Molecular linkage maps of the Populus genome

High-resolution mapping reveals hotspots and sex-biased recombination in Populus trichocarpa

Fine-scale meiotic recombination is fundamental to the outcome of natural and artificial selection. Here, dense genetic mapping and haplotype reconstruction were used to estimate recombination for a full factorial Populus trichocarpa cross of 7 males and 7 females. Genomes of the resulting 49 full-sib families (N = 829 offspring) were resequenced, and high-fidelity biallelic SNP/INDELs and pedigree information were used to ascertain allelic phase and impute progeny genotypes to recover gametic haplotypes. The 14 parental genetic maps contained 1,820 SNP/INDELs on average that covered 376.7 Mb of physical length across 19 chromosomes. Comparison of parental and progeny haplotypes allowed fine-scale demarcation of cross-over regions, where 38,846 cross-over events in 1,658 gametes were observed. Cross-over events were positively associated with gene density and negatively associated with GC content and long-terminal repeats. One of the most striking findings was higher rates of cross-overs in males in 8 out of 19 chromosomes. Regions with elevated male cross-over rates had lower gene density and GC content than windows showing no sex bias. High-resolution analysis identified 67 candidate cross-over hotspots spread throughout the genome. DNA sequence motifs enriched in these regions showed striking similarity to those of maize, Arabidopsis, and wheat. These findings, and recombination estimates, will be useful for ongoing efforts to accelerate domestication of this and other biomass feedstocks, as well as future studies investigating broader questions related to evolutionary history, perennial development, phenology, wood formation, vegetative propagation, and dioecy that cannot be studied using annual plant model systems.

A Novel Strategy for Constructing an Integrated Linkage Map in an F1 Hybrid Population of Populus deltoides and Populus simonii

The genetic linkage maps of the traditional F₂ population in inbred lines were estimated from the frequency of recombination events in both parents, providing full genetic information for genetic and genomic studies. However, in outbred forest trees, it is almost impossible to generate the F₂ population because of their high heterozygosity and long generation times. We proposed a novel strategy to construct an integrated genetic linkage map that contained both parental recombination information, with restriction-site-associated DNA sequencing (RADSeq) data in an F1 hybrid population of Populus deltoides and Populus simonii. We selected a large number of specific RAD tags to construct the linkage map, each of which contained two SNPs, one heterozygous only in the female parent and the other heterozygous only in the male. Consequently, the integrated map contained a total of 1154 RAD tags and 19 linkage groups, with a total length of 5255.49 cM and an average genetic distance of 4.63 cM. Meanwhile, the two parent-specific linkage maps were also constructed with SNPs that were heterozygous in one parent and homozygous in the other. We found that the integrated linkage map was more consensus with the genomic sequences of P. simonii and P. deltoides. Additionally, the likelihood of the marker order in each linkage group of the integrated map was greater than that in both parental maps. The integrated linkage map was more accurate than the parent-specific linkage maps constructed in the same F₁ hybrid population, providing a powerful genetic resource for identifying the quantitative trait loci (QTLs) with dominant effects, assembling genomic sequences, and performing comparative genomics in related Populus species. More importantly, this novel strategy can be used in other outbred species to build an integrated linkage map.

High-Quality SNP Linkage Maps Improved QTL Mapping and Genome Assembly in Populus

With the advances in high-throughput sequencing technologies and the development of new software for extracting single nucleotide polymorphisms (SNPs) across a mapping population, it is possible to construct high-quality genetic maps with thousands of SNPs in outbred forest trees. Two parent-specific linkage maps were constructed with restriction site-associated DNA sequencing data from an F₁ hybrid population derived from Populus deltoides and Populus simonii, and applied in QTL mapping and genome assembly. The female P. deltoides map contained 4018 SNPs, which were divided into 19 linkage groups under a wide range of LOD thresholds from 7 to 55. The male P. simonii map showed similar characteristics, consisting of 2097 SNPs, which also belonged to 19 linkage groups under LOD thresholds of 7 to 29. The SNP order of each linkage group was optimal among different ordering results from several available software. Moreover, the linkage maps allowed the detection of 39 QTLs underlying tree height and 47 for diameter at breast height. In addition, the linkage maps improved the anchoring of 689 contigs of P. simonii to chromosomes. The 2 parental genetic maps of Populus are of high quality, especially in terms of SNP data quality, the SNP order within linkage groups, and the perfect match between the number of linkage groups and the karyotype of Populus, as well as the excellent performances in QTL mapping and genome assembly. Both approaches for extracting and ordering SNPs could be applied to other species for constructing high-quality genetic maps.

De Novo Genome Assembly of Populus simonii Further Supports That Populus simonii and Populus trichocarpa Belong to Different Sections

Populus simonii is an important tree in the genus Populus, widely distributed in the Northern Hemisphere and having a long cultivation history. Although this species has ecologically and economically important values, its genome sequence is currently not available, hindering the development of new varieties with wider adaptive and commercial traits. Here, we report a chromosome-level genome assembly of P. simonii using PacBio long-read sequencing data aided by Illumina paired-end reads and related genetic linkage maps. The assembly is 441.38 Mb in length and contain 686 contigs with a contig N50 of 1.94 Mb. With the linkage maps, 336 contigs were successfully anchored into 19 pseudochromosomes, accounting for 90.2% of the assembled genome size. Genomic integrity assessment showed that 1,347 (97.9%) of the 1,375 genes conserved among all embryophytes can be found in the P. simonii assembly. Genomic repeat analysis revealed that 41.47% of the P. simonii genome is composed of repetitive elements, of which 40.17% contained interspersed repeats. A total of 45,459 genes were predicted from the P. simonii genome sequence and 39,833 (87.6%) of the genes were annotated with one or more related functions. Phylogenetic analysis indicated that P. simonii and Populus trichocarpa should be placed in different sections, contrary to the previous classification according to morphology. The genome assembly not only provides an important genetic resource for the comparative and functional genomics of different Populus species, but also furnishes one of the closest reference sequences for identifying genomic variants in an F1 hybrid population derived by crossing P. simonii with other Populus species.

QTLs for Woolly Poplar Aphid (Phloeomyzus passerinii L.) Resistance Detected in an Inter-Specific Populus deltoides x P. nigra Mapping Population

The genus Populus represents one of the most economically important groups of forest trees. It is composed by approximately 30 species used for wood and non-wood products, phytoremediation and biomass. Poplar is subjected to several biological and environmental threats although, compared to annual crops, we know far less about the genetic bases of biotic stress resistance. Woolly poplar aphid (Phloeomyzus passerinii) is considered a main pest of cultivated poplars in European and American countries. In this work we present two high density linkage maps in poplar obtained by a genotyping by sequencing (GBS) approach and the identification of QTLs involved in Ph. passerinii resistance. A total of 5,667 polymorphic markers (5,606 SNPs and 61 SSRs) identified on expressed sequences have been used to genotype 131 plants of an F1 population P ×canadensis obtained by an interspecific mate between Populus deltoides (resistant to woolly poplar aphid) and Populus nigra (susceptible to woolly poplar aphid). The two linkage maps, obtained following the two-way pseudo-testcross mapping strategy, have been used to investigate the genetic bases of woolly poplar aphid resistance. One major QTL and two QTLs with minor effects (mapped on LGV, LGXVI and LG XIX) explaining the 65.8% of the genetic variance observed in the progeny in response to Ph. passerinii attack were found. The high density coverage of functional markers allowed the identification of three genes belonging to disease resistance pathway as putative candidates for P. deltoides resistance to woolly poplar aphid. This work is the first report on genetic of woolly poplar aphid genetic resistance and the resistant loci associated markers identified represent a valuable tool in resistance poplar breeding programs.

Construction of High-Density Linkage Maps of Populus deltoides × P. simonii Using Restriction-Site Associated DNA Sequencing

Although numerous linkage maps have been constructed in the genus Populus, they are typically sparse and thus have limited applications due to low throughput of traditional molecular markers. Restriction-site associated DNA sequencing (RADSeq) technology allows us to identify a large number of single nucleotide polymorphisms (SNP) across genomes of many individuals in a fast and cost-effective way, and makes it possible to construct high-density genetic linkage maps. We performed RADSeq for 299 progeny and their two parents in an F1 hybrid population generated by crossing the female Populus deltoides 'I-69' and male Populus simonii 'L3'. A total of 2,545 high quality SNP markers were obtained and two parent-specific linkage maps were constructed. The female genetic map contained 1601 SNPs and 20 linkage groups, spanning 4,249.12 cM of the genome with an average distance of 2.69 cM between adjacent markers, while the male map consisted of 940 SNPs and also 20 linkage groups with a total length of 3,816.24 cM and an average marker interval distance of 4.15 cM. Finally, our analysis revealed that synteny and collinearity are highly conserved between the parental linkage maps and the reference genome of P. trichocarpa. We demonstrated that RAD sequencing is a powerful technique capable of rapidly generating a large number of SNPs for constructing genetic maps in outbred forest trees. The high-quality linkage maps constructed here provided reliable genetic resources to facilitate locating quantitative trait loci (QTLs) that control growth and wood quality traits in the hybrid population.

Biomass traits and candidate genes for bioenergy revealed through association genetics in coppiced European Populus nigra (L.)

BACKGROUND

Second generation (2G) bioenergy from lignocellulosic feedstocks has the potential to develop as a sustainable source of renewable energy; however, significant hurdles still remain for large-scale commercialisation. Populus is considered as a promising 2G feedstock and understanding the genetic basis of biomass yield and feedstock quality are a research priority in this model tree species.

RESULTS

We report the first coppiced biomass study for 714 members of a wide population of European black poplar (Populus nigra L.), a native European tree, selected from 20 river populations ranging in latitude and longitude between 40.5 and 52.1°N and 1.0 and 16.4°E, respectively. When grown at a single site in southern UK, significant Site of Origin (SO) effects were seen for 14 of the 15 directly measured or derived traits including biomass yield, leaf area and stomatal index. There was significant correlation (p < 0.001) between biomass yield traits over 3 years of harvest which identified leaf size and cell production as strong predictors of biomass yield. A 12 K Illumina genotyping array (constructed from 10,331 SNPs in 14 QTL regions and 4648 genes) highlighted significant population genetic structure with pairwise FST showing strong differentiation (p < 0.001) between the Spanish and Italian subpopulations. Robust associations reaching genome-wide significance are reported for main stem height and cell number per leaf; two traits tightly linked to biomass yield. These genotyping and phenotypic data were also used to show the presence of significant isolation by distance (IBD) and isolation by adaption (IBA) within this population.

CONCLUSIONS

The three associations identified reaching genome-wide significance at p < 0.05 include a transcription factor; a putative stress response gene and a gene of unknown function. None of them have been previously linked to bioenergy yield; were shown to be differentially expressed in a panel of three selected genotypes from the collection and represent exciting, novel candidates for further study in a bioenergy tree native to Europe and Euro-Asia. A further 26 markers (22 genes) were found to reach putative significance and are also of interest for biomass yield, leaf area, epidermal cell expansion and stomatal patterning. This research on European P. nigra provides an important foundation for the development of commercial native trees for bioenergy and for advanced, molecular breeding in these species.

The first genetic linkage map of Eucommia ulmoides

In accordance with pseudo-testcross strategy, the first genetic linkage map of Eucommia ulmoides Oliv. was constructed by an F1 population of 122 plants using amplified fragment length polymorphism (AFLP) markers. A total of 22 AFLP primer combinations generated 363 polymorphic markers. We selected 289 markers segregating as 1:1 and used them for constructing the parent-specific linkage maps. Among the candidate markers, 127 markers were placed on the maternal map LF and 108 markers on the paternal map Q1. The maternal map LF spanned 1116.1 cM in 14 linkage groups with a mean map distance of 8.78 cM; the paternal map Q1 spanned 929.6 cM in 12 linkage groups with an average spacing of 8.61 cM. The estimated coverage of the genome through two methods was 78.5 and 73.9% for LF, and 76.8 and 71.2% for Q1, respectively. This map is the first linkage map of E. ulmoides and provides a basis for mapping quantitative-trait loci and breeding applications.

Model selection for quantitative trait loci mapping in a full-sib family

Statistical methods for mapping quantitative trait loci (QTLs) in full-sib forest trees, in which the number of alleles and linkage phase can vary from locus to locus, are still not well established. Previous studies assumed that the QTL segregation pattern was fixed throughout the genome in a full-sib family, despite the fact that this pattern can vary among regions of the genome. In this paper, we propose a method for selecting the appropriate model for QTL mapping based on the segregation of different types of markers and QTLs in a full-sib family. The QTL segregation patterns were classified into three types: test cross (1:1 segregation), F₂ cross (1:2:1 segregation) and full cross (1:1:1:1 segregation). Akaike’s information criterion (AIC), the Bayesian information criterion (BIC) and the Laplace-empirical criterion (LEC) were used to select the most likely QTL segregation pattern. Simulations were used to evaluate the power of these criteria and the precision of parameter estimates. A Windows-based software was developed to run the selected QTL mapping method. A real example is presented to illustrate QTL mapping in forest trees based on an integrated linkage map with various segregation markers. The implications of this method for accurate QTL mapping in outbred species are discussed.

[Progress on whole genome sequencing in woody plants]

In recent years, the number of sequencing data of plant whole genome have been increasing rapidly and the whole genome sequencing has been also performed widely in woody plants. However, there are a set of obstacles in investigating the whole genome sequencing in woody plants, which include larger genome, complex genome structure, limitations of assembly, annotation, functional analysis, and restriction of the funds for scientific research. Therefore, to promote the efficiency of the whole genome sequencing in woody plants, the development and defect of this field should be analyzed. The three-generation sequencing technologies (i.e., Sanger sequencing, synthesis sequencing, and single molecule sequencing) were compared in our studies. The progress mainly focused on the whole genome sequencing in four woody plants (Populus, Grapevine, Papaya, and Apple), and the application of sequencing results also was analyzed. The future of whole genome sequencing research in woody plants, consisting of material selection, establishment of genetic map and physical map, selection of sequencing technology, bioinformatic analysis, and application of sequencing results, was discussed.

Genome scans for transmission ratio distortion regions in mice

Transmission ratio distortion (TRD) is the departure from the expected genotypic frequencies under Mendelian inheritance. This departure can be due to multiple physiological mechanisms during gametogenesis, fertilization, fetal and embryonic development, and early neonatal life. Although a few TRD loci have been reported in mouse, inheritance patterns have never been evaluated for TRD. In this article, we developed a Bayesian binomial model accounting for additive and dominant deviation TRD mechanisms. Moreover, this model was used to perform genome-wide scans for TRD quantitative trait loci (QTL) on six F2 mouse crosses involving between 296 and 541 mice and between 72 and 1854 genetic markers. Statistical significance of each model was checked at each genetic marker with Bayes factors. Genome scans revealed overdominance TRD QTL located in mouse chromosomes 1, 2, 12, 13, and 14 and additive TRD QTL in mouse chromosomes 2, 3, and 15, although these results did not replicate across mouse crosses. This research contributes new statistical tools for the analysis of specific genetic patterns involved in TRD in F2 populations, our results suggesting a relevant incidence of TRD phenomena in mouse with important implications for both statistical analyses and biological research.

A genetic basis for the manipulation of sink-source relationships by the galling aphid Pemphigus batae

We examined how the galling aphid Pemphigus batae manipulates resource translocation patterns of resistant and susceptible narrowleaf cottonwood Populus angustifolia. Using carbon-14 ((14)C)-labeling experiments in common garden trials, five patterns emerged. First, although aphid galls on resistant and susceptible genotypes did not differ in their capacity to intercept assimilates exported from the leaf they occupied, aphids sequestered 5.8-fold more assimilates from surrounding leaves on susceptible tree genotypes compared to resistant genotypes. Second, gall sinks on the same side of a shoot as a labeled leaf were 3.4-fold stronger than gall sinks on the opposite side of a shoot, which agrees with patterns of vascular connections among leaves of the same shoot (orthostichy). Third, plant genetic-based traits accounted for 26% of the variation in sink strength of gall sinks and 41% of the variation in sink strength of a plant's own bud sinks. Fourth, tree susceptibility to aphid gall formation accounted for 63% of the variation in (14)C import, suggesting strong genetic control of sink-source relationships. Fifth, competition between two galls was observed on a susceptible but not a resistant tree. On the susceptible tree distal aphids intercepted 1.5-fold more (14)C from the occupied leaf than did basal aphids, but basal aphids compensated for the presence of a distal competitor by almost doubling import to the gall from surrounding leaves. These findings and others, aimed at identifying candidate genes for resistance, argue the importance of including plant genetics in future studies of the manipulation of translocation patterns by phytophageous insects.

Potential chromosomal introgression barriers revealed by linkage analysis in a hybrid of Pinus massoniana and P. hwangshanensis

BACKGROUND

Exploring the genetic mechanisms underlying speciation is a hot topic in modern genetics and evolutionary studies. Distortion of marker transmission ratio is frequently ascribed to selection against alleles that cause hybrid incompatibility. The natural introgression between P. massoniana and P. hwangshanensis and their distribution ranges lead to the emergence of the two species as desirable organisms to study the genetic mechanisms for speciation.

RESULTS

Using seeds sampled from trees at different elevations, we consistently detected sharp decreases in seed germination rates of trees in the hybrid zone, which might be due largely to the hybrid incompatibility. A genetic map was established using 192 megagametophytes from a single tree in the hybrid zone of the two species. Segregation distortion analysis revealed that the percentage of significant-segregation-distortion (SSD) markers was extremely high, accounting for more than 25% of the segregating markers. The extension range, the distortion direction, and the distortion intensity of SSD markers also varied dramatically on different linkage groups.

CONCLUSIONS

In this study, we display the potential chromosomal introgression barriers between P. massoniana and P. hwangshanensis. Our study provides a valuable platform for conducting genome-wide association of hybrid incompatible QTLs and/or candidate genes with marker transmission ratio distortion in the hybrid.

High-density linkage mapping and evolution of paralogs and orthologs in Salix and Populus

BACKGROUND

Salix (willow) and Populus (poplar) are members of the Salicaceae family and they share many ecological as well as genetic and genomic characteristics. The interest of using willow for biomass production is growing, which has resulted in increased pressure on breeding of high yielding and resistant clones adapted to different environments. The main purpose of this work was to develop dense genetic linkage maps for mapping of traits related to yield and resistance in willow. We used the Populus trichocarpa genome to extract evenly spaced markers and mapped the orthologous loci in the willow genome. The marker positions in the two genomes were used to study genome evolution since the divergence of the two lineages some 45 mya.

RESULTS

We constructed two linkage maps covering the 19 linkage groups in willow. The most detailed consensus map, S1, contains 495 markers with a total genetic distance of 2477 cM and an average distance of 5.0 cM between the markers. The S3 consensus map contains 221 markers and has a total genetic distance of 1793 cM and an average distance of 8.1 cM between the markers. We found high degree of synteny and gene order conservation between willow and poplar. There is however evidence for two major interchromosomal rearrangements involving poplar LG I and XVI and willow LG Ib, suggesting a fission or a fusion in one of the lineages, as well as five intrachromosomal inversions. The number of silent substitutions were three times lower (median: 0.12) between orthologs than between paralogs (median: 0.37 - 0.41).

CONCLUSIONS

The relatively slow rates of genomic change between willow and poplar mean that the genomic resources in poplar will be most useful in genomic research in willow, such as identifying genes underlying QTLs of important traits. Our data suggest that the whole-genome duplication occurred long before the divergence of the two genera, events which have until now been regarded as contemporary. Estimated silent substitution rates were 1.28 x 10-9 and 1.68 x 10-9 per site and year, which are close to rates found in other perennials but much lower than rates in annuals.

A genetic linkage map for the ectomycorrhizal fungus Laccaria bicolor and its alignment to the whole-genome sequence assemblies

A genetic linkage map for the ectomycorrhizal basidiomycete Laccaria bicolor was constructed from 45 sib-homokaryotic haploid mycelial lines derived from the parental S238N strain progeny. For map construction, 294 simple sequence repeats (SSRs), single-nucleotide polymorphisms (SNPs), amplified fragment length polymorphisms (AFLPs) and random amplified polymorphic DNA (RAPD) markers were employed to identify and assay loci that segregated in backcross configuration. Using SNP, RAPD and SSR sequences, the L. bicolor whole-genome sequence (WGS) assemblies were aligned onto the linkage groups. A total of 37.36 Mbp of the assembled sequences was aligned to 13 linkage groups. Most mapped genetic markers used in alignment were colinear with the sequence assemblies, indicating that both the genetic map and sequence assemblies achieved high fidelity. The resulting matrix of recombination rates between all pairs of loci was used to construct an integrated linkage map using JoinMap. The final map consisted of 13 linkage groups spanning 812 centiMorgans (cM) at an average distance of 2.76 cM between markers (range 1.9-17 cM). The WGS and the present linkage map represent an initial step towards the identification and cloning of quantitative trait loci associated with development and functioning of the ectomycorrhizal symbiosis.

A nonlinear mixed-effect mixture model for functional mapping of dynamic traits

Functional mapping has emerged as a next-generation statistical tool for mapping quantitative trait loci (QTL) that affect complex dynamic traits. In this article, we incorporated the idea of nonlinear mixed-effect (NLME) models into the mixture-based framework of functional mapping, aimed to generalize the spectrum of applications for functional mapping. NLME-based functional mapping, implemented with the linearization algorithm based on the first-order Taylor expansion, can provide reasonable estimates of QTL genotypic-specific curve parameters (fixed effect) and the between-individual variation of these parameters (random effect). Results from simulation studies suggest that the NLME-based model is more general than traditional functional mapping. The new model can be useful for the identification of the ontogenetic patterns of QTL genetic effects during time course.

A dense linkage map of hybrid cottonwood (Populus fremontii × P. angustifolia) contributes to long-term ecological research and comparison mapping in a model forest tree

Cottonwoods are foundation riparian species, and hybridization among species is known to produce ecological effects at levels higher than the population, including effects on dependent species, communities and ecosystems. Because these patterns result from increased genetic variation in key cottonwood traits, novel applications of genetic tools (for example, QTL mapping) could be used to place broad-scale ecological research into a genomic perspective. In addition, linkage maps have been produced for numerous species within the genus, and, coupled with the recent publication of the Populus genome sequence, these maps present a unique opportunity for genome comparisons in a model system. Here, we conducted linkage analyses in order to (1) create a platform for QTL and candidate gene studies of ecologically important traits, (2) create a framework for chromosomal-scale perspectives of introgression in a natural population, and (3) enhance genome-wide comparisons using two previously unmapped species. We produced 246 backcross mapping (BC(1)) progeny by crossing a naturally occurring F(1) hybrid (Populus fremontii x P. angustifolia) to a pure P. angustifolia from the same population. Linkage analysis resulted in a dense linkage map of 541 AFLP and 111 SSR markers distributed across 19 linkage groups. These results compared favorably with other Populus linkage studies, and addition of SSR loci from the poplar genome project provided coarse alignment with the genome sequence. Preliminary applications of the data suggest that our map represents a useful framework for applying genomic research to ecological questions in a well-studied system, and has enhanced genome-wide comparisons in a model tree.

Genetic mapping of developmental instability: design, model and algorithm

Developmental instability or noise, defined as the phenotypic imprecision of an organism in the face of internal or external stochastic disturbances, has been thought to play an important role in shaping evolutionary processes and patterns. The genetic studies of developmental instability have been based on fluctuating asymmetry (FA) that measures random differences between the left and the right sides of bilateral traits. In this article, we frame an experimental design characterized by a spatial autocorrelation structure for determining the genetic control of developmental instability for those traits that cannot be bilaterally measured. This design allows the residual environmental variance of a quantitative trait to be dissolved into two components due to permanent and random environmental factors. The degree of developmental instability is quantified by the relative proportion of the random residual variance to the total residual variance. We formulate a mixture model to estimate and test the genetic effects of quantitative trait loci (QTL) on the developmental instability of the trait. The genetic parameters including the QTL position, the QTL effects, and spatial autocorrelations are estimated by implementing the EM algorithm within the mixture model framework. Simulation studies were performed to investigate the statistical behavior of the model. A live example for poplar trees was used to map the QTL that control root length growth and its developmental instability from cuttings in water culture.

A first linkage map of globe artichoke (Cynara cardunculus var. scolymus L.) based on AFLP, S-SAP, M-AFLP and microsatellite markers

We present the first genetic maps of globe artichoke (Cynara cardunculus var. scolymus L. 2n=2x=34), constructed with a two-way pseudo-testcross strategy. A F1 mapping population of 94 individuals was generated between a late-maturing, non-spiny type and an early-maturing spiny type. The 30 AFLP, 13 M-AFLP and 9 S-SAP primer combinations chosen identified, respectively, 352, 38 and 41 polymorphic markers. Of 32 microsatellite primer pairs tested, 12 identified heterozygous loci in one or other parent, and 7 were fully informative as they segregated in both parents. The female parent map comprised 204 loci, spread over 18 linkage groups and spanned 1330.5 cM with a mean marker density of 6.5 cM. The equivalent figures for the male parent map were 180 loci, 17 linkage groups, 1239.4 and 6.9 cM. About 3% of the AFLP and AFLP-derived markers displayed segregation distortion with a P value below 0.01, and were not used for map construction. All the SSR loci were included in the linkage analysis, although one locus did show some segregation distortion. The presence of 78 markers in common to both maps allowed the alignment of 16 linkage groups. The maps generated provide a firm basis for the mapping of agriculturally relevant traits, which will then open the way for the application of a marker-assisted selection breeding strategy in this species.

A joint model for nonparametric functional mapping of longitudinal trajectory and time-to-event

Background

The characterization of the relationship between a longitudinal response process and a time-to-event has been a pressing challenge in biostatistical research. This has emerged as an important issue in genetic studies when one attempts to detect the common genes or quantitative trait loci (QTL) that govern both a longitudinal trajectory and developmental event.

Results

We present a joint statistical model for functional mapping of dynamic traits in which the event times and longitudinal traits are taken to depend on a common set of genetic mechanisms. By fitting the Legendre polynomial of orthogonal properties for the time-dependent mean vector, our model does not rely on any curve, which is different from earlier parametric models of functional mapping. This newly developed nonparametric model is demonstrated and validated by an example for a forest tree in which stemwood growth and the time to first flower are jointly modelled.

Conclusion

Our model allows for the detection of specific QTL that govern both longitudinal traits and developmental processes through either pleiotropic effects or close linkage, or both. This model will have great implications for integrating longitudinal and event data to gain better insights into comprehensive biology and biomedicine.

A hyperspace model to decipher the genetic architecture of developmental processes: allometry meets ontogeny

To better utilize limited resources for their survival and reproduction, all organisms undergo developmental changes in both body size and shape during ontogeny. The genetic analysis of size change with increasing age, i.e., growth, has received considerable attention in quantitative developmental genetic studies, but the genetic architecture of ontogenetic changes in body shape and its associated allometry have been poorly understood partly due to the lack of analytical tools. In this article, we attempt to construct a multivariate statistical framework for studying the genetic regulation of ontogenetic growth and shape. We have integrated biologically meaningful mathematical functions of growth curves and developmental allometry into the estimation process of genetic mapping aimed at identifying individual quantitative trait loci (QTL) for phenotypic variation. This model defined with high dimensions can characterize the ontogenetic patterns of genetic effects of QTL over the lifetime of an organism and assess the interplay between genetic actions/interactions and phenotypic integration. The closed forms for the residual covariance matrix and its determinant and inverse were derived to overcome the computational complexity typical of our high-dimensional model. We used a worked example to validate the utility of this model. The implications of this model for genetic research of evo-devo are discussed.

A first linkage map of pecan cultivars based on RAPD and AFLP markers

We report here the first genetic linkage maps of pecan [Carya illinoinensis (Wangenh.) K. Koch], using random amplified polymorphic DNA (RAPD) and amplified fragment length polymorphism (AFLP) markers. Independent maps were constructed for the cultivars 'Pawnee' and 'Elliot' using the double pseudo-testcross mapping strategy and 120 F1 seedlings from a full-sib family. A total of 477 markers, including 217 RAPD, 258 AFLP, and two morphological markers were used in linkage analysis. The 'Pawnee' linkage map has 218 markers, comprising 176 testcross and 42 intercross markers placed in 16 major and 13 minor (doublets and triplets) linkage groups. The 'Pawnee' linkage map covered 2,227 cM with an average map distance of 12.7 cM between adjacent markers. The 'Elliot' linkage map has 174 markers comprising 150 testcross and 22 intercross markers placed in 17 major and nine minor linkage groups. The 'Elliot' map covered 1,698 cM with an average map distance of 11.2 cM between adjacent markers. Segregation ratios for dichogamy type and stigma color were not significantly different from 1:1, suggesting that both traits are controlled by single loci with protogyny and green stigmas dominant to protandry and red stigmas. These loci were tightly linked (1.9 cM) and were placed in 'Elliot' linkage group 16. These linkage maps are an important first step towards the detection of genes controlling horticulturally important traits such as nut size, nut maturity date, kernel quality, and disease resistance.

A fast algorithm for functional mapping of complex traits

By integrating the underlying developmental mechanisms for the phenotypic formation of traits into a mapping framework, functional mapping has emerged as an important statistical approach for mapping complex traits. In this note, we explore the feasibility of using the simplex algorithm as an alternative to solve the mixture-based likelihood for functional mapping of complex traits. The results from the simplex algorithm are consistent with those from the traditional EM algorithm, but the simplex algorithm has considerably reduced computational times. Moreover, because of its nonderivative nature and easy implementation with current software, the simplex algorithm enjoys an advantage over the EM algorithm in the dynamic modeling and analysis of complex traits.

Recombination difference between sexes: a role for haploid selection

Why the autosomal recombination rate differs between female and male meiosis in most species has been a genetic enigma since the early study of meiosis. Some hypotheses have been put forward to explain this widespread phenomenon and, up to now, only one fact has emerged clearly: In species in which meiosis is achiasmate in one sex, it is the heterogametic one. This pattern, known as the Haldane-Huxley rule, is thought to be a side effect, on autosomes, of the suppression of recombination between the sex chromosomes. However, this rule does not hold for heterochiasmate species (i.e., species in which recombination is present in both sexes but varies quantitatively between sexes) and does not apply to species lacking sex chromosomes, such as hermaphroditic plants. In this paper, we show that in plants, heterochiasmy is due to a male-female difference in gametic selection and is not influenced by the presence of heteromorphic sex chromosomes. This finding provides strong empirical support in favour of a population genetic explanation for the evolution of heterochiasmy and, more broadly, for the evolution of sex and recombination.

A general framework for analyzing the genetic architecture of developmental characteristics

The genetic architecture of growth traits plays a central role in shaping the growth, development, and evolution of organisms. While a limited number of models have been devised to estimate genetic effects on complex phenotypes, no model has been available to examine how gene actions and interactions alter the ontogenetic development of an organism and transform the altered ontogeny into descendants. In this article, we present a novel statistical model for mapping quantitative trait loci (QTL) determining the developmental process of complex traits. Our model is constructed within the traditional maximum-likelihood framework implemented with the EM algorithm. We employ biologically meaningful growth curve equations to model time-specific expected genetic values and the AR(1) model to structure the residual variance-covariance matrix among different time points. Because of a reduced number of parameters being estimated and the incorporation of biological principles, the new model displays increased statistical power to detect QTL exerting an effect on the shape of ontogenetic growth and development. The model allows for the tests of a number of biological hypotheses regarding the role of epistasis in determining biological growth, form, and shape and for the resolution of developmental problems at the interface with evolution. Using our newly developed model, we have successfully detected significant additive x additive epistatic effects on stem height growth trajectories in a forest tree.

Functional Mapping of Quantitative Trait Loci Underlying Growth Trajectories Using a Transform-Both-Sides Logistic Model

The incorporation of developmental control mechanisms of growth has proven to be a powerful tool in mapping quantitative trait loci (QTL) underlying growth trajectories. A theoretical framework for implementing a QTL mapping strategy with growth laws has been established. This framework can be generalized to an arbitrary number of time points, where growth is measured, and becomes computationally more tractable, when the assumption of variance stationarity is made. In practice, however, this assumption is likely to be violated for age-specific growth traits due to a scale effect. In this article, we present a new statistical model for mapping growth QTL, which also addresses the problem of variance stationarity, by using a transform-both-sides (TBS) model advocated by Carroll and Ruppert (1984, Journal of the American Statistical Association 79, 321-328). The TBS-based model for mapping growth QTL cannot only maintain the original biological properties of a growth model, but also can increase the accuracy and precision of parameter estimation and the power to detect a QTL responsible for growth differentiation. Using the TBS-based model, we successfully map a QTL governing growth trajectories to a linkage group in an example of forest trees. The statistical and biological properties of the estimates of this growth QTL position and effect are investigated using Monte Carlo simulation studies. The implications of our model for understanding the genetic architecture of growth are discussed.

Large-scale heterospecific segregation distortion in Populus revealed by a dense genetic map

We report the most complete genetic map to have been constructed for the genus Populus. This map includes 544 markers mapped onto 19 linkage groups, equivalent to the Populus chromosome number, with all markers displaying internally consistent linkage patterns. We estimate the genome length to be between 2,300 and 2,500 cM, based both on the observed number of crossovers in the maternal haplotypes, as well as the total observed map length. Genome coverage was estimated to be greater than 99.9% at 20 cM per marker. We did not detect obvious recombination repression in the maternal tree (a hybrid of Populus trichocarpa Hooker x P. deltoides Marsh.) compared to the paternal tree (pure P. deltoides). Finally, most markers exhibiting segregation distortion were derived from the donor parent in this backcross, and generally occurred in large contiguous blocks on two linkage groups. We hypothesize that divergent selection has occurred on chromosomal scales among the parental species used to create this pedigree, and explore the evolutionary implications of this observation. This genetic linkage map provides the most comprehensive view of the Populus genome reported to date and will prove invaluable for future inquiries into the structural and functional genomics, evolutionary biology, and genetic improvement of this ecologically important model species.

A likelihood approach for mapping growth trajectories using dominant markers in a phase-unknown full-sib family

Dominant markers have been commonly used in mapping quantitative trait loci (QTLs) in outcrossing species, in which not much prior genome information is available. But the dominant nature of these markers may lead to reduced QTL mapping precision and power. A new statistical method is proposed to incorporate growth laws into a QTL mapping framework, under which the use of the efficiency of dominant markers can be increased. This new method can be used to identify specific QTLs affecting differentiation in growth trajectories, and further estimate the timing of a QTL to turn on, or turn off, affecting growth during the entire ontogeny of a species. Using this method based on dominant markers we have successfully mapped a QTL for stem height growth trajectories to a linkage group in a forest tree. The implications of this method for the understanding of the genetic architecture of growth using dominant markers are discussed.

A General Statistical Framework for Mapping Quantitative Trait Loci in Nonmodel Systems: Issue for Characterizing Linkage Phases

Because of uncertainty about linkage phases of founders, linkage mapping in nonmodel, outcrossing systems using molecular markers presents one of the major statistical challenges in genetic research. In this article, we devise a statistical method for mapping QTL affecting a complex trait by incorporating all possible QTL-marker linkage phases within a mapping framework. The advantage of this model is the simultaneous estimation of linkage phases and QTL location and effect parameters. These estimates are obtained through maximum-likelihood methods implemented with the EM algorithm. Extensive simulation studies are performed to investigate the statistical properties of our model. In a case study from a forest tree, this model has successfully identified a significant QTL affecting wood density. Also, the probability of the linkage phase between this QTL and its flanking markers is estimated. The implications of our model and its extension to more general circumstances are discussed.

Functional mapping for quantitative trait loci governing growth rates: a parametric model

Are there-specific quantitative trait loci (QTL) governing growth rates in biology? This is emerging as an exciting but challenging question for contemporary developmental biology, evolutionary biology, and plant and animal breeding. In this article, we present a new statistical model for mapping QTL underlying age-specific growth rates. This model is based on the mechanistic relationship between growth rates and ages established by a variety of mathematical functions. A maximum likelihood approach, implemented with the EM algorithm, is developed to provide the estimates of QTL position, growth parameters characterized by QTL effects, and residual variances and covariances. Based on our model, a number of biologically important hypotheses can be formulated concerning the genetic basis of growth. We use forest trees as an example to demonstrate the power of our model, in which a QTL for stem growth diameter growth rates is successfully mapped to a linkage group constructed from polymorphic markers. The implications of the new model are discussed.

Nearly complete genetic maps of Pinus sylvestris L. (Scots pine) constructed by AFLP marker analysis in a full-sib family

We have constructed nearly complete linkage maps of Pinus sylvestris (L.) using AFLP markers based on a two-way pseudo-testcross strategy in a full-sib family founded in an advanced breeding program. With 39 primer combinations, a total of 737 markers (320 from the mother and 417 from the father) segregated in a 1:1 ratio, corresponding to DNA polymorphism: heterozygous in one parent and null in the other. In the maternal parent, 188 framework markers were mapped in 12 linkage groups, equivalent to the Pinus haploid chromosome number, with a total coverage of 1,695.5 cM. In the paternal parent, 245 framework markers established a map with 15 linkage groups, spanning a genome length of 1,718.5 cM. The estimated total map length was L(F) = 1,681 cM for the female and L(M) = 1,645 cM for the male using a modified method-of-moment estimator. Combining these values with those estimated from the observed map lengths in both parents, we estimated the genome length in Scots pine to be between 1,600 and 2,100 cM. Our genome coverage was estimated to be more than 98% with a framework marker interval of 20 cM for both parents. Most of the female and male linkage groups were associated through the analysis of the intercross markers.

Functional mapping of quantitative trait loci underlying the character process: a theoretical framework

Unlike a character measured at a finite set of landmark points, function-valued traits are those that change as a function of some independent and continuous variable. These traits, also called infinite-dimensional characters, can be described as the character process and include a number of biologically, economically, or biomedically important features, such as growth trajectories, allometric scalings, and norms of reaction. Here we present a new statistical infrastructure for mapping quantitative trait loci (QTL) underlying the character process. This strategy, termed functional mapping, integrates mathematical relationships of different traits or variables within the genetic mapping framework. Logistic mapping proposed in this article can be viewed as an example of functional mapping. Logistic mapping is based on a universal biological law that for each and every living organism growth over time follows an exponential growth curve (e.g., logistic or S-shaped). A maximum-likelihood approach based on a logistic-mixture model, implemented with the EM algorithm, is developed to provide the estimates of QTL positions, QTL effects, and other model parameters responsible for growth trajectories. Logistic mapping displays a tremendous potential to increase the power of QTL detection, the precision of parameter estimation, and the resolution of QTL localization due to the small number of parameters to be estimated, the pleiotropic effect of a QTL on growth, and/or residual correlations of growth at different ages. More importantly, logistic mapping allows for testing numerous biologically important hypotheses concerning the genetic basis of quantitative variation, thus gaining an insight into the critical role of development in shaping plant and animal evolution and domestication. The power of logistic mapping is demonstrated by an example of a forest tree, in which one QTL affecting stem growth processes is detected on a linkage group using our method, whereas it cannot be detected using current methods. The advantages of functional mapping are also discussed.