Background: The Aldehyde dehydrogenase 2 (ALDH2) mutant genotypes contain an allele encoding defective ALDH2 with reduced efficacy of alcohol metabolism leading to accumulation of highly toxic and carcinogenic acetaldehyde. It can induce unpleasant “Asian flush syndrome” and associate with increased risk of cancers. However, to date, little is known about ALDH2 genotypes in relation to the postoperative prognosis of hepatocellular carcinoma (HCC).Methods: From 2002 to 2012, 419 HCC patients receiving surgical resection of HCC were enrolled for ALDH2-rs671 genotyping and outcome correlation.Results: Of the patients included, 202 were ALDH2-rs671 “GG” (wild type) and 217 were mutant (defective) “AA” + “GA” genotype. Kaplan-Meier analysis indicated that “GG” genotype significantly associated with shorter metastasis-free (P = 0.034) and overall (P = 0.005) survival, but not recurrence-free survival (P = 0.281). Univariate followed by multivariate Cox proportional hazard analysis showed that “GG” genotype was an independent clinical predictor for shorter time-to-distant metastasis (adjusted P = 0.019) and shorter overall survival (adjusted P = 0.001). Subgroup analysis showed that in patients with negative hepatitis B surface antigen, Edmonson's histology grade < 3, and aspartate transaminase > alanine transaminase, the ALDH2-rs671-GG genotype was associated with both shorter time-to-metastasis and shorter overall survival.Conclusions: HCC patients carrying a defective allele of ALDH2 had a favorable postoperative outcome. Hepatocellular carcinoma (HCC), the major histological subtype of primary liver cancer, ranks the fifth most commonly diagnosed solid cancer in men and the seventh in women as well as the third leading cause of cancer-related death worldwide aldehyde dehydrogenase 2 gene (ALDH2), encodes a mitochondrial enzyme, which is the key enzyme responsible for alcohol metabolism. It contains two alternative alleles (rs617 - “G” or “A”) correlated with differential efficacy of alcohol metabolism ALDH2 have an enzyme possessing greatly reduced ability to metabolize acetaldehyde, which can reach to as low as 17-50% of the wild type. These individuals accumulate acetaldehyde when consuming alcohol, suffer from alcohol intolerance symptoms, but therefore carry a decreased risk for alcohol dependence ALDH2 genotype in the disease progression and the postoperative prognosis of HCC remains largely unstudied.Alcohol is oxidized to acetaldehyde by alcohol dehydrogenase, which in turn is oxidized to acetate by aldehyde dehydrogenase. The ALDH2 genotype associated with the postoperative outcome of HCC.In the present study, we aimed to investigate whether the This was a retrospective cohort study approved by the institutional review board, Chang Gung Medical Center, Taoyuan, Taiwan. In total, 419 consecutive HCC patients receiving surgical resection of liver tumors from 2002 to 2012 with available liver tissues in Chang Gung Medical Center, Taoyuan, Taiwan, were included. At our institute, all HCC patients must be evaluated before and after surgery to ensure that a clean margin of more than 1 cm was obtained. More importantly, the diagnosis of HCC was confirmed by the pathological results of surgical specimens. Therefore, the inclusion criteria included pathological diagnosis of HCC, curative resection, no anticancer therapy received before the surgery, complete clinicopathological data, regular follow‑up, and reliable medical records. The exclusion criteria included pregnancy, questionable pathological diagnosis of HCC, and other co‑existing malignancies prior to HCC resection. All samples were frozen to - 70° C immediately after surgical operation and stored in Tissue Bank, Chang Gung Medical Center until used. The clinicopathological data were retrospectively reviewed, including gender, age, HBV surface antigen (HBsAg), antibody against HCV (anti-HCV), alcoholism, liver cirrhosis status, presence of ascites on surgery, Edmonson's histology grading, microvascular invasion, macrovascular invasion, presence of tumor capsule, number of tumor, largest tumor size, alpha-fetoprotein (AFP), albumin, bilirubin, prothrombin time, creatinine, aspartate aminotransferase (AST), alanine aminotransferase (ALT), date of surgical resection, date of tumor recurrence or metastasis, and date of last follow-up or HCC related death.Alcoholism in this study was defined as documented daily alcohol consumption > 40 g/day for males or > 20 g/day for female, over a period of > 10 years, combined with psychological and physical dependence.ALDH2-rs671 SNP was performed on genomic DNA extracted from the liver tissues  using QIAamp DNA Mini kits . Primers were designed to amplify the region of ALDH2 gene containing the variant rs671. To ensure that specific amplicons were correctly amplified, nested PCR was carried out by using primers: (a) 5′- TAAAGACTTTGGGGCAATACAGG -3′, (b) 5′- CCCAGCAAATGACCGCATA -3′, (c) 5′- AAGAGTGATTTCTGCAATCTCG -3′, and (d) 5′-CCTCAGTATTTCTCATGGGAC -3′. The first amplification reaction mixture contained DNA (5 µl), the primers (a) and (b) , the Taq DNA pol 2.0 master mix red  and double-distilled water (19.5 µl). Temperature for the PCR procedure was set at 95° C for an initial denaturation of 5 min, followed by 35 cycles of denaturation-annealing-extension procedure at 94° C, 580 C and 72° C, respectively, holding denaturation and annealing temperature for 1 min and extension temperature for 3 min in a cycle. The procedure was then followed by a final extension with a temperature of 72°C for 10 min. Then, 5 μl of the first PCR products were used for amplification with the nested primers (c) and (d) for 35 cycles . An aliquot of water was included for parallel PCR amplification in each batch, as a negative control. Finally, conventional Sanger sequencing was performed for direct sequence reads of ALDH2 genotype.Genotyping of the Dichotomized data was expressed as numbers and ratios (%) and compared by use of Chi-square test or Fisher's exact tests, where appropriate. Parametric data was expressed as mean ± standard deviation and compared by use of two-sample t-test or the Mann-Whitney U-test, where appropriate. Overall survival was calculated from the date of surgery to the date of death or last follow-up. Time to recurrence or distant metastasis was calculated from the date of surgery to the date of recurrence or distant metastasis, respectively. Univariate and multivariate Cox proportional hazard models were used to estimate survivals for clinicopathological and genotypic variables. In this study, significant factors identified from univariate analysis were included for multivariate Cox proportional hazards. The Kaplan-Meier method was used to estimate the survival probability between the different genotype groups, and the log-rank test was used to compare the survivals. All tests were two-tailed, and a P < 0.05 was considered statistically significant. All statistical analyses were performed using Statistical Package for the Social Sciences (SPSS) statistics Version 20 .ALDH2 “GG” genotype. Their basic clinicopathological and genotypic characteristics were summarized in Table Of the 419 patients included, 202 were ALDH2 “GG” and “non-GG” (“AA” + “GA”) genotype was shown in Table A detailed comparison of all clinicopathological features between HCC patients carrying ALDH2 genotype , microvascular invasion (P < 0.001), macrovascular invasion (P = 0.006), larger tumor size (P = 0.017), and higher AFP (P = 0.003) remained as independent predictors for a shorter time-to-distant metastasis.Cox proportional hazard model was thus used to examine the association between clinical factors and time-to-distant metastasis after surgical resection of HCC Table . UnivariALDH2 “GG” genotype, presence of ascites on surgery, microvascular invasion, macrovascular invasion, higher tumor number, larger tumor size, albumin, and AST were significantly associated with shorter overall survival. After adjusted for other confounding factors, ALDH2 “GG” genotype (P = 0.001), presence of ascites on surgery (P = 0.021), microvascular invasion (P = 0.011), and higher AST (P = 0.019) remained to be independent predictors for a shorter overall survival.Similarly, Cox proportional hazard model was used to examine the association between clinical factors and overall survival after surgical resection of HCC Table . UnivariALDH2-GG genotype was associated with unfavorable postoperative outcomes, we divided patients into different clinical subgroups for further analysis . In Taiwan and many Asian countries, heavy alcohol drinking maybe needed on social occasions but not necessarily developed into a drinking habit. Most of these patients had AST > ALT and negative HBsAg. When diagnosed as HCC, patients with ALDH2-“AA” or “GA” genotype could easily abstain from the social-occasion-associated alcohol drinking (because of intolerance), whereas patients with ALDH2-“GG” were less likely to abstain themselves, partly because of established alcoholic addiction  were significantly outcome predictors. Out results argued that after HCC had developed, forced abstention from alcohol was needed for patients with ALDH2 “GG” genotype.Viral hepatitis plays a predominant role in the etiology and prognosis of HCC because of the high prevalence rate of chronic HBV or HCV infection in Asia ALDH2 genotype, and the results are inconsistent. The mutant genotype of ALDH2 may have direct or indirect impacts to be implicated in the development of HCC, whether or not it is combined with viral hepatitis or alcohol ingestion ALDH2 mutant genotype may instead have protective effect, while ALDH2 wild genotype serves as a predictor for HCC development ALDH2 mutant genotype has only limited  contribution for the risk of HCC ALDH2 genotype as an effective predictor for postoperative prognosis in HCC, but not as a risk factor for HCC development. Importantly, wild type ALDH2 can effectively metabolize alcohol and thus less likely to accumulate carcinogenic acetaldehyde. Therefore, one would expect that ALDH2 wild type should be associated with a better postoperative prognosis. However, our data argued against this view. According to our subgroup analysis, we believed that both ALDH2 genotypes and changes of drinking behavior after HCC resection were important determinants for postoperative prognosis (with the latter more important). As such, in patients receiving HCC surgical treatment, it is recommended to check the ALDH2 genotype and to give alcohol abstinence order to those with wild type ALDH2-“GG”.Many previous studies have focused on the relationship between HCC occurrence and ALDH2-“GG” (wild type). Compared to the “non-GG” mutant genotype, the HCC recurrence incidence of the “GG” genotype was borderline significantly higher . However, the “GG” genotype demonstrated no significantly difference for the incidence of distant metastasis and overall survival, albeit numerically higher . Taken together, despite that these patients were in a more advanced stage of cirrhosis, ALDH2-“GG” (wild type) still associated with a poorer prognosis (higher recurrence).In order to further decipher our findings, we had conducted a small-scale validation study in which 87 adult patients were enrolled, who were diagnosed as HCC and received curative radiofrequency ablation therapies owing to unsuitable for operation (with more advanced stages of cirrhosis). Of the 87 patients included, 45 (51.7%) were ALDH2 “GG” genotype is an independent predictor for shorter overall survival and metastasis-free survival in HCC patients treated by surgical resection.In conclusion, we have discovered that


In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold. We also show that a strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional curvature has negative Kodaira dimension under an extra condition. In this paper, we study the holomorphic sectional curvature of complex Finsler manifolds  with semi-positive but not identically zero holomorphic sectional curvature one has that For a compact Kähler manifold with positive holomorphic sectional curvature, Yau  gave a aG, there is a canonical (Finslerian) tensorM, For any strongly pseudoconvex complex Finsler metric t}V∗ see ). By takM, G) be a compact strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional curvature, and satisfy Let ::(F3): A F A F19]) G is called strongly pseudoconvex if F4): is called a (strongly pseudoconvex) complex Finsler manifold if G is a (strongly pseudoconvex) complex Finsler metric.Moreover, M is naturally a strongly pseudoconvex complex Finsler metric on it.Clearly, any Hermitian metric on G.We write, 18) The The18]) M, G) as follows.Let G at , 4) The  The 4]) G is a strongly pseudoconvex complex Finsler metric on M, then there is a canonical h-v decomposition of the holomorphic tangent bundle If M)o o .2.1G be a strongly pseudoconvex complex Finsler metric on M. One has, 18) Let Let18]) M with G, one can also define the holomorphic sectional curvature byP(TM). In this case, the two kinds of definitions for holomorphic sectional curvature coincide. More precisely, one hasFor the holomorphic vector bundle G is a strongly pseudoconvex complex Finsler metric on M, then() V on M, there exists a -type vector X such that Kobayashi pseudo-distanceM.For any tangent vector M is said to be Kobayashi hyperbolic if the pseudo-distance A complex manifold As a simple application, we have the following interesting result.N. In particular, N is Kobayashi hyperbolic., 18) Let Let18]) r-disc N is Kobayashi hyperbolic. We equip the M, G) is semi-positive but not identically zero, i.e., In this section, we assume that the holomorphic sectional curvature of a strongly pseudoconvex complex Finsler manifold ..M, G) isL a relative ample line bundle over L such that m denotes the dimension of fibers. For any smooth function Let L with For any smooth metric E is a holomorphic vector bundle. In fact, for any point p, then E. So E is a holomorphic vector bundle.The geodesic curvature E. SetL with Following Berndtsson cf. –9), we d, we d9])The following theorem actually was proved by Berndtsson [E, where  is a local coordinate system of TM with respect to the natural frame Recall that (P(TM) byMoreover, the natural projectionL and local frame G be a strongly pseudoconvex complex Finsler metric on M, it induces a metric on M. From (L byLet (-1). By , there eOn Without loss of generality, we may assume that has from ,4.16\docDenotewhereFor any ave from \documentCombining  with Lemk in n variables. Therefore, the sections of It is known that g one can always reduce to the case in which g one can always consider the Hermitian metricM, the two scalar curvatures are defined byBy , 4.19),,4.19), a side of , 4.17),,4.20\docg and   g and  be a strongly pseudoconvex complex Finsler metric which satisfies (Let (atisfies . If \doch and g on M such thatM. The same proof as in [By Proposition


In the present paper, we study a new kind of Kantorovich–Stancu type operators. For this modified form, we discuss a uniform convergence estimate. Some Voronovskaja-type theorems are given. Let }m∈N. In , D.D. Stynomials .When m byL.V. Kantorovich  introducombining  and (ii) We have thatFor anythere exists a constantindependent ofmandx, such thatfor everyFirst we havem, can be found in [The following inequalityfound in  for \doc) and in  for \docTaking ‾c(i) in , by (2.2p). From . □The first four central moments for (i)m and x such thatFor any (ii)m and x such thatFor any (iii)From (i) and (ii) it followsUsing the results obtained by Gavrea and Ivan  in . □Assume that Consequently, we getand from , it follNow, we can formulate a new quantitative Voronovskaja-type result:Forfixed, we have the following estimate:whereCis a positive constant independent ofmandx.m and x such that (Under the above assumptions, by applying Taylor’s formula to the operators Forfixed, we haveBy Theorem Forthe following estimate holds:whereis the uniform norm onSince We can reformulate Theorem Assumingforandwe haveK-functionalThe operators , and by , we haveIn this paper, we introduce and study a modified form of the Kantorovich–Stancu operators.


Interpretation of δ13C and δ15N values, however, is influenced by factors such as sample lipid content, tissue-specific isotope discrimination, and tissue turnover rates, which are typically species- and tissue-specific. In this study, we generated lipid normalization models for δ13C and investigated the effects of chemical lipid extractions on δ13C and δ15N in Pacific walrus (Odobenus rosmarus divergens) muscle, liver, and skin. We also evaluated tissue-specific isotope discrimination in walrus muscle, liver, skin, and bone collagen. Mean δ13Clipid-free of skin and bone collagen were similar, as were mean δ15N of muscle and liver. All other tissues differed significantly for both isotopes. Differences in δ13Clipid-free and δ15N among tissues agreed with published estimates of marine mammal tissue-specific isotope discrimination factors, with the exception of skin. The results of this work will allow researchers to gain a clearer understanding of walrus diet and the structure of Arctic food webs, while also making it possible to directly compare the results of contemporary walrus isotope research with those of historic and paleoecological studies.Analysis of stable carbon and nitrogen isotope values (δ Carbon and nitrogen stable isotope values (δ13C and δ15N) are particularly useful when evaluating animal diet and trophic position3. Consumer δ13C is driven mainly by the type of primary production at the base of the food web, as uptake of CO2 for use in photosynthesis involves discrimination of carbon isotopes5. Trophic discrimination of 13C is typically small (~1‰ per trophic level), but accounts for some variation in stable carbon isotope values3. In contrast, variability in δ15N is strongly influenced by trophic discrimination, which results in an increase of ~3.0‰ per trophic level6. By interpreting δ13C and δ15N values from animal tissues in the context of these sources of isotopic discrimination, information can be inferred about diet, trophic position, and the flow of energy through biological systems.Stable isotope analysis is widely-used as a tool to study animal movements, diet, and food web structure13C and 15N can complicate reconstructions of animal diet and trophic position. For example, discrimination against the heavier 13C during lipid synthesis results in differences of ~6–8‰ between lipids and proteins8. Lipid content therefore affects tissue δ13C and may lead to observed variability in δ13C among animals resulting from differences in lipid storage, rather than diet. Because lipids are not always homogenously distributed within a tissue9, lipid content can be an important source of isotopic variability even among multiple samples of a single tissue from one individual10. Furthermore, δ13C varies among fatty acids12, thus the δ13C of lipids depends on their fatty acid composition and uneven distribution of different types of lipids within a tissue may lead to heterogeneity in δ13C.Additional processes that result in discrimination of 14) and stable isotope values of the lipid-free sample are measured. This process allows for direct instrumental measurement of the lipid-free sample (δ13Clipid-free), but requires more time and effort. Additionally, in some  cases, chemical lipid extraction can alter sample δ15N by removing amino acids17. Thus, to ensure comparable measurements of both δ13C and δ15N across tissues, it is recommended that two aliquots of each sample be analyzed: one non-lipid extracted (bulk) and the other with lipids removed17. The δ15N value of the non-lipid extracted aliquot (δ15Nbulk) and the δ13Clipid-free can then be interpreted together; however, this approach increases the time and effort required for sample preparation and doubles the analytical cost.Chemical lipid extraction is one way to account for differences in sample lipid content. In this process, lipids are typically removed using polar organic solvents , and the difference between δ13C values of the lipid-free and non-lipid extracted aliquots of each sample (δ13Clipid-free − δ13Cbulk = Δδ13C). This relationship tends to be species- and tissue-specific, thus, one limitation of lipid normalization models is that they must be parameterized for each species and tissue by performing chemical lipid extractions and comparing δ13Cbulk to δ13Clipid-free. Consequently, there are many species and tissues for which lipid normalization models are not available in the literature.Lipid normalization is an alternative to chemical lipid extraction that allows δ13C and δ15N values. Stable isotope values in the tissues of an individual animal may vary substantially due to metabolic discrimination and differences in tissue composition19. Additionally, the degree of δ13C and δ15N discrimination between an animal’s diet and its tissues may be impacted by diet quality . Finally, metabolic routing of different diet components  impacts diet-tissue isotope discrimination and may mean that some tissues primarily reflect individual diet components , while others may be representative of whole diet21. Diet-tissue discrimination has been studied in a variety of animals and varies widely among species22. Thus, as with lipid normalization models, species- and tissue-specific discrimination factors are not currently available for many species.Tissue-specific isotope discrimination is another source of variability in stable isotope values that can impact diet reconstructions and the interpretation of δ13C and δ15N of different tissues of individual animals, is critical for adequate interpretation of stable isotope studies. Furthermore, quantifying the degree of tissue-specific isotope discrimination allows researchers to more directly compare the results of studies analyzing δ13C and δ15N in different tissues. This is particularly valuable for comparing modern studies, which typically sample soft tissues, to studies of historic and paleoecology, for which bone collagen is the primary tissue available for analysis23. It is also important because analyses of various soft tissues provide different advantages. For many vertebrates, skin can be obtained using a biopsy, which is typically non-lethal and relatively non-invasive25. Muscle is often analyzed because this tissue has relatively slow metabolic turnover, can provide diet information over a period of weeks or months, and is the most commonly used vertebrate tissue in the published stable isotope literature27. Tissues with more rapid metabolic turnover rates can provide shorter-term information about diet, and are particularly informative when analyzed in tandem with tissues that turn over more slowly. Blood has a rapid turnover rate26, but obtaining it can be logistically difficult for some animals . Liver also exhibits high metabolic turnover26, and can provide short-term diet information. Collection of liver samples can be logistically challenging, but may be feasible in instances where proper sampling and storage of blood are not.Understanding diet-tissue discrimination, as well as the relationships between δ29. Stable isotopes may provide a useful tool for understanding these changes. Examining δ13C and δ15N in marine mammal tissues can not only provide insight into the diet and movements of the animals themselves, but can also give important information about the food webs in which these animals feed8. Arctic marine mammals, including Pacific walruses (Odobenus rosmarus divergens), are important subsistence resources for Alaska Native communities, and monitoring the responses of these animals to climate change is critical to food security in the region. The overarching goal of this study was to address some of the factors that might confound the interpretation of stable isotope values in the tissues of Pacific walruses, with the goal of improving the ability of future research to draw conclusions about these animals and the food webs in which they feed. To accomplish this, δ13C and δ15N in walrus muscle, liver, skin, and bone collagen were analyzed to (1) assess the importance of lipid removal when comparing δ13C of various walrus tissues, (2) parameterize lipid normalization models for estimating Δδ13C based on C:Nbulk, and (3) estimate tissue-specific discrimination factors for Pacific walruses.Arctic marine mammals are ideal candidates for stable isotopic research. Biological systems in the Arctic have been historically understudied, and are currently undergoing rapid changes associated with warming of the regional climate13C and δ15N. Samples were collected in the field  by Alaska Native subsistence hunters using guidelines developed by researchers at the Alaska Department of Fish and Game (ADF&G). At the time of harvest, skin, blubber and muscle were collected in a single, full-thickness sample, and a single, large section of the liver was taken. These tissues were frozen and shipped to ADF&G, in Fairbanks, Alaska, before being transferred to the University of Alaska Fairbanks, where they were stored at −80 °C. Bone samples were also collected by subsistence hunters at the time of harvest. Samples consisted mostly of cranium and mandible fragments; however, the skeletal element from which a sample was taken was not always identifiable. Samples that appeared to come from distal limb bones  were not used for this study, as the stable isotope values of these bones may not be representative of the skeleton as a whole30. Bones were cleaned of adherent tissue with a wire brush, dried, and stored at room temperature. All tissues used in this study were obtained under a letter of authorization to L. Horstmann from the United States Fish and Wildlife Service.Skin, muscle, liver, and bone samples were collected from 30 adult walruses  taken as part of the Alaska Native subsistence harvests on St. Lawrence Island, Alaska, from 2014–2016. Additional muscle (n = 95), liver (n = 5), and skin (n = 5) samples from the 2012–2016 subsistence harvests were analyzed to generate mathematical lipid-corrections and test the effects of chemical lipid extraction on δ® grinding mill. Hair was typically relatively sparse on the skin samples, and surface hair was removed with a razor blade prior to homogenization. Any remaining pieces of hair were typically resistant to homogenization, thus remained intact and could be avoided during subsampling. Homogenized samples were divided into two equal parts. A 0.2–0.4 mg subsample was taken from one half and submitted for stable isotope analysis. The other half was lipid-extracted using methods modified from Folch et al.14 and Bligh and Dyer13. Briefly, samples were immersed in 2:1 chloroform:methanol and mixed thoroughly using a vortex mixer. Samples were then allowed to sit for 15 minutes before they were centrifuged and the chloroform:methanol was removed by pipet. This process was repeated until the supernatant remained clear, at which point samples were allowed to air dry overnight. A 0.2–0.4 mg subsample of the lipid-extracted sample was then submitted for stable isotope analysis.In preparation for stable isotope analysis, ~10 g of each soft tissue was subsampled, freeze-dried for 48 hours, and homogenized using a Wig-L-Buget al. (2009)31, as modified from Matheus (1995)32. A ~0.4 g subsample of solid, cortical bone was removed from each specimen using handheld cutting tools, cleaned in a sonic bath, and allowed to air dry for 1–2 days. Lipids were removed by soaking the bone in 2:1 chloroform:methanol for 8 hours and discarding the solvent. The mineral component of the bone was then removed using a mixture of 6N hydrochloric acid and ultrapure water. After demineralization, the sample was gelatinized at 65 °C, filtered through a 0.45 μm filter to remove any insoluble particles and non-collagen organic compounds, and freeze-dried. A 0.2–0.4 mg subsample of the resulting purified collagen was submitted for stable isotope analysis.Collagen was extracted from bone samples using the methods described by Misarti 13C: −15.8‰, δ15N: 7.0‰, %C: 44.3, %N: 15.3) was analyzed as a check standard after every 10 samples to estimate uncertainty. Precision  of these analyses was ±0.1‰ for both δ13C and δ15N, based on repeated measurements of this standard across all analytical runs (n = 81). Measurements were accurate (±1 SD) to within ±0.03‰ for δ13C and ±0.05‰ for δ15N, based on differences between observed and known values of the peptone standard. Sample composition (%C and %N) was measured during stable isotope analysis, and was used to calculate the C:N ratio of the sample using the formula:Stable carbon and nitrogen isotope values of tissue samples were analyzed in the Alaska Stable Isotope Facility at the University of Alaska Fairbanks, using a Costech ECS 4010 elemental analyzer and ThermoScientific Conflo IV, interfaced with a ThermoScientific DeltaV isotope ratio mass spectrometer. Stable isotopic compositions were calibrated relative to Vienna Pee Dee Belemnite (VPDB) and atmospheric nitrogen gas (air) using USGS40 and USGS41 as calibration standards. Results were reported in parts per thousand (‰) using δ notation. A commercially available peptone standard  were significant for walrus muscle (n = 125), liver (n = 35), and skin samples (n = 35). To generate arithmetic lipid-corrections, Δδ13C was regressed against the carbon:nitrogen ratio of the non-lipid extracted sample (C:Nbulk). Lipid-correction models from the literature were fitted to the relationship, using the nlstools package in R33 to estimate parameters. These non-linear least squares models assume that residual error is normally distributed, and this assumption was met for all three tissue types.Paired t-tests were used to determine whether changes in δet al. (2008)34, which was derived from McConnaughey and McRoy’s (1979)8 Equation The first model fitted was Equation 1a from Logan b/a) represents the estimated C:Nlipid-free, whereas the maximum Δδ13C is represented by a. The second model tested was Equation et al. (2008)34, as derived from Fry (2002)35:In this model, the x-intercept 34:The model-estimated C:NLipid-free is represented by In this model, the estimated C:N36. For each model, this technique was used to calculate mean squared error (MSE), mean absolute error (MAE), and the proportion of the samples for which the arithmetically estimated Δδ13C was within 0.5‰ of the measured Δδ13C. This 0.5‰ value represents roughly twice the measurement error commonly reported in ecological studies measuring δ13C, thus differences below this threshold are often not considered biologically important38. These metrics were compared to assess model fit, with the best fitting model defined as that with the lowest MSE and MAE, and the greatest proportion of samples for which Δδ13C was estimated to within 0.5‰ of measured Δδ13C.Predictive error was assessed using leave-one-out cross validation13Clipid-free. Because chemical lipid-extraction may impact stable nitrogen isotope values34, δ15N values from non-lipid extracted samples were used for these analyses. Linear mixed effects models were used to test whether δ13Clipid-free and δ15N differed among muscle, liver, skin, and bone collagen of 30 individual walruses. These models assume a Gaussian error distribution, and this assumption was met for all tissues. For each model, tissue was entered as a fixed effect. Individual was included as a by-subject random intercept to account for relationships among the isotope values of tissues from individual walruses. Models were fitted using the R package lme439, and p-values were obtained by likelihood ratio tests of the full model with the effect of tissue against the null model, which did not include tissue as an effect. Significance was assessed using an alpha of 0.05, and residuals were visually inspected for deviations from normality and homoscedasticity. Tukey’s Honest Significant Difference post hoc tests with a Holm-Bonferroni correction40 were conducted in the multcomp R package41 to examine differences among tissues. Tissue samples from female walruses were only available in 2016, and only 10 of the 30 animals sampled for this study were female. Additionally, there is no evidence to support the assumption that differences in stable isotope values between males and females observed in this study would remain consistent seasonally, inter-annually, and across broader time scales, thus sex of sampled walruses was not included in the models presented in here. However, visual examination of the data revealed apparent differences between the tissue stable isotope values of male and female walruses included in this study, thus additional linear mixed effects models including sex were run. The results of these models are presented and interpreted in the online supplementary material (Supplementary Discussion 1). All statistical analyses were conducted using R version 3.4.142 with RStudio version 1.0.15343.Comparisons among walrus tissues were made using δ13C, and/or δ15N of walrus tissues  and skin , but walrus muscle δ13C was unchanged . Lipid extraction significantly increased the δ15N of muscle  and liver , whereas changes to skin δ15N (Δδ15N) were not statistically significant . Regardless of whether mean δ15N was impacted by lipid extraction, the difference between δ15Nbulk and δ15Nlipid-free (Δδ15N = δ15Nbulk − δ15Nlipid-free) of a sample from an individual animal was frequently well beyond the range of analytical precision .Chemical lipid extraction changed the C:N ratios, δ13C and C:Nbulk . When model fit was considered for only these 10 samples, Equation 13C , followed by Equations 0.5 = 0.70) and 1 . The parameters p and ƒ were estimated for Equation 13C values from this study, resulting in the following equation:Lipid-normalization models were parameterized for walrus muscle, liver, and skin, but not for bone collagen, which is a purified protein. Of the three tissues examined in this portion of the study, only muscle and skin showed a relationship between Δδlk Table , Fig. 1.3C Table , Fig. 1.Which was simplified to:13C and the values predicted by this model were both 0.2‰. The maximum difference between the observed and predicted Δδ13C for a given individual was 1.2‰.The mean and median differences between the observed Δδ13C and C:Nbulk was best explained by Equation 13C to within 0.5‰ for >85% of samples ‰ higher than liver. Skin and bone collagen were enriched in 13C by an additional 2.0 (95% CI: 1.8–2.2)‰ compared with muscle. Post hoc tests showed that the δ13Clipid-free of all tissues differed significantly, except for skin and bone collagen ‰ in relation to bone collagen. Skin δ15N values were an average of 2.1 (95% CI: 1.9–2.3)‰ higher than those of liver and muscle. For δ15N, all tissues were significantly different, except for muscle and liver  and understanding tissue-specific discrimination are important for properly interpreting the results of stable isotope analyses of animal tissues. This is particularly true when δ13C and lipid content in animal tissues44. In this study, chemical lipid extractions significantly increased the δ13C values of walrus liver and skin, indicating that lipids affected δ13C in these tissues. Muscle δ13C remained unchanged, likely because marine mammal muscle is typically comprised of lean protein with little lipid content49. Lipids are stored primarily in the blubber layer in these animals, rather than interspersed among the muscles. Depending on the degree of precision desired, future studies measuring δ13C in walrus muscle may choose to forego lipid extraction and/or lipid normalization altogether. Because an arithmetic lipid correction could not be generated for walrus liver, lipids should be chemically extracted from this tissue if liver δ13C is to be used for future studies.Many studies have demonstrated the negative relationship between δ13C associated with lipid removal (Δδ13C) be statistically related to the carbon:nitrogen ratio of the bulk sample. For walrus skin, Δδ13C was proportional to C:Nbulk, such that higher C:N ratios prior to lipid extraction were associated with larger changes to δ13C values as a result of extraction. Though chemical lipid extraction did not affect the mean δ13C of walrus muscle, samples with high C:Nbulk were associated with the largest changes in δ13C. C:Nbulk is indicative of the lipid content18, thus, as expected, samples with a greater lipid content exhibited a larger change in δ13C after the lipids were removed. The top-performing model for walrus muscle 34, using experimental data. In this equation, the C:Nlipid-free can be estimated by the term f, which resulted in a value of 3.45 , indicating that a muscle sample with a C:Nbulk of ≤3.45 is comprised entirely of lean protein and need not be lipid extracted or corrected. Walrus muscle analyzed in this study appears to have contained very few lipids, with the model output indicating that more than 40% of samples had a carbon:nitrogen ratio less than or equal to 3.45. Some samples did contain a higher proportion of lipids, possibly as a result of the location from which the sample was taken . Future studies may wish to sample muscle from locations far from the blubber to reduce the amount of lipids in the tissue. In instances where this is not possible, the equation presented here may be used to estimate Δδ13C of muscle with a greater-than-average lipid content (C:Nbulk > 3.45).Mathematical lipid correction requires that the change in δEquation  was para18) ranged widely (C:Nbulk range = 2.7–10.5), and Δδ13C was proportional to C:Nbulk, making this tissue particularly well-suited for mathematical lipid correction. The top-performing lipid normalization model 34 derivation of the Fry (2002)35 mass balance equation , indicating that a skin sample with a C:Nbulk of ~2.8 is already composed of lean protein and need not be lipid-extracted or corrected. The lipid-protein discrimination parameter was estimated to be 8.45, which was greater than published estimates for various fishes and invertebrates34, but similar to estimates for baleen whale skin and blubber38. The best-fitting model was effective at predicting Δδ13C for walrus skin samples based on a wide range of C:Nbulk values. These predicted values were within 0.5‰ for greater than 85% of samples. This level of precision is likely acceptable for many ecological studies; however, in situations where researchers seek to address questions requiring greater precision, chemical lipid extraction may be necessary.The C:N ratio of walrus skin  is analyzed for stable isotopes, it is possible or even likely that two subsamples taken from an incompletely homogenized tissue may differ in their composition , resulting in δ13C and δ15N differences. Most of the negative Δδ13C values were small (~−0.1‰); however, some muscle samples had δ13Clipid-free values that were much lower (~−0.6‰) than their δ13Cbulk values. Ensuring samples are completely homogenized before subsampling for isotope analysis may help reduce this type of error in future studies. Complete homogenization is particularly important because differences in stable isotope values may exist at small spatial scales within a tissue. Todd et al. (2010) found little variability in pinnipeds skin and muscle sampled at different sites on the body50; however, Wild et al. (2018) described differences in both δ13C and δ15N among cetacean skin layers51, indicating that this tissue represents a dietary time series, and stable isotope values may not be homogenous at different depths within a sample. Improper subsampling or incomplete homogenization prior to analysis could thus result in δ13C and δ15N differences driven by these spatial variations in isotope values within the skin. Further investigations into how δ13C and δ15N vary within individual tissues are warranted. In particular, it would be valuable to examine variations among different muscle groups, as well as differences between glycolytic and oxidative muscles.Removal of lipids from walrus tissues sometimes resulted in unexpected changes in δ15N values, thus, a lipid extracted and non-lipid extracted aliquot of each sample must be run to ensure comparability across tissues and studies of both δ13C and δ15N values. Sotiropoulos et al. (2004)17 hypothesized that δ15N increases as the organic solvent removes amino acids contained within structural lipids; however, as Ryan et al. (2012)38 also noted for cetacean skin and blubber samples, changes in δ15N observed in our study were not unidirectional. The δ15N values of some walrus skin samples decreased by as much as 0.6‰, while others increased by as much as 0.8‰, indicating that the removal of 15N was not uniform across samples. The same pattern was observed for walrus muscle and liver, though the observed changes in δ15N were smaller. This may have resulted from the removal of amino acids from the sample during chemical lipid extraction17, but may also have been related to incomplete homogenization during sample processing and/or variation in sample lipid content. The effects of lipid extractions on δ15N in this study suggest that, for studies using chemical lipid extraction on walrus tissues, isotope values of samples must be analyzed both before and after extraction. This makes chemical lipid extraction at least twice as expensive as mathematical lipid correction. Though lipid extraction with chloroform:methanol did not significantly alter the mean δ15N values of walrus skin samples used in this study, the δ15N of the lipid-free samples was often different enough from the bulk sample (up to 0.8‰) to alter interpretation of the results. Such changes to δ15N would be particularly problematic for studies using mixing models to estimate animal diet53. In the future, researchers should assess the level of precision required to investigate their hypotheses, as well as the number of samples they are able to run, if laboratory costs are a limiting factor, before deciding whether to use chemical lipid extractions or the arithmetic lipid-correction for walrus tissues.A substantial drawback to chemical lipid extractions is that they may alter δ13C and δ15N among animal tissues arise from multiple factors that impact stable isotope values, including tissue-specific isotope discrimination54, inter-tissue variability in turnover rates46, and differences in metabolic routing of dietary macromolecules, such as proteins, fats, and carbohydrates55. Disentangling the effects of these different processes is difficult, and many controlled feeding experiments have investigated the role that each of these processes plays in determining the stable isotope values of individual tissues within an organism56. For studies of free-ranging animals, these processes must be considered together and the likely importance of each weighed when interpreting stable isotope data. Though the specific factors driving inter-tissue variability in δ13C and δ15N may remain unknown, general patterns in the differences among tissues can be observed and compared with those reported in the literature. For example, the −0.5 (95% CI: −0.7–−0.3)‰ offset in δ13Clipid-free between walrus muscle and liver in the present study appears to be standard among marine mammals, for which reported values range from −0.8 to −0.1‰  as compared with muscle values 57 measured δ13C and δ15N in skin (n = 20) and liver (n = 19) of Atlantic walruses (Odobenus rosmarus rosmarus). Liver δ13Clipid-free averaged 0.4‰ lower than muscle δ13Clipid-free, closely matching the average difference of −0.5 (95% CI: −0.7–−0.3)‰ observed in this study. In contrast, Atlantic walrus liver δ15N was 0.4‰ greater than muscle δ15N, as compared to a difference of 0.0 (95% CI: −0.2–0.2)‰ in our study. The contrasting results for δ15N may have arisen due to a variety of factors, including sample size, timing of sample collection, and differences in the physiology, ecology, diet, and seasonal movements of Pacific and Atlantic walruses.Differences in δ13Clipid-free and δ15N , animals consuming a monotonous diet would have consistent stable isotope values throughout their bodies, regardless of turnover rate. An animal’s diet must change for tissue turnover rates to drive differences in δ13C and δ15N among tissues. For walruses in this study, differences in δ13Clipid-free and δ15N of liver and muscle likely resulted from changes in diet  associated with the annual migration. Pacific walrus migration is sex-segregated58. The entire population winters together in the Bering Sea. In the summer, females and juveniles move northward into the Chukchi Sea, whereas most males move in the coastal waters of the Bering Sea, including Bristol Bay and the Russian coastline. Female walruses had liver δ15N values that were 1.4 (95% CI: 1.0–1.8) ‰ greater than those of males; whereas female δ15N was only 0.7 (95% CI: 0.3–1.1) to 0.8(95% CI: 0.4–1.2)‰ greater than that of males for all other tissues (Supplementary Discussion 1). Stomach content analysis indicates that the diets of male and female walruses are essentially identical when they are in the same location59, thus these sex-related differences are probably driven by changes in diet during the summers, when males and females are separated. These differences likely result from shifts in diet composition and geographic variability in baseline δ15N values, and provide further support for the hypothesis that the observed differences in isotope values between liver and other tissues were driven primarily by differences in turnover rate.Variation in turnover rate alone will not drive differences in the δ60. Though direct estimates are not available for walruses, the turnover rates of muscle, liver, skin, and bone collagen have been established for many other species and typically follow the order liver <muscle/skin <bone collagen46. Turnover rate is fastest in liver, with a typical reported half-life of <10 days61, whereas bone collagen turns over more slowly and can represent an average of years of foraging63. The turnover rate of muscle is intermediate, with a half-life that is on the order of weeks to months61. When considering values from the published literature, it is critical to note that the rate of tissue turnover is directly related to the animal’s mass-specific metabolic rate64, and is proportional to body size60. Most of the studies cited above measured tissue turnover in small animals  that are readily studied in the lab. These animals have high mass-specific metabolic rates, and their tissues almost certainly turn over much faster than those of larger animals. For example, the stable carbon isotope half-lives of liver (37.3 days) and muscle (178.7 days) in alpacas (Lama pacos) are approximately six times those reported  for gerbils64. Domestic cattle (Bos taurus) have similarly slow δ13C and δ15N turnover in their skeletal muscle (~134–157 days65). Tissue turnover rates in walruses are likely to be much closer to those of larger mammals than the values estimated for small animals, and may be even slower given their large body size.The relative turnover rates of animal tissues have been the subject of many studies66. Estimates for cetacean skin turnover range from roughly one to six months70. Research by Wild et al. (2018)51 showed that cetacean skin, which grows continuously at its innermost margin and is sloughed off upon reaching the surface, contains a time series of stable isotope values that may reflect diet over a longer period of time. They suggested that the inner layer of the skin alone might represent diet from an entire summer feeding period (~4 months). It is important to note that the structure and function of cetacean skin is different from that of pinnipeds73, and these estimates might not be appropriate for walruses.In contrast to liver, muscle, and bone collagen, the metabolic turnover of skin is not well studied. Most estimates in the literature come from studies of marine mammals, for which skin biopsy is a commonly used sampling method74. These different pathways result in some amino acids exhibiting greater isotopic discrimination than others. The difference between the δ13Clipid-free values of walrus skin and bone collagen compared with those of liver and muscle likely results from variation in the amino acid composition of these tissues. Walrus skin contains an unusually high proportion of collagen fibrils71, making it especially tough. Skin and bone collagen share similar chemical compositions and both contain a large amount of glycine75. This amino acid tends to be enriched in 13C by ~8.0‰ compared with other amino acids and, as a result, collagen typically has higher δ13C values than other tissues76. This is likely why, in the present study, walrus skin and bone collagen δ13Clipid-free values were similar to one another, and were greater than those of muscle and liver by around 2.0 (95% CI: 1.8–2.2)‰ , whereas others do not (‘source amino acids’)77. Walrus skin δ15N values were 2.5 (95% CI: 2.3–2.7)‰ greater than those of bone collagen, indicating important differences with regards to discrimination of nitrogen isotopes. In humans, skin collagen has greater proportions of the trophic amino acids alanine, asparagine, and glutamine than bone collagen75. This difference may be responsible for the high δ15N values of walrus skin in this study, though this could also be due in part to dietary changes and differences in tissue turnover rates.Tissue-specific stable isotope discrimination typically results from differences in the chemical composition of tissues. Proteins that differ in the relative abundance of their constituent amino acids may be subject to varying degrees of isotopic discrimination due to the various biochemical synthetic pathways for amino acids13C discrimination factor (Δ13C) of +1.2‰  of +2.8‰ between diet and muscle; however the range of these estimates is much greater (range: +1.7–4.3‰). A rough estimate of diet-muscle discrimination can be made for walruses using published prey stable isotope values. Average reported δ13C and δ15N of bivalve species common in walrus diet  are ~−18.8‰ and ~9.2‰, respectively79. Using these values to estimate diet-muscle discrimination estimates for walruses in this study results in a value of +1.8‰ (Δ13C) and +3.3‰ (Δ15N). Though bivalves comprise a large portion of their diet, walruses consume a wide variety of prey items, including higher trophic level prey such as predatory snails, seabirds, and seals80. The estimate for Δ15Nmuscle-diet may thus be high, as inclusion of these higher trophic level prey items would increase the estimated average δ15N of walrus prey. These estimates are generated from a limited number of prey items, collected in different years than this study’s specimens, so these values are approximations and should be interpreted with caution. Further research is warranted to more precisely estimate diet-tissue discrimination for walruses.Quantifying diet-tissue discrimination is important for reconstructing animal diet and understanding food web structure. The results of this study provide information about the relative degree of isotope discrimination among tissues, but their relationship to walrus diet remains unknown. Estimates from other marine mammals indicate an average diet-muscle δ13Clipid-free and δ15N of muscle, liver, skin, and bone collagen. The differences in δ13Clipid-free and δ15N among tissues observed in this study generally agree with published values for mammals, with the exception of skin, which differed more substantially from muscle for both δ13Clipid-free and δ15N. Lipid normalization models were parameterized for walrus muscle and skin. Walrus liver Δδ13C was not related to C:Nbulk, so a mathematical lipid correction could not be generated. Both lipid normalization models performed well, and can be used in future studies as an alternative to chemical lipid extractions. Many walrus muscle samples analyzed in this study had a C:Nbulk that indicated they were composed primarily of lean protein (≤3.4) and did not require chemical lipid extraction or mathematical lipid extraction.Stable isotopic analysis of walrus tissues indicates considerable differences among the δ13C and δ15N in walrus tissues, giving researchers more flexibility in stable isotope studies of subsistence harvested walruses. Our results will also make studies of δ13C and δ15N using non-lethal sample collection  a more viable approach, by decreasing the costs of analysis and providing context for interpreting the results. Finally, the results of this study will be particularly useful for comparing contemporary studies, which typically analyze soft tissues, with historic and paleoecological studies, which generally measure δ13C and δ15N in bone collagen23. The δ13C values of walrus skin and bone collagen were indistinguishable, indicating that these tissues likely both primarily represent dietary protein and are suitably comparable. Skin δ15N was 2.5 (95% CI: 2.3–2.7)‰ greater than that of bone collagen on average, suggesting differences in nitrogen isotope discrimination between these tissues or a change in diet. The results of this study will also help refine stable isotope mixing models and provide better estimates of walrus diet. Future research measuring the degree of trophic discrimination between the δ13C and δ15N values of walrus prey and tissues will be important for further improving these reconstructions, as well as for a better understanding of Arctic food web structure and energy flow.The results of the present research will allow for better comparison of δThis article does not contain any studies with human participants or animals performed by any of the authors.Supplementary Information


A2Zr2O6Oʹ  and Yb2Ti2O6Oʹ, that exists despite ideal stoichiometry, ideal cation-ordering, the absence of lone pair effects, and a lack of magnetic order. Though these materials appear to have good long-range order, local structure probes find displacements, of the order of 0.01 nm, within the pyrochlore framework. The pattern of displacements of the A2Oʹ sublattice mimics the entropically-driven fluxional motions characteristic of and well-known in the silica mineral β-cristobalite. The universality of such displacements within the pyrochlore structure adds to the known structural diversity and explains the extreme sensitivity to composition found in quantum spin ices and the lack of ferroelectric behavior in pyrochlores.Materials with the pyrochlore/fluorite structure have diverse technological applications, from magnetism to nuclear waste disposal. Here we report the observation of structural instability present in the pyrochlores  The family of pyrochlore complex oxides includes many materials of fundamental or practical interest, such as spin ices and dielectrics. Trump et al. show that flexibility of the pyrochlores’ structure leads to local displacements that explain some of their unusual physical properties. This makes knowledge of the structural flexibility of the pyrochlore structure, A2B2O6OʹOʺ0, a derivative of the fluorite structure, crucial. The structure contains interpenetrating, corner-sharing OʹA4 and OʺB4 tetrahedra, shown in Fig. A is typically a larger (~0.1 nm) cation while B is a smaller cation (~0.05 nm), where the central Oʺ site is unoccupied.From catalysis, ferroelectricity, luminescence, magnetism, and even nuclear waste storage, compounds which crystallize in the pyrochlore structure are utilized for countless applications4Nb3O12 (Y2(Y0.14Nb0.86)2O6.91) which contains both an A cation on the B site and O vacancies4. Additional disorder, such as A/B site-mixing is not uncommon8, and can lead to the weberite structure9, unless optimal cation ordering occurs. Lastly, polyhedral distortions can also occur, where the tetrahedral corners move in or out. If in/out displacements have long-range order then the global symmetry drops from Fdm to Fm evidenced by the addition of 2h 0 0 reflections, as seen for Pb2Ru2O6.5, due to a combination of lone pair effects and off-stoichiometry10. If in-out ordering only exists over short-length scales, it is equivalent to 2-in/2-out (2I2O) ordering, which is expected to be disordered on long-length scales due to degenerate configurations11. This is observed for Nb-pyrochlores due to charge disproportionation4, and also for Y2Mo2O7 observed as split peaks in X-ray absorption spectroscopy12. Though this disorder is often not magnetically driven, for pyrochlores with magnetic cations, it is this same short-range order with degenerate configurations which leads to non-trivial magnetic states14. Furthermore, understanding the magnitude and direction of these displacements elucidates next-nearest neighbor magnetic cation distances, which are especially important for pyrochlores with quantum magnetism.Stoichiometric flexibility is common for the pyrochlore structure, such as in Y2Ti2O7 and Bi2Ru2O7, and is attributed to lone-pair effects17. Ferroelectric behavior is expected from this disorder, though these materials are only dielectrics18, with ferroelectric behavior attributed to impurities19. Better understanding this type of disorder is essential to describe why these pyrochlores are not ferroelectric, despite the local structure deviating from cubic symmetry, as well as understanding why so few pyrochlores are ferroelectrics despite having large dielectric constants1.An alternative type of disorder, cooperative tetrahedral tilting, also exists for compounds such as Bi2Zr2O7 (PZO), La2Zr2O7 (LZO), and Yb2Ti2O7 (YTO), due to static A and O displacements  hint at structural disorder, where pair-distribution function (PDF) analysis refinements prefer static, rather than thermally dynamic, displacements. Additionally, 91Zr NQR on a PZO series indicate an inhomogeneous bonding environment of Zr as a function of A/B cation ratio, while high-angle annular dark field scanning transmission electron microscopy (HAADF STEM) reveals a static displacement of ~0.01 nm for A and O. Though previous works have observed similar displacements and the associated structural frustration22, we generalize that these static displacements are common in pyrochlore structures and are driven by cation size mismatch, rather than defect concentrations or electronic effects.Here we provide evidence for this disorder in the pyrochlores Prsee Fig. . These dsee Fig. 20. The d24 respectively. All A-site cations have pancake-like ADE, suggesting tetrahedron tilting, rather than the rod-like ADE indicative of in/out ordering. Systematic refinement tests were conducted for PZO, LZO, and YTO for off-stoichiometry, cation site-mixing, or O off-stoichiometry and each test indicated the absence of these effects (see Supplementary Discussion for more details). This allows us to conclude that the stoichiometry and occupancies are within 0.5% of nominal values , 96h:(0 y −y) and 96g:(z x x) Wyckoff positions. Pr, Zr, La, and Yb all showed an equal preference for the 96g and 96h sites, and Ti showed only a preference for the 32e site. To obtain reliable information about O displacements, similar tests were conducted using neutron diffraction data, confirming that La and Zr prefer the 96g/96h sites, O prefers the 96g site, and Oʹ does not move. Though alternative Wyckoff positions (static ordering) improve refinement statistics, this improvement was not statistically significant from fits with ADP (dynamic ordering). This analysis merely suggests displacements are static, which would have significant impacts on both magnetic and ferroelectric behavior.Additional tests were conducted for evidence of structural displacements, by placing the A, B, or O displacements25. Although none of the powder diffraction data have intensity on the {442} reflection, Supplementary Figure δ > 0.02 nm is present, while the displacements we measure are only ≤ 0.01 nm , but are still imperfect, especially at short distances (r < 0.35 nm).To further understand the local structure, and hence the effects on physical properties, neutron PDF (NPDF) was collected on PZO and X-ray PDF (XPDF) data was collected on YTO see Fig. . Fits wig/96h Pr displacements, 0.004(2) nm 96g/96h Zr displacements, 0.010(3) nm 96g O displacements, and a robust Oʹ position for PZO; also, yielding 0.0098(9) nm Yb 96g/96h displacements, 0.011(3) nm Ti 32e displacements, 0.015(4) nm 96g O displacements, and a robust Oʹ position for YTO  nm 96 nm 96g/9P43212 refinement improves fit statistics (Rw = 9.09 vs. Rw = 8.76 for PZO and Rw = 9.53 vs. Rw = 8.68 for YTO), and visual inspection of Fig. A–Oʹ and A–O bond lengths (r < 0.35 nm). Refinements using a range of Qmax values produced equivalent fits, and refinements with similar degrees of freedom also preferred a static P43212 model. These lower symmetry refinements, which are quantitatively and qualitatively preferred, model only several A–Oʹ/A–O distances, rather than a large collection of distances modeled by higher symmetry refinements with ADPs. However, Fig. r < 0.60 nm, and only slightly improves modeling at longer distances (r > 0.60 nm). This implies that the local symmetry is lowered due to static displacements in each OʹA4 tetrahedra (r < 0.35 nm), more disorder exists between tetrahedra (0.35 nm < r < 0.60 nm), and that a locally disordered model accurately describes the long-range ordered structure. Further, the increased A–Oʹ/A–O bond distances which lower the local symmetry, would suggest frustrated, rather than cooperative, motion between tetrahedra, interrupting any long-range ordered states.A 91Zr NQR is shown in Fig. x decreases in Prx2 + Zrx2 − Ox/27 − . The broad and non-symmetric peak shape indicates that the electric field gradient (EFG) around 91Zr is not homogeneous for x = 0 and x = −0.02. This behavior is only expected if the compound has discrete structural displacements , HAADF STEM is a long timescale measurement, of the order of seconds, much longer than the timescale expected for dynamic motion (at most ≈10−6–10−12 s). The longer timescale and increased resolution makes HAADF STEM ideal for distinguishing between fluctuations around an ideal position (dynamic) and averaged positions that are displaced from the ideal (static).If these displacements are static, then a shift from the A/B cation ordering, as indicated from Rietveld refinement tests. Determining precise atomic column composition from on-axis EELS data is known to be challenging due to beam propagation effects and the quantification of atomically-resolved EELS data would normally require a careful comparison with inelastic image simulations30 or a relatively complex inversion process31. Nevertheless, in contrast to a recent report for off-stoichiometric Yb2Ti2O7 samples where significant site mixing could be observed visually even in unprocessed maps32, the uniformity of the map shown in Fig. Figure Z-contrast. Figure 32, even assuming this column contains two defects, only suggests a stuffing defect concentration of 0.11%, well below the 0.5% limit as indicated by powder diffraction and PDF refinements (see SI for details), further indicating that the crystals are nearly defect free.Rather than attempting to quantify the EELS results in terms of column composition, intensity profiles from HAADF images were instead examined to attempt to estimate the uniformity of the observed 33, while ideal atomic positions were calculated from the Fdm structure for comparison. Figure 33 and an ideal pyrochlore structure, the averaged displacements of [111] atomic columns are observed to be 0.013(6) nm, which are markedly larger than the precision typically achieved with this workflow (consecutive acquisition followed by rigid or non-rigid registration) with this instrument34, and is in phenomenal agreement with NPDF refinements (0.013(2) nm). The displacements in the [111] orientation appear to be in a moderate agreement with those expected from the PZO NPDF refinements  was used to acquire representative HAADF images, following which the script Ranger was used to identify the coordinates of the atomic columns from the resulting high-resolution scanning transmission electron microscopy (HRSTEM) imagesP43212 model and PZO [110] STEM image  is not unexpected given the disorder indicated by the SAED patterns in Fig. r < 0.60 nm) as suggested by the XPDF and NPDF analyses. This again indicates the tetrahedra tilting is frustrated rather than cooperative.The larger mismatch between the static The tetrahedra connectivity in each orientation is important, as a single unit cell can have four single atom types in the [110] direction, and only one single atom type in the [111] direction. This explains why the PZO [110] orientation is more sensitive to tetrahedra–tetrahedra disorder and has more imperfect agreement between the PZO NPDF model and HRSTEM images. However, our PDF analysis indicates that the expected length scale of order is only <0.35 nm, smaller than the thickness of the HAADF STEM samples. For this reason, it is surprising that any displacement can be observed in this way, even though it is a statistically real value, and may indicate that the structure is more ordered than anticipated in the [111] direction. To prove the validity of the observed displacement, we further this analysis by comparing the rows in two separate [111] images, taken at different locations on the same sample, with the expected pattern of displacements for the β-cristobalite structure.1), and alternating left and right in the next row (2). Binning these rows separately, using the median and standard deviation (across 153 atomic columns) to create the bin locations and width, Fig. 1) retains a small distribution around a single distance while the other rows (2) have two maxima, indicating Pr displaces in alternating directions, as expected for a β-cristobalite displacement in this orientation  while Zr, which has a larger cation radius that farther splits its p and d orbitals36, prefers the 96g/96h site . This observation might indicate that second-order Jahn-Teller displacements prefer in-out rather than β-cristobalite type displacements. Knowing the symmetry of the mixing p and d orbitals would help resolve this, as the symmetry of the displacement must match the symmetry of the mixing HOMO and LUMO bands36.To understand our results, summarized in Table 40. The fluorite structure, which resembles the pyrochlore structure when A and B cation sizes are similar and equally mixed, follows body center cubic packing. The pyrochlore structure similarly follows face center cubic packing, but the B4 tetrahedra are smaller than the OʹA4 tetrahedra. For large A/B ionic radii ratios, the size of the OʹA4 tetrahedra are constricted in size by the smaller B4 tetrahedra. Much like β-cristobalite, the tetrahedra distort, allowing longer A–Oʹ bond distances, which relieve the constrained OʹA4 tetrahedra, and displace the surrounding O. If this is the case, then β-cristobalite disorder would be present in all pyrochlores with larger A/B ionic radii ratios.Another obvious reason for these displacements is inherent strain, well known to exist in the pyrochlore structure5, indicative of β-cristobalite distortions27, proposing that tetrahedral distortions occur in non-magnetic La2Zr2O6Oʹ to relieve La–Oʹ overbonding22. In contrast to previous work, we additionally rule out the effects of impurity elements, site mixing or stuffing, and off-stoichiometry, by analyzing crystals grown as part of series, whose physical properties match those of stoichiometric powders24, further confirmed by Rietveld and PDF refinements. Given that our work also concludes that the diffuse scattering is due to static, rather than dynamic, displacements, we generalize that if these displacements are due to A/B cation size mismatch, then static displacements exist in all zircanates and titanates at the very least. EXAFS investigations on the ruthenate Pr2Ru2O7 likewise found evidence for Pr disorder and deviations in the Pr–Oʹ bonding41. These types of displacements may even explain the structural details for other pyrochlores as well, such as Y disorder in the recently contested Y2Mo2O729 or the disorder observed in hafnates42. If this is the case, then these static displacements, which exist at room temperature, have a significant impact on the properties of these materials.Tabira, Withers et al. have observed diffuse scattering for myriad zircanate and titanate pyrochlores44, and are important for understanding the underlying physics of the spin-ice state. More thoroughly, a β-cristobalite distortion may not significantly alter bond distances, but bond angles, such as A–O–A, change drastically, and next-nearest neighbor distances are altered even more dramatically. Hence these small changes in bond distances have extremely large effects on magnetic interactions, explaining why 1–2% changes in stoichiometry have drastic changes in magnetic susceptibility and heat capacity for pyrochlores45. Likewise, this also explains why 2% level adjustments in the cation stoichiometry of PZO toward excess Pr leads to a sharper 91Zr NQR line. As the larger Pr is placed on the smaller Zr site, it allows for the OʹPr4 tetrahedra to expand without distorting, creating more uniform next-nearest neighbor distances. This suggests a design principle of tuning the stoichiometry of these materials to obtain desired properties.This structural disorder adds to the number of entropic possibilities at low temperatures. In geometrically and magnetically frustrated compounds, like pyrochlores, this would induce a large array of degenerate magnetically ordered states, creating many zero-gap or small gap equivalent ground states, and preventing such a material from reaching a theoretical ground state. This does not necessitate that frustration is magnetically driven; rather our results suggest that the frustration is structurally driven with significant impacts on the magnetic ordering, enhancing spin-liquid behavior and at the very least creating spin-glass behavior. Such effects have recently been observed2Ti2O7, lowers the temperature of the transition seen in heat capacity data;24 as placing the smaller Ti on Yb sites (stuffing) requires the OʹYb4 tetrahedra to expand less while placing the larger Yb on the smaller Ti sites (anti-stuffing) allows the OʹYb4 tetrahedra to expand without distorting, both of which normalizes the next-nearest neighbor distances. In both situations, more uniform magnetic interactions should exist, but for both stuffing and anti-stuffing the transition temperature and magnitude of the heat capacity significantly decreases24. This indicates that these delicate magnetically ordered states, which already contain magnetic disorder, are easily interrupted by either a lack of magnetic cations on the A-framework, or extra magnetic cations on the B-framework. Site-mixing would additionally interrupt the delicately magnetically ordered degeneracies, suggesting that ideal magnetic order in pyrochlores cannot exist without non-uniform magnetic interactions.Curiously, ideal stoichiometry leads to optimal magnetic ordering, despite non-uniform magnetic interactions. For instance, any deviation away from nominal stoichiometry in Yb2Ir2O7, Pr2Ir2O7, and Sm2Ir2O746, though its appearance is likely complicated by other excitations. This feature unexpectedly extends to higher energy for Pr2Ir2O7 than Eu2Ir2O78, as a result of the larger cationic ratio of Pr/Ir, inducing more disorder for Pr2Ir2O7. Similarly, because the local symmetry is lowered, higher energy excitations would also appear – though their intensities would be severely diminished based on the magnitude of the displacements, as is the intensity of the allowed {442} reflection for diffraction data.Signatures of this disorder should be readily observable in spectroscopic measurements, arising as a continuum of non-magnetic, temperature independent, low energy excitations. Resonant inelastic X-ray scattering has observed such a feature for EuP43212 may not accurately describe the disorder between tetrahedra, it is the highest symmetry space group which allows for tetrahedra to rotate in all three directions, and conveniently contains only one symmetry-equivalent A and B cation. Similarly, the disorder due to frustrated tilting of the tetrahedra, prevents the pyrochlore structure from being ferroelectric, despite the local structure deviating from cubic symmetry. It is this same local disorder which prevents these materials from ordering in their ferroelectric ground state18 that also enhances the dielectric properties. This lattice frustration has been previously proposed, though only in the context of lone-pair active cations with large displacements21. Our results generalize that hypothesis to likely include all pyrochlores, even when they contain minimal defects, which emphasizes that frustrated tetrahedral motion is the defect-free pyrochlore ground state. The inherent geometric frustration of the pyrochlore structure necessitates that the displacements, and hence dipoles, point in different directions, canceling each other out over a single, or several, unit cells. This behavior prevents displacive spontaneous polarization such as for perovskites BaTiO3 or PbTiO3, but enhances dielectric behavior due to small, localized electric dipoles. Given enough disorder to relieve the geometric frustration, i.e. O vacancies and A/B site mixing, long-range order and ferroelectric behavior might be recovered and is likely the origin of ferroelectric behavior in materials such Cd2Nd2O7 and Pb2Nd2O747.Though space group 2Zr2O7, La2Zr2O7, and Yb2Ti2O7, show both indirect and direct evidence for a static displacement in pyrochlores in the absence of any type of defects or electronic effects, further experiments, which look at atomic positions as a function of temperature, would prove even more conclusively that this displacement is static, and not dynamic. However, if these displacements are due to A/B cation size mismatch they exist in all pyrochlores and not only resolve several long standing issues, such as the discrepancy between experimental and calculated pyrochlore lattice parameters51, but also many recently contested issues42. Since the A-Oʹ bond distance appears longer, these conclusions indicate that the bond valence sums, which were revised for the bonding coordination in these compounds52, may need to be updated. Since these displacements are frustrated, they also explain why pyrochlores are excellent dielectrics but almost never ferroelectric; this same structural frustration also explains why pyrochlores are excellent candidates for spin-ice/liquid behavior but also extremely sensitive to defect concentrations.Though the diverse variety of techniques herein, with multiple complementary techniques applied to Pr53. Growth conditions were individually optimized to produce homogenous single crystals with physical properties indistinguishable from stoichiometric polycrystalline samples. LZO was prepared by grinding stoichiometric amounts of La2O3  and ZrO2 , after they were individually dried overnight at 1000 °C. Large sample masses were used to minimize mass error (~20 g) and final oxygen content was corrected by heating in ambient atmosphere. Ground, mixed precursors were placed into an alumina crucible and heated under ambient atmosphere to 1350 °C for 12 h. Upon further heat treatments at 1500 °C for 40 h, with intermediate grindings and pelletizing, powder X-ray diffraction confirmed phase purity. Polycrystalline feed rods made from the powder were then sintered at 1500 °C in air. Finally, a pure, stoichiometric single crystal  was grown from the feed rods in a four mirror image furnace  using a growth rate of 4 mm/h and a rotation rate of 0.1 Hz. Details of similarly prepared PZO and YTO single crystals are found in refs. 24 respectively, as well as their associated sintered powder equivalents.Stoichiometric single crystals of LZO, PZO, and YTO were prepared by the optical floating zone methodλavg = 0.15418 nm) on a Bruker D8 Focus diffractometer with LynxEye detector at 295 K. Synchrotron powder X-ray diffraction was collected for a ground piece of the PZO single crystal, on the high-resolution 11-BM-B diffractometer at the Advanced Photon Source (APS), Argonne National Laboratory (ANL), with an incident wavelength of λ = 0.0413973 nm at 298 K. SiO2 was added to attenuate absorption and Si was added as an internal standard. To verify phase purity Rietveld analyses were conducted using Topas Academic and GSAS-II54, then systematic tests were conducted to verify stoichiometry, A/B cation mixing, and alternative Wyckoff positions as discussed in Supplementary Discussion. Structures were visualized using VESTA55.Laboratory powder X-ray diffraction patterns were collected for ground single crystals of PZO, LZO, and LTO using Cu-Kα radiation (2Zr2O7 (LZO) at the POWGEN powder diffractometer at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory (ORNL). The data were collected with a central wavelength of 0.1066 nm.Room temperature time of flight neutron diffraction was collected on a ground single crystal of La2 standard was used to estimate the resolution of the instrument. Data was reduced using Fit2D56 and PDFgetX257. Time of flight neutron pair distribution data (NPDF) was collected on a piece of well ground, sintered, stoichiometric PZO feed rod, on NOMAD diffractometer at the SNS, ORNL58. The 3 mm diameter quartz capillary containing the sample was held in the beam using a linear automated sample changer. Data were collected on the sample and an empty quartz capillary at 298 K for 415 min for each specimen. The scattering data were corrected by subtracting background scattering from the instrument and empty capillary, and normalizing against the scattering from a solid vanadium rod. The PDFgui software package was used for PDF refinements59, including systematic tests to verify stoichiometry, A/B cation mixing, and alternative Wyckoff positions.Room temperature X-ray pair distribution data (XPDF) was collected on a well-ground piece of the YTO single crystal on the 11-ID-B diffractometer at the APS, ANL, with an incident energy of 58.6 keV. A CeO91Zr NQR measurements on a piece of stoichiometric, sintered PZO were conducted with a conventional pulse-echo method at 4.2 K. The frequency swept NQR spectra were obtained by recording the integrated intensity of the spin-echo signal at discrete frequencies. Since the Zr sites have threefold rotational symmetry around the [111] crystallographic axis, the electric field gradient (EFG) around the Zr sites are axially symmetric, Vxx = Vyy = −1/2 Vzz. Then, two NRQ lines appear at νQ ( = 3eQVzz/2I(2I−1)h) and 2νQ in a zero external field, where Q and I are the quadrupole and the spin moment of the 91Zr nucleus, respectively, and h is the Plank constant. These NQR lines correspond to the transition Iz = ± 1/2 ↔ ± 3/2 and Iz = ± 3/2 ↔ ± 5/2. The latter transition lines were observed at 2νQ~17 MHz. Fits for the 91Zr NQR spectra were conducted using a Lorentzian function given by Supplementary Eq. Selected area electron diffraction (SAED) was conducted on ion-milled slices of PZO, LZO, and YTO single crystals, oriented down the [111] direction, using a Phillips CM300 FEG TEM, operating at an accelerating voltage of 297 kV. Off-center images were collected on an Orius CCD camera, while centered images were collected on film (Kodak SO 163). Patterns were collected under a large variety of exposure times (10 s–10 min) to determine the best exposure time to highlight the diffuse scattering, as demonstrated by Supplementary Figures 60, series of up to one hundred successively scanned images were systematically collected over a duration of several seconds. Subsequently, each image was realigned by an autocorrelation algorithm  to remove time dependent drift before summing the series to form the final image. No filtering was performed on the images. Alternatively, the non-rigid registration algorithm SmartAlign was applied to some of the images to provide the highest precision possible61. The automatic peak finding algorithm Ranger33 was used to extract experimental atomic positions from the STEM data, which uses 2-D Gaussian fit to obtain sub-pixel precision on the location of each column.High-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) imaging was conducted on the PZO and LZO samples using a Nion UltraSTEM 100 with a C5 Nion QO aberration corrector, operated at 100 kV at the Daresbury SuperSTEM Laboratory. The optics of the microscope were adjusted to form a 0.09 nm probe with 60 pA current. The beam convergence semi-angle was 30 mrad, while the detector angular range was calibrated at 85–190 mrad. In order to take advantage in recent developments in high-precision HAADF imaging through (non-)rigid registration techniquesM4,5 EELS edge onsets over a 50 eV energy window, after subtraction of the continuously decaying background using a power law model. Prior to integration, the signal was denoised using principal component analysis62, taking great care that no artifact was introduced by this process through thorough inspection of the residuals. To remove the effects of multiple scattering, the signal was also deconvoluted using the Fourier-ratio method63 using a low-loss spectrum image acquired immediately after the core loss dataset – the remarkably low drift and high stability of the instrument making this practical. Finally, the signal intensity for both elements was normalized to unity, such that the color map cannot be interpreted in terms of absolute composition, but nevertheless provide a useful indication on the relative distribution of the chemical elements across the field of view. Numerous chemical maps were acquired, systematically displaying close composition in atomic columns based on the elemental signal. The sample thickness varied from area to area, ranging between 0.45 and 0.70 inelastic mean free paths in the material , was 21.92(19) 106 a.u. for Zr columns (taken over 30 atomic columns), and 22.7(2) 106 a.u. for Pr columns (taken over 30 atomic columns). The magnitude of the standard deviation, a 1% deviation from the average intensity for all column types, indicates that each contain similar errors, suggesting merely experimental effects rather than defect chemistry. Given that two standard deviations account for the intensity fluctuation of the mixed column rows, we use two standard deviations as the metric of experimental error for individual rows. Only one atomic column , using a experimentally consistent 44 nm thick sample (119 atoms in the [110] orientation), suggests a defect concentration of 0.007%. Similarly, if we assume that this column contains two defect atoms, it would still only require a defect concentration of 0.11%. Finally, if we assume the sample is half as thick, with eight times as many columns with defects, this still only suggests a defect concentration of 0.12%. indicating that the defect concentration is well below the 0.5% limit proposed by powder diffraction and PDF refinements.To obtain the intensity maximum for each column a Gaussian was fit to each peak using DigitalMicrograph, and profiles were lined up for better comparison. The average intensity for mixed columns was 22.4(2) 10Fdm lattice parameters derived from room temperature powder diffraction and image length scale. An example is shown for PZO in the [110] and [111] orientations in Supplementary Figure To obtain displacement vectors for high-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images simulated pattern of cation spots were matched and refined to the experimental images using MATLAB. Simulated patterns were created using 40, and given the proposed structural strain from A/B cation size mismatch.Using a least-squares analysis the calculated patterns were translated and rotated, and finally scaled to account for slight lattice mismatch or sample tilting, though scaling never exceeded a 3% difference. The edges of final images were cropped due to an observed “fish-eye” type image distortion, shown in Supplementary Figure Finally, to obtain an average displacement distance between sub-pixel 2D Gaussian refined experimental distances and the least square refined ideal structure, we use the distance formula to obtain the distance between the spots in sub-pixels, convert this distance to nanometer using the image scale, and finally averaged all the calculated displacements, over 45 atomic columns, to obtain 0.013(6) nm.www.ccdc.cam.ac.uk/data_request/cif (CCDC-1520136-1520137).The authors declare that the data supporting the conclusions of this study are available within the article and its Supplementary Information file or from the corresponding author upon reasonable request. The crystallographic data (Supplementary Data Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2


The rice chromosome segment substitution lines (CSSLs) of ‘Khao Dawk Mali 105’ (‘KDML105’) genetic background were developed by backcrossing with ‘KDML105’ rice and transferring the region from chromosome 1 of DH212 which was expected to contain the full putative salt tolerance genetic region. Line of CSSL11, CSSL12, and CSSL16 contained the full putative salt tolerance genetic region were evaluated with the parental lines, ‘KDML105’ and DH212 at seedling stage of rice. The physiological responses in rice plants were grown under normal condition and 75 mM of NaCl, and then comparative photosynthetic parameters, chlorophyll fluorescence parameters, PhiPS2, ETR, NPQ, as well as growth analysis. In this article, the data of physiological response evaluation in rice at seedling stage after salt stress treatment can be found. This can be useful as the information of the photosynthesis response to salt stress to other rice cultivars and related species. Specifications tableValue of the data•The data are valuable for understanding the response of photosynthesis process of rice at seedling stage under salt stress.•The data provide the detail information of growth analysis fresh and dry weight at seedling stage.•The data of the chlorophyll fluorescence parameters, Fv/Fm, PhiPS2, ETR, and NPQ of rice under salt stress show the adaptation of the photosynthetic system in the tolerance lines of rice at seedling stage. This can be benchmark for the similar studies in other rice cultivars or related species.1Amax), stomatal conductance (gs), intercellular CO2 concentration (Ci), transpiration rate (Trans), v/FmF, PhiPS2, ETR, and NPQ.Data describe performance of rice seedlings of 3 chromosome segment substitution lines (CSSL), CSSL11, CSSL12, CSSL16 and parental lines, ‘KDML105’ and DH212 rice under normal and salt stressed conditions. The performance includes fresh weight and dry weight of above ground tissues, maximum photosynthesis rate (22.1P < 0.05 was used as the threshold for significance).The chromosome segment substitution lines (CSSLs) of ‘Khao Dawk Mali 105’ (‘KDML105’) were developed, by transferring the region between the RM1003 and RM3362 markers on chromosome 1 from DH212 which was expected to contain the putative drought tolerance genetic region 33.1CSSL11, CSSL12, and CSSL16 seeds with a ‘KDML105’ genetic background and their DH212 and ‘KDML105’ as their parents were provided from the Rice Gene Discovery Unit, National Center for Genetic Engineering and Biotechnology. CSSL11, CSSL12, and CSSL16 included the full segment containing the putative drought tolerance genes between RM1003 and RM3362 on chromosome 1 of DH212 3.23, 12.5 g/L NH4H2PO4, 8.5 g/L KH2PO4, 0.4 g/L Mn-EDTA, micronutrient 0.8 g/L, 100 g/L Ca(NO3)2, and 3 g/L Fe-EDTA. Fourteen-day old plants were treated with nutrient solution supplemented with 75 mM NaCl to simulate salt stress conditions  value of 7.8–8.2 dS m−1), EC was directly determined at 5 points in each pond and EC value was verified and adjusted, if needed, every day. The control plants were grown normally and treated with a nutrient solution lacking NaCl. Soil EC value for the controls was 1.1–1.2 dS m−1. The complete block design (CRD) with 4 replications (three plants per replication) was used to evaluate the different responses to salt stress. Plant seedlings were treated for 9 days. Fresh weight and dry weight of the above ground tissues were shown in All rice seeds were germinated until roots were visible in plastic cups that contain distilled water for 5 days, the which they were transplanted into clay soil in pots with diameter of 25 cm and 40 cm of pot high. Clay soil was filled to ¾ capacity in the supplied pot. Pots were placed in the cement tank that can be flooded with nutrient solution or nutrient solution supplemented with NaCl solution for salt stress treatment. During flooding with Bangsai nutrient solution (1:100), rice plants were constantly supplied with fresh air by an aquarium pump. The nutrient solution consists of 50 g/L MgSO4, 80 g/L KNO3.3Amax, gs, Ci, Trans  according to the recommended procedures while PhiPS2, and ETR were determined by LI-6400 XT. NPQ was calculated from (mF/m′F)−1 −1 m−2 s−1; leaf surface photosynthetically active radiation: 1200 mol m−2 s−1; leaf temperature: 30.0–37.0 °C; and CO2 concentration: 380.0 mol mol−1. For photosynthesis parameters, the measurement was performed on the youngest fully expanded leaves, and each measurement was done on 3 positions of the leaf and the average was used for the analysis. Fv/Fm, PhiPS2, ETR, and NPQ were analyzed. The data with statistical analysis of the normal grown seedlings were shown in To evaluate the physiological responses at seedling stage: photosynthetic parameters and chlorophyll fluorescence parameters of treated plants, the following characteristics were evaluated on days 0, 3, 6, and 9 after treatment. Gas exchange was measured during the same period with a LI-6400 XT portable were evaluated including i, Trans . Chlorop