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A central question in sea-state modeling is the role that various physical effects have on the evolution of the statistical properties of random sea states. This becomes a critical issue when one is concerned with the likelihood of rare events such as rogue, or freak, waves which can have significant destructive potential on deep sea ships and other offshore structures. In this paper then, using a recently derived higher-order model of deep water nonlinear waves, we examine the impact of constant vorticity currents on the statistical properties of nonlinearly evolving random sea states. As we show, these currents can both decrease and increase the kurtosis of the affiliated distributions of the sea states, thereby diminishing or enhancing the likelihood of rare events. We likewise numerically study the relationship between the kurtosis and a non-dimensional parameter, the Benjamin–Feir Index, which has proven to be a useful measure of when rare events are likely in oceanographic application.

Developing crops with better root systems is a promising strategy to ensure productivity in both optimum and stress environments. Root system architectural traits in 397 soybean accessions were characterized and a high-density single nucleotide polymorphisms (SNPs)-based genome-wide association study was performed to identify the underlying genes associated with root structure. SNPs associated with root architectural traits specific to landraces and elite germplasm pools were detected. Four loci were detected in landraces for lateral root number (LRN) and distribution of root thickness in diameter Class I with a major locus on chromosome 16. This major loci was detected in the coding region of unknown protein, and subsequent analyses demonstrated that root traits are affected with mutated haplotypes of the gene. In elite germplasm pool, 3 significant SNPs in alanine-glyoxalate aminotransferase, Leucine-Rich Repeat receptor/No apical meristem, and unknown functional genes were found to govern multiple traits including root surface area and volume. However, no major loci were detected for LRN in elite germplasm. Nucleotide diversity analysis found evidence of selective sweeps around the landraces LRN gene. Soybean accessions with minor and mutated allelic variants of LRN gene were found to perform better in both water-limited and optimal field conditions.

Some crops inhibit shoot growth but maintain root growth under water-deficit conditions. Unraveling the molecular mechanisms of root plasticity under water deficit conditions in plants remains a major challenge. We developed an efficient platform for identifying core transcription factors (TFs) that collectively regulate each other and/or themselves in response to water stress, and exploring their interconnected regulatory circuitry involved in root growth maintenance under water deficit in soybean. We performed multi-species phylogenetic footprinting combined with spatial-temporal transcriptome analysis of soybean (Glycine max) roots under water deficit to identify conserved motifs that function in the water-stress response. Using these functional conserved cis-motifs, we applied a new approach to trace back motifs-associated core TFs ingroup as signal mediators, which mediate signaling between abiotic and endogenous stimuli. We integrated a co-functional TF–TF network and conserved motif-centered TF–DNA networks to construct a core TF network defined by mutual cross-regulation among core TFs. We found that core TF ARG (Abscisic acid response element binding factor-like Root Growth regulator) represses BRG (Brassinosteroid enhanced expression-like Root Growth regulator) expression through binding to its promoter at a conserved binding site. ARG and BRG antagonistically regulate Phytochrome-interacting factor-like Root Growth regulator (PRG) and combinatorially regulate some other core TFs. These core TFs form complex regulatory circuits to integrate light and multiple hormone signaling pathways and maintain root growth in response to varying degrees of water stress. Our study provides valuable information to unravel the complicated mechanisms of molecular networks involved in the regulation of root growth under water deficit.

The root angle and fibrous root score determines soybean [Glycine max (L.) Merr.] productivity in water-limited environments. Studying root traits in the field is technically difficult to do nondestructively, and varying agroclimatic and edaphic factors create challenges, which could be circumvented using laboratory-based root studies with higher precision. In this study, we developed and validated a nondestructive root imaging platform and derived three-dimensional (3D) root features using algorithms that would predict the root response under field conditions. Nine soybean genotypes (five landrace accessions and four cultivars) were evaluated at seedling and reproductive stages in controlled environments and the field. Irrespective of the phenotyping platforms, soybean landraces showed higher phenotypic variation for different root architectural traits than cultivars. The plant introductions 200471 and 567731 had higher phenotypic values for root and shoot traits than cultivars Dunbar, Magellan, and Maverick. The seedling 3D root features—volume and surface area/volume ratio—were found to be the best predictors of field root response evaluated. This positive association is a promising step in using a nondestructive imaging system to screen soybean with a desired root system that matches different target environments. Thus, the selection based on accurate 3D root features will hasten the inclusion of root traits in soybean breeding programs specifically to improve productivity in harsh environments.

Limited information is available for soybean root traits and their plasticity under drought stress. To date, no studies have focused on examining diverse soybean germplasm for regulation of shoot and root response under water limited conditions across varying soil types. In this study, 17 genetically diverse soybean germplasm lines were selected to study root response to water limited conditions in clay (trial 1) and sandy soil (trial 2) in two target environments. Physiological data on shoot traits was measured at multiple crop stages ranging from early vegetative to pod filling. The phenotypic root traits, and biomass accumulation data are collected at pod filling stage. In trial 1, the number of lateral roots and forks were positively correlated with plot yield under water limitation and in trial 2, lateral root thickness was positively correlated with the hill plot yield. Plant Introduction (PI) 578477A and 088444 were found to have higher later root number and forks in clay soil with higher yield under water limitation. In sandy soil, PI458020 was found to have a thicker lateral root system and higher yield under water limitation. The genotypes identified in this study could be used to enhance drought tolerance of elite soybean cultivars through improved root traits specific to target environments.

Limited information is available for soybean root traits and their plasticity under drought stress. To date, no studies have focused on examining diverse soybean germplasm for regulation of shoot and root response under water limited conditions across varying soil types. In this study, 17 genetically diverse soybean germplasm lines were selected to study root response to water limited conditions in clay (trial 1) and sandy soil (trial 2) in two target environments. Physiological data on shoot traits was measured at multiple crop stages ranging from early vegetative to pod filling. The phenotypic root traits, and biomass accumulation data are collected at pod filling stage. In trial 1, the number of lateral roots and forks were positively correlated with plot yield under water limitation and in trial 2, lateral root thickness was positively correlated with the hill plot yield. Plant Introduction (PI) 578477A and 088444 were found to have higher later root number and forks in clay soil with higher yield under water limitation. In sandy soil, PI458020 was found to have a thicker lateral root system and higher yield under water limitation. The genotypes identified in this study could be used to enhance drought tolerance of elite soybean cultivars through improved root traits specific to target environments.

Background Root system architecture is important for water acquisition and nutrient acquisition for all crops. In soybean breeding programs, wild soybean alleles have been used successfully to enhance yield and seed composition traits, but have never been investigated to improve root system architecture. Therefore, in this study, high-density single-feature polymorphic markers and simple sequence repeats were used to map quantitative trait loci (QTLs) governing root system architecture in an inter-specific soybean mapping population developed from a cross between Glycine max and Glycine soja. Results Wild and cultivated soybean both contributed alleles towards significant additive large effect QTLs on chromosome 6 and 7 for a longer total root length and root distribution, respectively. Epistatic effect QTLs were also identified for taproot length, average diameter, and root distribution. These root traits will influence the water and nutrient uptake in soybean. Two cell division-related genes (D type cyclin and auxin efflux carrier protein) with insertion/deletion variations might contribute to the shorter root phenotypes observed in G. soja compared with cultivated soybean. Based on the location of the QTLs and sequence information from a second G. soja accession, three genes (slow anion channel associated 1 like, Auxin responsive NEDD8-activating complex and peroxidase), each with a non-synonymous single nucleotide polymorphism mutation were identified, which may also contribute to changes in root architecture in the cultivated soybean. In addition, Apoptosis inhibitor 5-like on chromosome 7 and slow anion channel associated 1-like on chromosome 15 had epistatic interactions for taproot length QTLs in soybean. Conclusion Rare alleles from a G. soja accession are expected to enhance our understanding of the genetic components involved in root architecture traits, and could be combined to improve root system and drought adaptation in soybean. Electronic supplementary material The online version of this article (doi:10.1186/s12864-015-1334-6) contains supplementary material, which is available to authorized users.

Highlight Altering root xylem developmental plasticity by increasing the number of vessels and decreasing their diameter enhances water uptake and reduces yield loss in soybean under water-limited conditions., We tested the hypothesis that increasing the number of metaxylem vessels would enhance the efficiency of water uptake in soybean (Glycine max) and decrease the yield gap in water-limited environments. A panel of 41 soybean accessions was evaluated in greenhouse, rainout shelter, and rain-fed field environments. The metaxylem number influenced the internal capture of CO2 and improved stomatal conductance, enhancing water uptake/use in soybeans exposed to stress during the reproductive stage. We determined that other root anatomical features, such as cortex cell area and the percentage of stele that comprised cortical cells, also affected seed yield under similar growth parameters. Seed yield was also impacted by pod retention rates under drought stress (24–80 pods/plant). We surmise that effective biomass allocation, that is, the transport of available photosynthates to floral structures at late reproductive growth stages (R6–R7), enables yield protection under drought stress. A mesocosm study of contrasting lines for yield under drought stress and root anatomical features revealed that increases in metaxylem number as an adaptation to drought in the high-yielding lines improved root hydraulic conductivity, which reduced the metabolic cost of exploring water in deeper soil strata and enhanced water transport. This allowed the maintenance of shoot physiological processes under water-limited conditions.

Drought and its interaction with high temperature are the major abiotic stress factors affecting soybean yield and production stability. Ongoing climate changes are anticipated to intensify drought events, which will further impact crop production and food security. However, excessive water also limits soybean production. The success of soybean breeding programmes for crop improvement is dependent on the extent of genetic variation present in the germplasm base. Screening for natural genetic variation in drought- and flooding tolerance-related traits, including root system architecture, water and nitrogen-fixation efficiency, and yield performance indices, has helped to identify the best resources for genetic studies in soybean. Genomic resources, including whole-genome sequences of diverse germplasms, millions of single-nucleotide polymorphisms, and high-throughput marker genotyping platforms, have expedited gene and marker discovery for translational genomics in soybean. This review highlights the current knowledge of the genetic diversity and quantitative trait loci associated with root system architecture, canopy wilting, nitrogen-fixation ability, and flooding tolerance that contributes to the understanding of drought- and flooding-tolerance mechanisms in soybean. Next-generation mapping approaches and high-throughput phenotyping will facilitate a better understanding of phenotype-genotype associations and help to formulate genomic-assisted breeding strategies, including genomic selection, in soybean for tolerance to drought and flooding stress.