysis of a quantitative trait

A new approach was developed which succeeded in tagging for the first time a major gene and two QTLs controlling grain aroma in rice. It involved a combination of two techniques, quantification of volatile compounds in the cooking water by gas chromatography, and molecular marker mapping. Four types of molecular marker were used (RFLPs, RAPDs, STSs, isozymes). Evaluation and mapping were performed on a doubled haploid line population which (1) conferred a precise character evaluation by enabling the analysis of large quantities of grains per genotype and (2) made possible the comparison of gas chromatography results and sensitive tests. The population size (135 lines) provided a good mapping precision. Several markers on chromosome 8 were found to be closely linked to a major gene controlling the presence of 2-acetyl-1-pyrroline (AcPy), the main compound of rice aroma. Moreover, our results showed that AcPy concentration in plants is regulated by at least two chromosomal regions. Estimations of recombination fractions on chromosome 8 were corrected for strong segregation distortion. This study confirms that AcPy is the major component of aroma. Use of the markers linked to AcPy major gene and QTLs for marker-assisted selection by successive backcrosses may be envisaged.     

Modeling expression quantitative trait loci in data combining ethnic populations

Background  

Combining data from different ethnic populations in a study can increase efficacy of methods designed to identify expression quantitative trait loci (eQTL) compared to analyzing each population independently. In such studies, however, the genetic diversity of minor allele frequencies among populations has rarely been taken into account. Due to the fact that allele frequency diversity and population-level expression differences are present in populations, a consensus regarding the optimal statistical approach for analysis of eQTL in data combining different populations remains inconclusive.     

A bivariate quantitative genetic model for a threshold trait and a survival trait

Many of the functional traits considered in animal breeding can be analyzed as threshold traits or survival traits with examples including disease traits, conformation scores, calving difficulty and longevity. In this paper we derive and implement a bivariate quantitative genetic model for a threshold character and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted in which model parameters were augmented with unobserved liabilities associated with the threshold trait. The fully conditional posterior distributions associated with parameters of the threshold trait reduced to well known distributions. For the survival trait the two baseline Weibull parameters were updated jointly by a Metropolis-Hastings step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. The Gibbs sampler was tested in a simulation study and illustrated in a joint analysis of calving difficulty and longevity of dairy cattle. The simulation study showed that the estimated marginal posterior distributions covered well and placed high density to the true values used in the simulation of data. The data analysis of calving difficulty and longevity showed that genetic variation exists for both traits. The additive genetic correlation was moderately favorable with marginal posterior mean equal to 0.37 and 95% central posterior credibility interval ranging between 0.11 and 0.61. Therefore, this study suggests that selection for improving one of the two traits will be beneficial for the other trait as well.     

Environmental stress-dependent effects of deletions encompassing Hsp70Ba on canalization and quantitative trait asymmetry in Drosophila melanogaster

Hsp70 genes may influence the expression of wing abnormalities in Drosophila melanogaster but their effects on variability in quantitative characters and developmental instability are unclear. In this study, we focused on one of the six Hsp70 genes, Hsp70Ba, and investigated its effects on within- and among-individual variability in orbital bristle number, sternopleural bristle number, wing size and wing shape under different environmental conditions. To do this, we studied a newly constructed deletion, Df(3R)ED5579, which encompasses Hsp70Ba and nine non-Hsp genes, in the heterozygous condition and another, Hsp70Ba(304), which deletes only Hsp70Ba, in the homozygous condition. We found no significant effect of both deletions on within-individual variation quantified by fluctuating asymmetry (FA) of morphological traits. On the other hand, the Hsp70Ba(304)/Hsp70Ba(304) genotype significantly increased among-individual variation quantified by coefficient of variation (CV) of bristle number and wing size in female, while the Df(3R)ED5579 heterozygote showed no significant effect. The expression level of Hsp70Ba in the deletion heterozygote was 6 to 20 times higher than in control homozygotes, suggesting that the overexpression of Hsp70Ba did not influence developmental stability or canalization significantly. These findings suggest that the absence of expression of Hsp70Ba increases CV of some morphological traits and that HSP70Ba may buffer against environmental perturbations on some quantitative traits.     

Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry

Background

Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry.

Results

We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis.

Conclusions

The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.