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Ratoon rice occupies an important position in rice production owing to its time-saving, labor-saving and low-pollution planting, and increased benefits. However, the impact of tillage management on the yield in rice ratooning system has not yet been reported. Thus, field experiments were carried out to investigate the impact of seven tillage methods on the yield of ratoon rice crop in Jingzhou City in 2021–2022. The managements included winter plowing + rotary 2 times (PTw + RT2) or 3 times (PTw + RT3), spring plowing + rotary 2 times (PTs + RT2) or 3 times (PTs + RT3), no plowing + rotary 2 times (P0 + RT2) or 3 times (P0 + RT3) and no tillage (NT). PTw + RT3 had the highest total rice yield. The experimental data were collected in 2021 and 2022. In terms of main season rice yield, the order of ranking was PTw > PTs ≈ NT ≈ P0, while for ratoon rice yield, the ranking was NT > PTw ≈ PTs > P0. Generally, the root function ranked as PTw > PTs > P0 > NT. The photosynthetic capacity of the main season rice always maximized in PTw, those of the ratoon rice all maximized in NT, and those of both the main season rice and ratoon rice always minimized in P0. In the three tillage modes (PTw, PTs, P0), an additional rotary tillage did not affect the growth or yield of rice. PTw + 3RT was the highest yielding tillage management, but it is still necessary to explore other PTw + 3RT methods and more economical tillage management to increase the yield of ratoon rice. [ABSTRACT FROM AUTHOR]

The growth of forest trees in the relatively young soils of Europe has historically been limited by nitrogen (N). The high anthropogenic N deposition and intense forest management during the last century, however, have caused forest trees in large areas to show signs of being limited by phosphorus (P) or base cations. This indicates that the current situation is not sustainable. The net addition of N to forests here stems from deposition and N fixation, both processes that add N to the topsoil. Phosphorus and cations are released by weathering in the mineral soil. Do European trees have what it takes to efficiently take up P and cation nutrients when they become scarce? Important factors influencing their capacity to take up P and cations are their roots' distribution and function, mycorrhizal distribution and type, and the response of their root and mycorrhizal growth and function to N depositions and nutrient deficiencies. The literature shows that the ability to be limited by something other than nitrogen will be hardest for shallow-rooted conifer trees, followed by ectomycorrhizal deciduous trees; arbuscular mycorrhizal trees will handle the shift best. This knowledge should be incorporated into forest growth models to promote sustainable management decisions. [ABSTRACT FROM AUTHOR]

Drought is a major abiotic stress in mustard. In the present investigation, the interactive effects of rhizobacterium Bacillus sp. MRD-17 and nutrients nitrogen, phosphorus, and potassium (N, P, K), 100% and 50% of the recommended dose of fertiliser (RDF) on shoot-root growth and nutrient uptake by mustard under well-watered (−0.33 bar) and water deficit (−8 bar) conditions were determined. Drought stress for 30 days, reduced root growth, but rhizobacterial inoculation under drought and nutrient stress improved root viability (73%, and 39%, respectively) and architecture, nitrate reductase (20% and 12%, respectively) and glutamine synthetase activity (21% and 14%, respectively), shoot nitrogen, phosphorus, and potassium and seed K content. The protective effects of Bacillus sp. MRD-17 to mustard under drought stress was also accompanied by decreased acid phosphatase activity. However, rhizobacterial and macro-nutrient interactions had no impact on seed N and P content on drought and nutrient-stressed plants. Therefore, in terms of plant growth and nutrient uptake, the efficiency of Bacillus sp. MRD-17 was dependent on the soil nutrient status. Furthermore, rhizobacterial application might facilitate a higher uptake of water and nutrients by the plant from the soil and thus sustain crop productivity under water and nutrient stress scenarios. [ABSTRACT FROM AUTHOR]

Ascorbic acid (AsA) improves plant tolerance against abiotic stresses, but key mechanisms of salt tolerance by its different application modes are obscure. In this study, 5 mM AsA was applied in seed priming (SP), foliar spray (FS) and medium supplementation (MS) modes to explore their comparative effectiveness in improving salinity (170 mM) tolerance in wheat (Triticum aestivum L. cv. Galaxy-2013). For SP, seeds were primed while FS and MS were administered at tillering. One set of plants was harvested 30 days after treatment to record data for growth, pigments, leaf gas exchange and water relations, as well as shoot and root osmolytes accumulation, antioxidative defence and ionic contents. Another set was harvested at ripening to measure grain yield (GY) components. Salinity stress reduced growth, photosynthesis, water relations, antioxidants defence, enhanced free amino acids, soluble sugars, free proline and glycine betaine, hydrogen peroxide and malondialdehyde. The correlations heatmap revealed positive associations among growth, physiological and GY; being stronger in MS mode. All AsA modes reduced salinity damage, but MS was highly promising. Conclusively, maintenance of a balance in reactive oxygen species dousing and antioxidant production following tissue absorption of AsA in diminishing oxidative damage is a plausible mechanism of wheat salt tolerance. [ABSTRACT FROM AUTHOR]

Ratoon rice occupies an important position in rice production owing to its time-saving, labor-saving and low-pollution planting, and increased benefits. However, the impact of tillage management on the yield in rice ratooning system has not yet been reported. Thus, field experiments were carried out to investigate the impact of seven tillage methods on the yield of ratoon rice crop in Jingzhou City in 2021–2022. The managements included winter plowing + rotary 2 times (PTw + RT2) or 3 times (PTw + RT3), spring plowing + rotary 2 times (PTs + RT2) or 3 times (PTs + RT3), no plowing + rotary 2 times (P0 + RT2) or 3 times (P0 + RT3) and no tillage (NT). PTw + RT3 had the highest total rice yield. The experimental data were collected in 2021 and 2022. In terms of main season rice yield, the order of ranking was PTw > PTs ≈ NT ≈ P0, while for ratoon rice yield, the ranking was NT > PTw ≈ PTs > P0. Generally, the root function ranked as PTw > PTs > P0 > NT. The photosynthetic capacity of the main season rice always maximized in PTw, those of the ratoon rice all maximized in NT, and those of both the main season rice and ratoon rice always minimized in P0. In the three tillage modes (PTw, PTs, P0), an additional rotary tillage did not affect the growth or yield of rice. PTw + 3RT was the highest yielding tillage management, but it is still necessary to explore other PTw + 3RT methods and more economical tillage management to increase the yield of ratoon rice.

Abstract The rhizosphere is a nexus for plant–microbe interactions and, as a host-structured environment, a location of high activity for distinct microbes and plant species. Although our insights into this habitat have exploded in recent years, we are still limited in our ability to answer key questions about the specificity of these root-microbial relationships. In particular, it can be difficult to confirm or reject microbiome heritability in many plant systems and to pinpoint which microbial taxa are key to plant functioning. Like other host-structured environments, the rhizosphere is structurally, chemically, and biologically complex, driven largely by differences in root anatomy, location, and function. In this Correspondence, we describe a review of 377 “rhizosphere microbiome” research papers and demonstrate how matching a sampling method to the biological question can advance our understanding of host-microbe interactions in a functionally heterogeneous environment. We found that the vast majority of studies (92%) pool all roots from a root system during sampling, ignoring variation in microbial composition between roots of different function and limiting insight into key root-microbial relationships. Furthermore, approaches for removing root-associated microbes are highly variable and non-standard, complicating multi-study analyses. Our understanding of the strength and nature of host-microbe relationships in heterogenous host-microbiome environments can be clarified by targeting sampling to locations of high interaction. While the high complexity of the rhizosphere creates logistical challenges, we suggest that unambiguous language and refined approaches will improve our ability to match methods to research questions and advance our understanding of the specificity of plant-microbial interactions.

Fine roots are essential for water and nutrient uptake in plants, but little is known about the variation in fine root traits and the underlying mechanisms that drive it. Understanding the responses of fine root function traits to changing environmental conditions and the role of fine root traits as drivers of forest ecosystem processes are critical for informing physiological and ecological theory as well as ecosystem management. We measured morphological and physiological traits of fine roots from six soil layers and three diameter classes in Schrenk's spruce (Picea shrenkiana) forests of the Tianshan mountains, China. We found significant effects of nitrogen addition on these morphological and physiological traits, which varied by soil layer and root diameter. Specifically, specific root length (SRL) was higher in medium N addition group (N2) than in control group (N0). Specific root area (SRA) was higher in the control group (N0) than fertilized groups (N1, N2 and N3). Root tissue density (RTD) was higher in low N addition group (N1) than in the other group. Root dry matter content had no significant difference among four treatment groups. SRL, SRA, and RTD of fine roots in different diameter classes were all significantly different between high N addition (N3) and the control (N0) groups. The physiological characteristics of fine roots showed that soluble sugar (SS), fine root vitality (FRV), and tissue water content (TWC) in different soil layers were higher in the control group than in the fertilized groups. While soluble protein (SP), malondialdehyde (MDA) and free proline (FP) were lower in the control group (N0) than in the fertilized groups. In addition, SS, FRV, SP, TWC, FP, and MDA in all N addition treatments groups were significantly different from the control group. Fine root morphological traits were closely related to physiological traits, and added nitrogen inputs change these correlations. Our study confirms that nitrogen addition has specific effects on the morphological and physiological traits of fine roots of Schrenk's spruce, and the effects of N addition vary according to the amount added.

While improved crop water‐deficit tolerance is considered of primary importance, many phenotyping efforts focusing on quantifying structural root traits make assumptions about architecture representing root function. Therefore, the aim of this study was to quantify whole plant water‐use traits among disparate peanut (Arachis hypogaea L.) genotypes and determine their impact on water‐deficit tolerance. Mini‐rhizotrons were installed to evaluate genotypic root architecture and developmental changes to two irrigation regimes imposed during early development. Following the early‐season irrigation regimes, above‐ and below‐ground traits were studied across a range of soil water conditions through measures of: (a) leaf‐level gas exchange and (b) soil water depletion quantified using a novel soil water probe inserted into mini‐rhizotrons allowing for matched root architecture and soil water depletion measures. While differential water treatments influenced root system architecture development among the genotypes, soil water depletion locations were primarily determined by water availability in the soil profile, not simply by having greater root length at a given soil location. This contradicts the assumption that greater root presence is a consistent indicator of increased root activity. Phenotypic selection of root traits for improving the efficiency of crop water use should consider both structural and functional traits in relation to the intended production environments slated for future cultivar development. [ABSTRACT FROM AUTHOR]

The rhizosphere is a nexus for plant–microbe interactions and, as a host-structured environment, a location of high activity for distinct microbes and plant species. Although our insights into this habitat have exploded in recent years, we are still limited in our ability to answer key questions about the specificity of these root-microbial relationships. In particular, it can be difficult to confirm or reject microbiome heritability in many plant systems and to pinpoint which microbial taxa are key to plant functioning. Like other host-structured environments, the rhizosphere is structurally, chemically, and biologically complex, driven largely by differences in root anatomy, location, and function. In this Correspondence, we describe a review of 377 "rhizosphere microbiome" research papers and demonstrate how matching a sampling method to the biological question can advance our understanding of host-microbe interactions in a functionally heterogeneous environment. We found that the vast majority of studies (92%) pool all roots from a root system during sampling, ignoring variation in microbial composition between roots of different function and limiting insight into key root-microbial relationships. Furthermore, approaches for removing root-associated microbes are highly variable and non-standard, complicating multi-study analyses. Our understanding of the strength and nature of host-microbe relationships in heterogenous host-microbiome environments can be clarified by targeting sampling to locations of high interaction. While the high complexity of the rhizosphere creates logistical challenges, we suggest that unambiguous language and refined approaches will improve our ability to match methods to research questions and advance our understanding of the specificity of plant-microbial interactions. [ABSTRACT FROM AUTHOR]

Alternate tillage (AT) has the potential to reduce inputs and improve soil quality and crop yield, but there has been no research on the effect of AT on soil and wheat in a rice–wheat rotation system. In this study, field experiments were conducted to examine the effects of four tillage management methods (conventional tilling (CT) in each crop (RCT–WCT), no tilling (NT) in rice and conventional tilling in wheat (RNT–WCT, AT1), conventional tilling in rice and no tilling in wheat (RCT–WNT, AT2), and no tilling in each crop (RNT–WNT)) on the physical properties of soil, wheat growth, and yield. At the 0–5 cm soil layer, CT in the wheat season increased bulk density (BD) and decreased total properties, but it decreased BD at the 5–40 cm soil layer, and the effect of RCT–WCT was significantly greater than that of RNT–WCT. CT in the wheat season increased the root activity, root dry weight, net photosynthetic rate, leaf area index, antioxidant enzyme activities, and yield, and there was no significant effect between RCT–WCT and RNT–WCT. RNT-WCT has the potential to reduce inputs and maintain wheat yields. [ABSTRACT FROM AUTHOR]

Fine root anatomy plays an important role in understanding the relationship between fine root function and soil environment. However, in different soil environments, the variation of fine root anatomical structure in different root sequences is not well studied. We measured the soil conditions and anatomical structure characteristics (root diameter, cortical tissue, vascular tissue and xylem) of fine roots of Cupressus funebris in four experimental sites, and analyzed each level of fine roots separately. We link these data to understand the relationship between fine root anatomy and soil conditions. We found that the anatomical structure of fine roots is closely related to soil environmental factors. The fine roots of lower root order are mainly affected by soil nutrients. Among them, the cortical tissue of first-order fine roots was positively correlated with potassium and phosphorus, but negatively correlated with nitrogen, while second- and thirdorder fine roots was positively correlated with soil total potassium and negatively correlated with nitrogen and phosphorus. For the fine roots of high root order, the cortical tissue disappeared, and the secondary vascular tissue was mainly affected by soil moisture. In addition, we also found that the division of fine root functional groups is not fixed. On the one hand, the function of third-order fine roots will slip. For example, the decrease of soil moisture will promote the transformation of third-order fine roots into transport roots, and the reduction of nitrogen will promote the transformation of third-order fine roots into absorption roots to fix nitrogen. This transformation strategy can effectively prevent the restriction of soil nutrients on plant growth. On the other hand, with the change of habitat, the first- and second-order fine roots are still the absorbing root, and the fourth- and fifth-order fine roots are still the transport root, but the efficiency of absorption and transport will be affected. In conclusion, our findings emphasize the fine roots in different soil environment to show high levels of plasticity, shows that fine root anatomical structure changes may make plants, and reveals that the fine is just order of reaction and its mechanism in the soil environment. [ABSTRACT FROM AUTHOR]

The rice–ratoon rice cropping system has the advantages of saving labor and imparting economic benefits. Optimizing tillage and straw management is beneficial for improving ratoon rice growth and yield. In this study, field experiments were conducted to examine the effects of four tillage and straw managements on the growth and yield of a rice–ratoon rice cropping system in central China in 2020 to 2021. The managements included no-till with main-season and ratoon-season rice residues retained on the soil's surface (NT+S), plow tillage with residue retention (CT+S), no-till with residues removed (NT-S), and plow tillage with residues removed (CT-S). Compared to NT, CT significantly increased yield by 33.70% and 29.12% in the main and ratoon seasons, respectively. Compared to straw removal, straw returning significantly increased yield by 13.37% and 27.29% in the main and ratoon seasons, respectively. In general, both CT and straw returning improved root function (root activity and root dry weight) and photosynthetic capacity (leaf area index, net photosynthetic rate, and leaf chlorophyll content). CT combined with straw returning was able to achieve the highest annual rice yield. [ABSTRACT FROM AUTHOR]

In the article, the spectral properties of a multipoint problem for a differential operator equation of order $2n$ are studied. The operator of the problem has an infinite number of multiple eigenvalues. Each multiple eigenvalue corresponds to a finite set of root functions. A commutative group of transmutation operators is constructed. Each element of the group corresponds to the isospectral perturbation of the problem operator with antiperiodic conditions. The conditions for the existence and uniqueness of the solution are established for the selected family of multipoint problems, and this solution is constructed too.

Conservation tillage is an environmentally friendly and economical farming method, but its impact on rice yield is controversial. Artificially applied side deep fertilizing of machine-transplanted rice is when fertilizer is applied to the deep soil along with the machine transplantation of rice; this may improve the fertilizer utilization rate and rice yield and eliminate the possible negative effects of conservation tillage on rice yield. Using on machine-transplanted rice, this study aims to compare the effects of side deep fertilizing (SDF). We investigated the effects of artificially applying fertilizer (AAF) on rice growth and yield under conventional tillage (CT), reduced tillage (RT), and no tillage (NT). The rice root activity, root dry weight, leaf area index (LAI), net photosynthetic rate (Pn), chlorophyll content, panicle density, spikelets per panicle, and yield were all ranked as NT > RT > CT and SDF > AAF. The 1000-grain weight was also ranked as SDF > AAF. In addition, under NT conditions, the positive effect of SDF on rice growth and yield was higher than under RT and CT conditions. In general, conservation tillage combined with SDF saved costs and increased rice yield. [ABSTRACT FROM AUTHOR]

Preliminary studies observed a lower growth activity during the vegetative stage with higher growth attributes at the pod-filling stage among the high nitrogen (N) utilisation efficiency (NUtE) oilseed rape (Brassica napus L.) genotypes, compared with the low NUtE genotypes. Therefore, we hypothesised that there would exist a critical growth stage when distinctive phenotypic traits are exhibited to regulate yield formation and NUE. A field experiment and a hydroponic culture were conducted to characterise the differences in shoot and root physiological indicators of the high and low NUtE oilseed rape genotypes at seedling, bud, bolting, flowering and pod-filling stages. We found that flowering was the critical period when the reverse growth habit occurred between high and low NUtE genotypes. The high NUtE genotypes displayed larger values of root traits, stronger N uptake kinetics parameters, higher activity of leaf glutamine synthetase (GS) and glutamate synthetase (GOGAT), larger SPAD values and net photosynthetic rate, ultimately leading to higher seed yield and NUE. Our results indicate that flowering is the critical growth stage to distinguish the high from low NUtE oilseed rape genotypes, and plant breeders may focus on selecting root and shoot phenotypic traits from flowering stage onwards to achieve both high yields and NUE for oilseed rape genotypes. [ABSTRACT FROM AUTHOR]

Conservation tillage is an environmentally friendly and economical farming method, but its impact on rice yield is controversial. Artificially applied side deep fertilizing of machine-transplanted rice is when fertilizer is applied to the deep soil along with the machine transplantation of rice; this may improve the fertilizer utilization rate and rice yield and eliminate the possible negative effects of conservation tillage on rice yield. Using on machine-transplanted rice, this study aims to compare the effects of side deep fertilizing (SDF). We investigated the effects of artificially applying fertilizer (AAF) on rice growth and yield under conventional tillage (CT), reduced tillage (RT), and no tillage (NT). The rice root activity, root dry weight, leaf area index (LAI), net photosynthetic rate (Pn), chlorophyll content, panicle density, spikelets per panicle, and yield were all ranked as NT > RT > CT and SDF > AAF. The 1000-grain weight was also ranked as SDF > AAF. In addition, under NT conditions, the positive effect of SDF on rice growth and yield was higher than under RT and CT conditions. In general, conservation tillage combined with SDF saved costs and increased rice yield.

We study a nonlocal problem for ordinary differential equations of 2 ⁢ n {2n} -order with involution. Spectral properties of the operator of this problem are analyzed and conditions for the existence and uniqueness of its solution are established. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis. [ABSTRACT FROM AUTHOR]

The root is the main organ through which water and mineral nutrients enter the plant organism. In addition, root fulfils several other functions. Here, we propose that the root also performs the barrier function, which is essential not only for plant survival but for plant acclimation and adaptation to a constantly changing and heterogeneous soil environment. This function is related to selective uptake and avoidance of some soil compounds at the whole plant level. We review the toolkit of morpho-anatomical, structural, and other components that support this view. The components of the root structure involved in selectivity, permeability or barrier at a cellular, tissue, and organ level and their properties are discussed. In consideration of the arguments supporting barrier function of plant roots, evolutionary aspects of this function are also reviewed. Additionally, natural variation in selective root permeability is discussed which suggests that the barrier function is constantly evolving and is subject of natural selection. Plant roots perform important functions anchoring the plant and providing it with minerals and water. At the same time, they are involved in selective uptake and avoidance of certain soil compounds and thus accomplish barrier function which is not considered in the contemporary literature. In this critical review, we analyse the toolkit of morpho-anatomical, structural, and other components which operate at a cellular, tissue, and organ level that support the view that the root as organ fulfils barrier function. [ABSTRACT FROM AUTHOR]

Fine roots are essential for water and nutrient uptake in plants, but little is known about the variation in fine root traits and the underlying mechanisms that drive it. Understanding the responses of fine root function traits to changing environmental conditions and the role of fine root traits as drivers of forest ecosystem processes are critical for informing physiological and ecological theory as well as ecosystem management. We measured morphological and physiological traits of fine roots from six soil layers and three diameter classes in Schrenk’s spruce (Picea shrenkiana) forests of the Tianshan mountains, China. We found significant effects of nitrogen addition on these morphological and physiological traits, which varied by soil layer and root diameter. Specifically, specific root length (SRL) was higher in medium N addition group (N2) than in control group (N0). Specific root area (SRA) was higher in the control group (N0) than fertilized groups (N1, N2 and N3). Root tissue density (RTD) was higher in low N addition group (N1) than in the other group. Root dry matter content had no significant difference among four treatment groups. SRL, SRA, and RTD of fine roots in different diameter classes were all significantly different between high N addition (N3) and the control (N0) groups. The physiological characteristics of fine roots showed that soluble sugar (SS), fine root vitality (FRV), and tissue water content (TWC) in different soil layers were higher in the control group than in the fertilized groups. While soluble protein (SP), malondialdehyde (MDA) and free proline (FP) were lower in the control group (N0) than in the fertilized groups. In addition, SS, FRV, SP, TWC, FP, and MDA in all N addition treatments groups were significantly different from the control group. Fine root morphological traits were closely related to physiological traits, and added nitrogen inputs change these correlations. Our study confirms that nitrogen addition has specific effects on the morphological and physiological traits of fine roots of Schrenk’s spruce, and the effects of N addition vary according to the amount added.

We study a nonlocal multipoint problem for an ordinary differential equation of even order with coefficients containing an involution operator. The spectral properties of a self-adjoint operator with boundary conditions generalizing the conditions of antiperiodicity are investigated. For a differential equation of even order, we consider a problem with multipoint conditions that are perturbations of self-adjoint boundary conditions. We study cases when multipoint conditions include boundary conditions that are regular, but not strongly regular according to Birkhoff, or irregular. The eigenvalues and elements of the system of the root functions of the operator of the problem are determined. It is proved that the system is complete and contains an infinite number of associated functions. Sufficient conditions are obtained for which this system is a Riesz basis. Similar results are obtained for the operator generated by the multipoint problem for an ordinary differential equation of even order with coefficients containing the involution operator. [ABSTRACT FROM AUTHOR]

• Background and Aims Temporal flooding is a common environmental stress for terrestrial plants. Aquatic adventitious roots (aquatic roots) are commonly formed in flooding-tolerant plant species and are generally assumed to be beneficial for plant growth by supporting water and nutrient uptake during partial flooding. However, the actual contribution of these roots to plant performance under flooding has hardly been quantified. As the investment into aquatic root development in terms of carbohydrates may be costly, these costs may - depending on the specific environmental conditions - offset the beneficial effects of aquatic roots. This study tested the hypothesis that the balance between potential costs and benefits depends on the duration of flooding, as the benefits are expected to outweigh the costs in long-term but not in short-term flooding. • Methods The contribution of aquatic roots to plant performance was tested in Solanum dulcamara during 1-4 weeks of partial submergence and by experimentally manipulating root production. Nutrient uptake by aquatic roots, transpiration and photosynthesis were measured in plants differing in aquatic root development to assess the specific function of these roots. • Key Results As predicted, flooded plants benefited from the presence of aquatic roots. The results showed that this was probably due to the contribution of roots to resource uptake. However, these beneficial effects were only present in long-term but not in short-term flooding. This relationship could be explained by the correlation between nutrient uptake and the flooding duration-dependent size of the aquatic root system. • Conclusions The results indicate that aquatic root formation is likely to be selected for in habitats characterized by long-term flooding. This study also revealed only limited costs associated with adventitious root formation, which may explain the maintenance of the ability to produce aquatic roots in habitats characterized by very rare or short flooding events. [ABSTRACT FROM AUTHOR]

The operator ℒ generated by a linear ordinary differential expression of nth order and regular boundary conditions of general form is considered on a closed interval. The characteristic determinant of the spectral problem for the operator ℒ, where ℒ is an operator with the integral perturbation of one of its boundary conditions, is constructed, assuming that the unperturbed operator ℒ possesses a system of eigenfunctions and associated functions generating an unconditional basis in L (0, 1). Using the obtained formula, we derive conclusions about the stability or instability of the unconditional basis properties of the system of eigenfunctions and associated functions of the problem under an integral perturbation of the boundary condition. The Samarskii-Ionkin problem with integral perturbation of its boundary condition is used as an example of the application of the formula. [ABSTRACT FROM AUTHOR]

Breeders have seldom considered the selection for root traits during the genetic improvement in soybean. It is hypothesized that grain yield would be increased by the root function improvement, especially for the current cultivars. The objective of this grafting experiment was to determine the effect of record-yield cultivars L14 or Z35 as rootstocks on agronomic traits of cultivars released in different decades. A total of 11 cultivars, released in different decades, were used to graft onto L14 or Z35 rootstocks. The agronomic traits were measured in the pot-culture experiments. Grafting cultivars released in different decades onto L14 or Z35 rootstocks resulted in higher yield, 100-seed mass and apparent harvest index as compared with those of non-grafted or self-grafted plants. Grain yield gain of cultivars grafted onto record-yield cultivar rootstocks was 0.40 g/plant/year from 1966 to 2006, which was larger than that of non-grafts and self-grafts (0.27 g/plant/year). The yield of current cultivars should increase more if their root functions were improved. [ABSTRACT FROM AUTHOR]

Understanding the fundamental mechanistic processes within large environmental models has great implications in model interpretation and future improvement. However, obtaining a good understanding of these processes can be challenging due to the complexities in model structures and software configurations. This paper introduces a functional test framework - with unique approaches to tackling software complexities in large environmental models – to facilitate process-based model exploration and validation. A Virtual Ecosystem Dynamic Model is developed as a case study to better understand and validate root-related processes in the Community Land Model (CLM). The proposed framework could help empiricists better access the inner workings of large environmental models, and facilitate integrative collaborations among broad scientific communities including field scientists, environmental system modelers, and computer scientists. [ABSTRACT FROM AUTHOR]

This article is a Commentary on Jiang et al. (2020), 225: 222–233. [ABSTRACT FROM AUTHOR]