Tukey's Depth for Object Data.

We develop a novel exploratory tool for non-Euclidean object data based on data depth, extending celebrated Tukey's depth for Euclidean data. The proposed metric halfspace depth, applicable to data objects in a general metric space, assigns to data points depth values that characterize the centrality of these points with respect to the distribution and provides an interpretable center-outward ranking. Desirable theoretical properties that generalize standard depth properties postulated for Euclidean data are established for the metric halfspace depth. The depth median, defined as the deepest point, is shown to have high robustness as a location descriptor both in theory and in simulation. We propose an efficient algorithm to approximate the metric halfspace depth and illustrate its ability to adapt to the intrinsic data geometry. The metric halfspace depth was applied to an Alzheimer's disease study, revealing group differences in the brain connectivity, modeled as covariance matrices, for subjects in different stages of dementia. Based on phylogenetic trees of 7 pathogenic parasites, our proposed metric halfspace depth was also used to construct a meaningful consensus estimate of the evolutionary history and to identify potential outlier trees.

A genetic tradeoff for tolerance to moderate and severe heat stress in US hybrid maize.

Global climate change is increasing both average temperatures and the frequencies of extreme high temperatures. Past studies have documented a strong negative effect of exposures to temperatures >30°C on hybrid maize yields. However, these studies could not disentangle genetic adaptation via artificial selection from changes in agronomic practices. Because most of the earliest maize hybrids are no longer available, side-by-side comparisons with modern hybrids under current field conditions are generally impossible. Here, we report on the collection and curation of 81 years of public yield trial records covering 4,730 maize hybrids, which enabled us to model genetic variation for temperature responses among maize hybrids. We show that selection may have indirectly and inconsistently contributed to the genetic adaptation of maize to moderate heat stress over this time period while preserving genetic variance for continued adaptation. However, our results reveal the existence of a genetic tradeoff for tolerance to moderate and severe heat stress, leading to a decrease in tolerance to severe heat stress over the same time period. Both trends are particularly conspicuous since the mid-1970s. Such a tradeoff poses challenges to the continued adaptation of maize to warming climates due to a projected increase in the frequency of extreme heat events. Nevertheless, given recent advances in phenomics, enviromics, and physiological modeling, our results offer a degree of optimism for the capacity of plant breeders to adapt maize to warming climates, assuming appropriate levels of R&D investment.

Discriminating features of ground reaction forces in overweight old and young adults during walking using functional principal component analysis.

BACKGROUND: Limited attention has been paid to age- or body size-related changes in the ground reaction forces (GRF) during walking despite their strong associations with lower limb injuries and pathology. RESEARCH QUESTION: Do the features of GRF during walking associate with age or body size? METHODS: Fifty-four participants were subdivided into four groups according to their age and body size: overweight old (n = 12), non-overweight old (n = 13), overweight young (n = 13), and non-overweight young (n = 16). Participants were asked to walk at their self-selected speeds on level ground with force plates embedded in the center of walkway. Functional principal component analysis (FPCA) was performed to extract major modes of variation and functional principal component scores (FPCs) in three-dimensional GRFs. Analysis of variance models were employed to investigate the effect of age, body size, or their interactions on the FPCs of each component of the GRF, with the adjustment to gait speed. RESULTS: Significant age and body size effects were observed in FPC1 across all three-dimensional GRF. Both overweight and older groups showed greater braking force after heel-strike and greater propulsive forces during pre-swing when compared to the non-overweight and younger groups, respectively. The overweight old group displayed greater medial forces during mid-stance and the overweight young group showed prominently larger medial forces during pre-swing, while non-overweight old showed a tendency of flatter medial-lateral GRF waveforms during the entire stance phase. FPC2 revealed that only body size had an effect on three-dimensional GRF with the highest FPC2 scores in the overweight old group. SIGNIFICANCE: Three-dimensional GRF during walking could be altered by the body size and age, which were more pronounced in the overweight and older group. The more dynamic GRF pattern with greater and/or lower peaks could be contributing factors to the increased joint load and injury rates observed in overweight aged individuals.

Modeling sparse longitudinal data on Riemannian manifolds.

Modern data collection often entails longitudinal repeated measurements that assume values on a Riemannian manifold. Analyzing such longitudinal Riemannian data is challenging, because of both the sparsity of the observations and the nonlinear manifold constraint. Addressing this challenge, we propose an intrinsic functional principal component analysis for longitudinal Riemannian data. Information is pooled across subjects by estimating the mean curve with local Fréchet regression and smoothing the covariance structure of the linearized data on tangent spaces around the mean. Dimension reduction and imputation of the manifold-valued trajectories are achieved by utilizing the leading principal components and applying best linear unbiased prediction. We show that the proposed mean and covariance function estimates achieve state-of-the-art convergence rates. For illustration, we study the development of brain connectivity in a longitudinal cohort of Alzheimer's disease and normal participants by modeling the connectivity on the manifold of symmetric positive definite matrices with the affine-invariant metric. In a second illustration for irregularly recorded longitudinal emotion compositional data for unemployed workers, we show that the proposed method leads to nicely interpretable eigenfunctions and principal component scores. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database.

Correction to: Recombination between homoeologous chromosomes induced in durum wheat by the Aegilops speltoides Su1-Ph1 suppressor.

Unfortunately, the 9th author name was incorrectly published in the original publication. The complete correct name is given below.

Recombination between homoeologous chromosomes induced in durum wheat by the Aegilops speltoides Su1-Ph1 suppressor.

KEY MESSAGE: Su1-Ph1, which we previously introgressed into wheat from Aegilops speltoides, is a potent suppressor of Ph1 and a valuable tool for gene introgression in tetraploid wheat. We previously introgressed Su1-Ph1, a suppressor of the wheat Ph1 gene, from Aegilops speltoides into durum wheat cv Langdon (LDN). Here, we evaluated the utility of the introgressed suppressor for inducing introgression of alien germplasm into durum wheat. We built LDN plants heterozygous for Su1-Ph1 that simultaneously contained a single LDN chromosome 5B and a single Ae. searsii chromosome 5Sse, which targeted them for recombination. We genotyped 28 BC1F1 and 84 F2 progeny with the wheat 90-K Illumina single-nucleotide polymorphism assay and detected extensive recombination between the two chromosomes, which we confirmed by non-denaturing fluorescence in situ hybridization (ND-FISH). We constructed BC1F1 and F2 genetic maps that were 65.31 and 63.71 cM long, respectively. Recombination rates between the 5B and 5Sse chromosomes were double the expected rate computed from their meiotic pairing, which we attributed to selection against aneuploid gametes. Recombination rate between 5B and 5Sse was depressed compared to that between 5B chromosomes in the proximal region of the long arm. We integrated ND-FISH signals into the genetic map and constructed a physical map, which we used to map a 172,188,453-bp Ph1 region. Despite the location of the region in a low-recombination region of the 5B chromosome, we detected three crossovers in it. Our data show that Su1-Ph1 is a valuable tool for gene introgression and gene mapping based on recombination between homoeologous chromosomes in wheat.

Longitudinal associations between white matter maturation and cognitive development across early childhood.

From birth to 5 years of age, brain structure matures and evolves alongside emerging cognitive and behavioral abilities. In relating concurrent cognitive functioning and measures of brain structure, a major challenge that has impeded prior investigation of their time-dynamic relationships is the sparse and irregular nature of most longitudinal neuroimaging data. We demonstrate how this problem can be addressed by applying functional concurrent regression models (FCRMs) to longitudinal cognitive and neuroimaging data. The application of FCRM in neuroimaging is illustrated with longitudinal neuroimaging and cognitive data acquired from a large cohort (n = 210) of healthy children, 2-48 months of age. Quantifying white matter myelination by using myelin water fraction (MWF) as imaging metric derived from MRI scans, application of this methodology reveals an early period (200-500 days) during which whole brain and regional white matter structure, as quantified by MWF, is positively associated with cognitive ability, while we found no such association for whole brain white matter volume. Adjusting for baseline covariates including socioeconomic status as measured by maternal education (SES-ME), infant feeding practice, gender, and birth weight further reveals an increasing association between SES-ME and cognitive development with child age. These results shed new light on the emerging patterns of brain and cognitive development, indicating that FCRM provides a useful tool for investigating these evolving relationships.

Aegilops tauschii Genome Sequence: A Framework for Meta-analysis of Wheat QTLs.

Numerous quantitative trait loci (QTL) have been mapped in tetraploid and hexaploid wheat and wheat relatives, mostly with simple sequence repeat (SSR) or single nucleotide polymorphism (SNP) markers. To conduct meta-analysis of QTL requires projecting them onto a common genomic framework, either a consensus genetic map or genomic sequence. The latter strategy is pursued here. Of 774 QTL mapped in wheat and wheat relatives found in the literature, 585 (75.6%) were successfully projected onto the Aegilops tauschii pseudomolecules. QTL mapped with SNP markers were more successfully projected (92.2%) than those mapped with SSR markers (66.2%). The QTL were not distributed homogeneously along chromosome arms. Their frequencies increased in the proximal-to-distal direction but declined in the most distal regions and were weakly correlated with recombination rates along the chromosome arms. Databases for projected SSR markers and QTL were constructed and incorporated into the Ae. tauschii JBrowse. To facilitate meta-QTL analysis, eight clusters of QTL were used to estimate standard deviations ([Formula: see text]) of independently mapped QTL projected onto the Ae. tauschii genome sequence. The standard deviations [Formula: see text] were modeled as an exponential decay function of recombination rates along the Ae. tauschii chromosomes. We implemented four hypothesis tests for determining the membership of query QTL. The hypothesis tests and estimation procedure for [Formula: see text] were implemented in a web portal for meta-analysis of projected QTL. Twenty-one QTL for Fusarium head blight resistance mapped on wheat chromosomes 3A, 3B, and 3D were analyzed to illustrate the use of the portal for meta-QTL analyses.

Age-dynamic networks and functional correlation for early white matter myelination.

The maturation of the myelinated white matter throughout childhood is a critical developmental process that underlies emerging connectivity and brain function. In response to genetic influences and neuronal activities, myelination helps establish the mature neural networks that support cognitive and behavioral skills. The emergence and refinement of brain networks, traditionally investigated using functional imaging data, can also be interrogated using longitudinal structural imaging data. However, few studies of structural network development throughout infancy and early childhood have been presented, likely owing to the sparse and irregular nature of most longitudinal neuroimaging data, which complicates dynamic analysis. Here, we overcome this limitation and investigate through concurrent correlation the co-development of white matter myelination and volume, and structural network development of white matter myelination between brain regions as a function of age, using statistically well-supported methods. We show that the concurrent correlation of white matter myelination and volume is overall positive and reaches a peak at 580 days. Brain regions are found to differ in overall magnitudes and patterns of time-varying association throughout early childhood. We introduce time-dynamic developmental networks based on temporal similarity of association patterns in the levels of myelination across brain regions. These networks reflect groups of brain regions that share similar patterns of evolving intra-regional connectivity, as evidenced by levels of myelination, are biologically interpretable and provide novel visualizations of brain development. Comparing the constructed networks between different maternal education groups, we found that children with higher and lower maternal education differ significantly in the overall magnitude of the time-dynamic correlations.

Birth and Death of LTR-Retrotransposons in Aegilops tauschii.

Long terminal repeat-retrotransposons (LTR-RTs) are a major component of all flowering plant genomes. To analyze the time dynamics of LTR-RTs, we modeled the insertion rates of the 35 most abundant LTR-RT families in the genome of Aegilops tauschii, one of the progenitors of wheat. Our model of insertion rate (birth) takes into account random variation in LTR divergence and the deletion rate (death) of LTR-RTs. Modeling the death rate is crucial because ignoring it would underestimate insertion rates in the distant past. We rejected the hypothesis of constancy of insertion rates for all 35 families and showed by simulations that our hypothesis test controlled the false-positive rate. LTR-RT insertions peaked from 0.064 to 2.39 MYA across the 35 families. Among other effects, the average age of elements within a family was negatively associated with recombination rate along a chromosome, with proximity to the closest gene, and weakly associated with the proximity to its 5' end. Elements within a family that were near genes colinear with genes in the genome of tetraploid emmer wheat tended to be younger than those near noncolinear genes. We discuss these associations in the context of genome evolution and stability of genome sizes in the tribe Triticeae. We demonstrate the general utility of our models by analyzing the two most abundant LTR-RT families in Arabidopsis lyrata, and show that these families differed in their insertion dynamics. Our estimation methods are available in the R package TE on CRAN.

Structural variation and rates of genome evolution in the grass family seen through comparison of sequences of genomes greatly differing in size.

Homology was searched with genes annotated in the Aegilops tauschii pseudomolecules against genes annotated in the pseudomolecules of tetraploid wild emmer wheat, Brachypodium distachyon, sorghum and rice. Similar searches were performed with genes annotated in the rice pseudomolecules. Matrices of collinear genes and rearrangements in their order were constructed. Optical BioNano genome maps were constructed and used to validate rearrangements unique to the wild emmer and Ae. tauschii genomes. Most common rearrangements were short paracentric inversions and short intrachromosomal translocations. Intrachromosomal translocations outnumbered segmental intrachromosomal duplications. The densities of paracentric inversion lengths were approximated by exponential distributions in all six genomes. Densities of collinear genes along the Ae. tauschii chromosomes were highly correlated with meiotic recombination rates but those of rearrangements were not, suggesting different causes of the erosion of gene collinearity and evolution of major chromosome rearrangements. Frequent rearrangements sharing breakpoints suggested that chromosomes have been rearranged recurrently at some sites. The distal 4 Mb of the short arms of rice chromosomes Os11 and Os12 and corresponding regions in the sorghum, B. distachyon and Triticeae genomes contain clusters of interstitial translocations including from 1 to 7 collinear genes. The rates of acquisition of major rearrangements were greater in the large wild emmer wheat and Ae. tauschii genomes than in the lineage preceding their divergence or in the B. distachyon, rice and sorghum lineages. It is suggested that synergy between large quantities of dynamic transposable elements and annual growth habit have been the primary causes of the fast evolution of the Triticeae genomes.

Genome sequence of the progenitor of the wheat D genome Aegilops tauschii.

Aegilops tauschii is the diploid progenitor of the D genome of hexaploid wheat (Triticum aestivum, genomes AABBDD) and an important genetic resource for wheat. The large size and highly repetitive nature of the Ae. tauschii genome has until now precluded the development of a reference-quality genome sequence. Here we use an array of advanced technologies, including ordered-clone genome sequencing, whole-genome shotgun sequencing, and BioNano optical genome mapping, to generate a reference-quality genome sequence for Ae. tauschii ssp. strangulata accession AL8/78, which is closely related to the wheat D genome. We show that compared to other sequenced plant genomes, including a much larger conifer genome, the Ae. tauschii genome contains unprecedented amounts of very similar repeated sequences. Our genome comparisons reveal that the Ae. tauschii genome has a greater number of dispersed duplicated genes than other sequenced genomes and its chromosomes have been structurally evolving an order of magnitude faster than those of other grass genomes. The decay of colinearity with other grass genomes correlates with recombination rates along chromosomes. We propose that the vast amounts of very similar repeated sequences cause frequent errors in recombination and lead to gene duplications and structural chromosome changes that drive fast genome evolution.