Restriction site-associated DNA sequencing (RADseq) is a powerful technology that has been extensively applied in population genetics, phylogenetics and genetic mapping. Although many software packages are available for ecological and evolutionary studies, a few effective tools are available for extracting genotype data with RADseq for genetic mapping, a prerequisite for quantitative trait locus mapping, comparative genomics and genome scaffold assembly. Here, we present an integrated pipeline called gmRAD for generating single nucleotide polymorphism (SNP) genotypes from RADseq data, de novo, across a genetic mapping population derived by crossing two parents. As an analytical strategy, the software takes five steps to implement the whole algorithms, including clustering the first (forward) reads of each parent, building two parental references, generating parental SNP catalogs, calling SNP genotypes across all individuals and filtering the genotype data for genetic linkage mapping. All the steps can be completed with a simple command line, but they can be also performed optionally if prerequisite files are available. To validate its application, we also performed a real data analysis with RADseq data from an F1 hybrid population derived by crossing Populus deltoides and Populus simonii. The software gmRAD is freely available at https://github.com/tongchf/gmRAD.

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. 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. 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.

As a group of important plant species in agriculture and biology, polyploids have been increasingly studied in terms of their genome structure and organization. There are two types of polyploids, allopolyploids and autopolyploids, each resulting from a different genetic origin, which undergo meiotic divisions of a distinct complexity. A set of statistical models has been developed for linkage analysis, respectively for each type, by taking into account their unique meiotic behavior, i.e. preferential pairing for allopolyploids and double reduction for autopolyploids. We synthesized these models and modified them to accommodate the linkage analysis of less informative dominant markers. By reanalysing a published data set of varying ploidy in Arabidopsis, we corrected the estimates of the meiotic recombination frequency aimed to study the significance of polyploidization.

Despite a tremendous effort to map quantitative trait loci (QTLs) responsible for agriculturally and biologically important traits in plants, our understanding of how a QTL governs the developmental process of plant seeds remains elusive. In this article, we address this issue by describing a model for functional mapping of seed development through the incorporation of the relationship between vegetative and reproductive growth. The time difference of reproductive from vegetative growth is described by Reeve and Huxley’s allometric equation. Thus, the implementation of this equation into the framework of functional mapping allows dynamic QTLs for seed development to be identified more precisely. By estimating and testing mathematical parameters that define Reeve and Huxley’s allometric equations of seed growth, the dynamic pattern of the genetic effects of the QTLs identified can be analyzed. We used the model to analyze a soybean data, leading to the detection of QTLs that control the growth of seed dry weight. Three dynamic QTLs, located in two different linkage groups, were detected to affect growth curves of seed dry weight. The QTLs detected may be used to improve seed yield with marker-assisted selection by altering the pattern of seed development in a hope to achieve a maximum size of seeds at a harvest time.

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.

As a group of economically important species, linkage mapping of polysomic autotetraploids, including potato, sugarcane and rose, is difficult to conduct due to their unique meiotic property of double reduction that allows sister chromatids to enter into the same gamete. We describe and assess a statistical model for mapping quantitative trait loci (QTLs) in polysomic autotetraploids. The model incorporates double reduction, built in the mixture model-based framework and implemented with the expectation-maximization algorithm. It allows the simultaneous estimation of QTL positions, QTL effects and the degree of double reduction as well as the assessment of the estimation precision of these parameters. We performed computer simulation to examine the statistical properties of the method and validate its use through analyzing real data in tetraploid switchgrass.

Because of its widespread occurrence and role in shaping evolutionary processes in the biological kingdom, especially in plants, polyploidy has been increasingly studied from cytological to molecular levels. By inferring gene order, gene distances and gene homology, linkage mapping with molecular markers has proven powerful for investigating genome structure and organization. Here we review and assess a general statistical model for three-point linkage analysis in autotetraploids by integrating double reduction, a phenomenon that commonly occurs in autopolyploids whose chromosomes are derived from a single ancestral species. This model does not require any assumption on the distribution of the occurrence of double reduction and can handle the complexity of multilocus linkage in terms of crossover interference. Implemented with the expectation-maximization (EM) algorithms, the model can estimate and test the recombination fractions between less informative dominant markers, thus facilitating its practical implications for any autopolyploids in most of which inexpensive dominant markers are still used for their genetic and evolutionary studies. The model was applied to reanalyze a published data in tetraploid switchgrass, validating its practical usefulness and utilization.

An allotetraploid has four paired sets of chromosomes derived from different diploid species, whose meiotic behavior is qualitatively different from the underlying diploids. According to a traditional view, meiotic pairing occurs only between homologous chromosomes, but new evidence indicates that homoeologous chromosomes may also pair to a lesser extent compared with homolog pairing. Here, we describe and assess a unifying analytical framework that incorporates differential chromosomal pairing into a multilocus linkage model. The preferential pairing factor is used to quantify the probability difference of pairing occurring between homologous chromosomes and homoeologous chromosomes. The unifying framework allows simultaneous estimation of the linkage, genetic interference and preferential pairing factor using commonly existing multiplex markers. We compared the unifying approach and traditional approaches assuming random chromosomal pairing by analyzing marker data collected in a full-sib family of tetraploid switchgrass, a bioenergy species whose diploid origins are undefined, but with subgenomes that are genetically well differentiated. The unifying framework provides a better tool for estimating the meiotic linkage and constructing a genetic map for allotetraploids.

All organisms face the problem of how to perform a sequence of developmental changes and transitions during ontogeny. We revise functional mapping, a statistical model originally derived to map genes that determine developmental dynamics, to take into account the entire process of ontogenetic growth from embryo to adult and from the vegetative to reproductive phase. The revised model provides a framework that reconciles the genetic architecture of development at different stages and elucidates a comprehensive picture of the genetic control mechanisms of growth that change gradually from a simple to a more complex level. We use an annual flowering plant, as an example, to demonstrate our model by which to map genes and their interactions involved in embryo and postembryonic growth. The model provides a useful tool to study the genetic control of ontogenetic growth in flowering plants and any other organisms through proper modifications based on their biological characteristics.

MOTIVATION: Functional mapping that embeds the developmental mechanisms of complex traits shows great power to study the dynamic pattern of genetic effects triggered by individual quantitative trait loci (QTLs). A full-sib family, produced by crossing two heterozygous parents, is characteristic of uncertainties about cross-type at a locus and linkage phase between different loci. Integrating functional mapping into a full-sib family requires a model selection procedure capable of addressing these uncertainties. 3FunMap, written in VC++ 6.0, provides a flexible and extensible platform to perform full-sib functional mapping of dynamic traits. Functions in the package encompass linkage phase determination, marker map construction and the pattern identification of QTL segregation, dynamic tests of QTL effects, permutation tests and numerical simulation. We demonstrate the features of 3FunMap through real data analysis and computer simulation. AVAILABILITY: http://statgen.psu.edu/software.