An allometric model for mapping seed development in plants

Functional Mapping of Genes Modulating Plant Shade Avoidance Using Leaf Traits

Shade avoidance syndrome (SAS) refers to a set of plant responses that increases light capture in dense stands. This process is crucial for plants in natural and agricultural environments as they compete for resources and avoid suboptimal conditions. Although the molecular, biochemical, and physiological mechanisms underlying the SAS response have been extensively studied, the genetic basis of developmental variation in leaves in regard to leaf area, petiole length, and leaf length (i.e., their allometric relationships) remains unresolved. In this study, with the recombinant inbred line (RIL) population, the developmental traits of leaves of Arabidopsis were investigated under two growth density conditions (high- and low-density plantings). The observed changes were then reconstructed digitally, and their allometric relationships were modelled. Taking the genome-wide association analysis, the SNP genotype and the dynamic phenotype of the leaf from both densities were combined to explore the allometry QTLs. Under different densities, leaf change phenotype was analyzed from two core ecological scenarios: (i) the allometric change of the leaf area with leaf length, and (ii) the change of the leaf length with petiole length. QTLs modulating these two scenarios were characterized as 'leaf shape QTLs' and 'leaf position QTLs'. With functional mapping, results showed a total of 30 and 24 significant SNPs for shapeQTLs and positionQTLs, respectively. By annotation, immune pathway genes, photosensory receptor genes, and phytohormone genes were identified to be involved in the SAS response. Interestingly, genes modulating the immune pathway and salt tolerance, i.e., systemic acquired resistance (SAR) regulatory proteins (MININ-1-related) and salt tolerance homologs (STH), were reported to mediate the SAS response. By dissecting and comparing QTL effects from low- and high-density conditions, our results elucidate the genetic control of leaf formation in the context of the SAS response. The mechanism with leaf development × density interaction can further aid the development of density-tolerant crop varieties for agricultural practices.

The genetic control of leaf allometry in the common bean, Phaseolus vulgaris

BACKGROUND

To maximize photosynthetic efficiency, plants have evolved a capacity by which leaf area scales allometrically with leaf mass through interactions with the environment. However, our understanding of genetic control of this allometric relationship remains limited.

RESULTS

We integrated allometric scaling laws expressed at static and ontogenetic levels into genetic mapping to identify the quantitative trait loci (QTLs) that mediate how leaf area scales with leaf mass and how such leaf allometry, under the control of these QTLs, varies as a response to environment change. A major QTL detected by the static model constantly affects the allometric growth of leaf area vs. leaf mass for the common bean (Phaseolus vulgaris) in two different environments. The ontogenetic model identified this QTL plus a few other QTLs that determine developmental trajectories of leaf allometry, whose expression is contingent heavily upon the environment.

CONCLUSIONS

Our results gain new insight into the genetic mechanisms of how plants program their leaf morphogenesis to adapt to environmental perturbations.

Model-based QTL detection is sensitive to slight modifications in model formulation

Classical crop models have been developed to predict crop yield and quality, and they are based on physiological and environmental inputs. After molecular discoveries, models should integrate genetic variation to allow predictions that are more genotype-dependent. An interesting approach, Quantitative Trait Locus (QTL)-based ecophysiological modeling, has shown promising results for the design of ideotypes that are adapted to biotic and abiotic stresses, but there are still limitations to attaining a fully integrated model. The aim of this case study is to clarify the impact of choosing different model equations (closely related and with different numbers of parameters) and optimization methods on the detection of QTLs controlling the parameters of crop growth. Different growth equations were parameterized based on a genetic population by following different approaches. The correlations between parameters were analyzed, and two different strategies were adopted to address the correlation issue. QTL analysis was performed on the optimized values of the parameters of the growth equations and on the observed dry mass (DM) data to validate the QTLs detected. Overall, models and strategies resulted in different QTLs being detected. Similar LOD profiles but with peaks of different heights were observed, some of which were significant, resulting in different numbers of QTLs. In some cases, peaks had slightly different positions or were absent. Even closely related growth models led to the detection of different QTLs. The goodness of fit and complexity of the growth models were found to be insufficient to select the best model. Calculating parameters independently of observed data may not be a good strategy, whereas setting parameters independent of the genotype is recommended. Given the large-scale global optimization problem and the strong correlations between parameters, the two algorithms tested showed poor performance. Currently, the lack of effective algorithms is the main obstacle to answering the question posed. The authors therefore suggest testing different model formulations and comparing the QTLs detected before choosing the best formulation to use in an ecophysiological modeling approach based on QTLs.

A dissection model for mapping complex traits

Many quantitative traits are composites of other traits that contribute differentially to genetic variation. Quantitative trait locus (QTL) mapping of these composite traits can benefit by incorporating the mechanistic process of how their formation is mediated by the underlying components. We propose a dissection model by which to map these interconnected components traits under a joint likelihood setting. The model can test how a composite trait is determined by pleiotropic QTLs for its component traits or jointly by different sets of QTLs each responsible for a different component. The model can visualize the pattern of time-varying genetic effects for individual components and their impacts on composite traits. The dissection model was used to map two composite traits, stemwood volume growth decomposed into its stem height, stem diameter and stem form components for Euramerican poplar adult trees, and total lateral root length constituted by its average lateral root length and lateral root number components for Euphrates poplar seedlings. We found the pattern of how QTLs for different components contribute to phenotypic variation in composite traits. The detailed understanding of the genetic machineries of composite traits will not only help in the design of molecular breeding in plants and animals, but also shed light on the evolutionary processes of quantitative traits under natural selection.

A Computational Model for Inferring QTL Control Networks Underlying Developmental Covariation

How one trait developmentally varies as a function of others shapes a spectrum of biological phenomena. Despite its importance to trait dissection, the understanding of whether and how genes mediate such developmental covariation is poorly understood. We integrate developmental allometry equations into the functional mapping framework to map specific QTLs that govern the correlated development of different traits. Based on evolutionary game theory, we assemble and contextualize these QTLs into an intricate but organized network coded by bidirectional, signed, and weighted QTL-QTL interactions. We use this approach to map shoot height-diameter allometry QTLs in an ornamental woody species, mei (Prunus mume). We detect "pioneering" QTLs (piQTLs) and "maintaining" QTLs (miQTLs) that determine how shoot height varies with diameter and how shoot diameter varies with height, respectively. The QTL networks inferred can visualize how each piQTL regulates others to promote height growth at a cost of diameter growth, how miQTL regulates others to benefit radial growth at a cost of height growth, and how piQTLs and miQTLs regulate each other to form a pleiotropic web of primary and secondary growth in trees. Our approach provides a unique gateway to explore the genetic architecture of developmental covariation, a widespread phenomenon in nature.

MVQTLCIM: composite interval mapping of multivariate traits in a hybrid F1 population of outbred species

Background

With the plummeting cost of the next-generation sequencing technologies, high-density genetic linkage maps could be constructed in a forest hybrid F₁ population. However, based on such genetic maps, quantitative trait loci (QTL) mapping cannot be directly conducted with traditional statistical methods or tools because the linkage phase and segregation pattern of molecular markers are not always fixed as in inbred lines.

Results

We implemented the traditional composite interval mapping (CIM) method to multivariate trait data in forest trees and developed the corresponding software, mvqtlcim. Our method not only incorporated the various segregations and linkage phases of molecular markers, but also applied Takeuchi’s information criterion (TIC) to discriminate the QTL segregation type among several possible alternatives. QTL mapping was performed in a hybrid F₁ population of Populus deltoides and P. simonii, and 12 QTLs were detected for tree height over 6 time points. The software package allowed many options for parameters as well as parallel computing for permutation tests. The features of the software were demonstrated with the real data analysis and a large number of Monte Carlo simulations.

Conclusions

We provided a powerful tool for QTL mapping of multiple or longitudinal traits in an outbred F₁ population, in which the traditional software for QTL mapping cannot be used. This tool will facilitate studying of QTL mapping and thus will accelerate molecular breeding programs especially in forest trees. The tool package is freely available from https://github.com/tongchf /mvqtlcim.

Electronic supplementary material

The online version of this article (10.1186/s12859-017-1908-1) contains supplementary material, which is available to authorized users.

Composite Interval Mapping Based on Lattice Design for Error Control May Increase Power of Quantitative Trait Locus Detection

Experimental error control is very important in quantitative trait locus (QTL) mapping. Although numerous statistical methods have been developed for QTL mapping, a QTL detection model based on an appropriate experimental design that emphasizes error control has not been developed. Lattice design is very suitable for experiments with large sample sizes, which is usually required for accurate mapping of quantitative traits. However, the lack of a QTL mapping method based on lattice design dictates that the arithmetic mean or adjusted mean of each line of observations in the lattice design had to be used as a response variable, resulting in low QTL detection power. As an improvement, we developed a QTL mapping method termed composite interval mapping based on lattice design (CIMLD). In the lattice design, experimental errors are decomposed into random errors and block-within-replication errors. Four levels of block-within-replication errors were simulated to show the power of QTL detection under different error controls. The simulation results showed that the arithmetic mean method, which is equivalent to a method under random complete block design (RCBD), was very sensitive to the size of the block variance and with the increase of block variance, the power of QTL detection decreased from 51.3% to 9.4%. In contrast to the RCBD method, the power of CIMLD and the adjusted mean method did not change for different block variances. The CIMLD method showed 1.2- to 7.6-fold higher power of QTL detection than the arithmetic or adjusted mean methods. Our proposed method was applied to real soybean (Glycine max) data as an example and 10 QTLs for biomass were identified that explained 65.87% of the phenotypic variation, while only three and two QTLs were identified by arithmetic and adjusted mean methods, respectively.