How to estimate isotope fractionations of a Rayleigh-like but diffusion-limited disequilibrium process?

The Rayleigh distillation isotope fractionation(RDIF) model is one of the most popular methods used in isotope geochemistry. Numerous isotope signals observed in geologic processes have been interpreted with this model. The RDIF model provides a simple mathematic solution for the reservoir-limited equilibrium isotope fractionation effect. Due to the reservoir effect, tremendously large isotope fractionations will always be produced if the reservoir is close to being depleted. However, in real situations, many prerequisites assumed in the RDIF model are often difficult to meet. For instance, it requires the relocated materials, which are removed step by step from one reservoir to another with different isotope compositions(i.e., with isotope fractionation), to be isotopically equilibrated with materials in the first reservoir simultaneously. This ‘‘quick equilibrium requirement’’ is indeed hard to meet if the first reservoir is sufficiently large or the removal step is fast. The whole first reservoir will often fail to re-attain equilibrium in time before the next removal starts.This problem led the RDIF model to fail to interpret isotope signals of many real situations. Here a diffusion-coupled and Rayleigh-like(i.e., reservoir-effect included) separation process is chosen to investigate this problem. We find that the final isotope fractionations are controlled by both the diffusion process and the reservoir effects via the disequilibrium separation process. Due to its complexity, we choose to use a numerical simulation method to solve this problem by developing specific computing codes for the working model.According to our simulation results, the classical RDIF model only governs isotope fractionations correctly at the final stages of separation when the reservoir scale(or thickness of the system) is reduced to the order of magnitude of the quotient of the diffusivity and the separation rate. The RDIF model fails in other situations and the isotope fractionations will be diffusion-limited when the reservoir is relatively large, or the separation rate is fast. We find that the effect of internal isotope distribution inhomogeneity caused by diffusion on the Rayleigh-like separation process is significant and cannot be ignored. This method can be applied to study numerous geologic and planetary processes involving diffusion-limited disequilibrium separation processes including partial melting,evaporation, mineral precipitation, core segregation, etc.Importantly, we find that far more information can be extracted through analyzing isotopic signals of such ‘‘disequilibrium’’processes than those of fully equilibrated ones, e.g., reservoir size and the separation rate. Such information may provide a key to correctly interpreting many isotope signals observed from geochemical and cosmochemical processes.

SHEsis,a powerful software platform for analyses of linkage disequilibrium,haplotype construction,and genetic association at polymorphism loci

In multiloci-based genetic association studies of complex diseases, a powerful and high efficient tool for analyses oflinkage disequilibrium (LD) between markers, haplotype distributions and many chi-square/p values with a large numberof samples has been sought for long. In order to achieve the goal of obtaining meaningful results directly from raw data,we developed a robust and user-friendly software platform with a series of tools for analysis in association study withhigh efficiency. The platform has been well evaluated by several sets of real data.

Analysis of Disequilibrium Hybridization in Hybrid and Backcross Progenies of Saccharum officinarum × Erianthus arundinaceus

Erianthus arundinaceus is an important, closely related genus of Saccharum officinarum L. It is therefore important to understand how the chromosomes are transmitted when it hybridizes with sugarcane. The hybrids and backcross progenies of S. officinarum and E. arundinaceus and their parents were used for Karyotype analysis and to study the law of chromosome transmission. The results showed that the somatic chromosome number of both of the E. arundinaceus Hainan92-105 and Hainan92-77 were 2n = 60 = 60sm, belonging to type 1 A, and the BC1 YC01-21 was 2n = 104 = 100m ＋ 4sm, belonging to type 2C. The other six tested clones belonged to type 2B. The both F1s YC96-66 and YC96-40 that originated from Badila （2n = 80 = 70m ＋ 10sm） with E. Arundinaceus were 2n = 70 = 68m ＋ 2sm, which suggests an n ＋ n transmission. The cross between YC96-66 （female parent） and CP84-1198 （male parent, 2n = 120 = 114m ＋ 6sm） also followed the same genetic law and the somatic chromosome number of their progeny, YC01-3 （2n = 105 = 95m ＋ 10sm）. The cross derived from YC96- 40 （female） and CP84-1198 （male）, YC01-21 had 2n = 104 = 100m ＋ 4sm chromosomes, following the same genetic law of n ＋ n. However, YC01-36 had 2n = 132 = 130m ＋ 2sm chromosomes, which suggests a 2n ＋ n chromosome transmission. It can be inferred that the inheritance of chromosomes was very complex in the BC1. The difference in chromosome number between clones was as high as 28. This could be explained by the 2n ＋ n transmission of chromosomes. In addition, as there was not be a regular number of haploids, this phenomenon is termed as disequilibrium hybridization.

^(234)Th/^(238)U disequilibrium and particulate organic carbon export in the northwestern South China Sea

234Th was utilized as a tracer of particulate organic carbon （POC） export in the northwestern South China Sea （SCS） on the basis of the data collected at four stations during a spring cruise. Depth profiles of dissolved and particulate 234Th activities were measured in the upper 60m, showing a significant deficit relative to 23Su over the investigated stations. A stratified structure of 234Th-23su disequilibrium was in general observed in the upper 60 m water column, indicating that the euphotic zone of the northwestern SCS in this reason can be divided into two layers, an upper and lower layer, with different export rates. POC export fluxes were estimated from a one-dimensional steady state model of 234Th fluxes in combination with the measurement of POC/234Th ratios on suspended particles. The POC export in this region ranged from 8.2 to 20.0 mmol/（m2.d）, with an average of 16.0 mmol/（m2-d）, and was slightly higher than those previously reported in the southern SCS.

Measurement of nuclides of uranium and thorium series of disequilibrium using γ-spectroscopy

The decay dynamic equations of two daughters were resolved as initial activities of daughters are not zero, and gave calculation formula of activities for measuring uranium and thorium series of disequilibrium using γ-spectroscopy. 238U, 234Th, 226Ra, 222Rn, 228Ra, 228Th, 224Ra, 212Pb, 210Pb and 40K in two sediment samples were determined as application.

An approach to incorporate linkage disequilibrium structure into genomic association analysis

In this study, we propose to use the principal component analysis （PCA） and regression model to incorporate linkage disequilibrium （LD） in genomic association data analysis. To accommodate LD in genomic data and reduce multiple testing, we suggest performing PCA and extracting the PCA score to capture the variation of genomic data, after which regression analysis is used to assess the association of the disease with the principal component score. An empirical analysis result shows that both genotype-based correlation matrix and haplotype-based LD matrix can produce similar results for PCA. Principal component score seems to be more powerful in detecting genetic association because the principal component score is quantitatively measured and may be able to capture the effect of multiple loci.

Distribution Characteristics and Linkage Disequilibrium of TIM4 Promoter Polymorphisms in Asthma Patients of Chinese Han Population

To investigate the distribution characteristics and linkage disequilibrium of T cell immunoglobulin domain and mucin domain protein 4 （TIM4） promoter polymorphisms in asthma patients of Chinese Han population, the promoter region of TIM4 was re-sequenced by PCR-sequencing, and linkage disequilibrium was analyzed by SHEsis software. Four single nucleotide polymor- phisms （SNPs） in the promoter region of TIM4 were detected, including two new SNPs （at positions -1609, -153） and two reported SNPs （rs6874202, rs6882076）. The frequency distribution of rs6882076 was different among different races （P〈0.05）. In addition, linkage disequilibrium among the SNPs of the promoter region of TIM4 was found and GGTG was the predominant haplotype. There were four SNPs in the promoter region of TIM4 in asthma patients of Chinese Han population, which were in linkage disequilibrium.

Linkage Disequilibrium in Wild and Cultured Populations of Pacific Oyster(Crassostrea gigas)

Linkage disequilibrium(LD) can be applied for mapping the actual genes responsible for variation of economically important traits through association mapping.The feasibility and efficacy of association studies are strongly dependent on the extent of LD which determines the number and density of markers in the studied population,as well as the experimental design for an association analysis.In this study,we first characterized the extent of LD in a wild population and a cultured mass-selected line of Pacific oyster(Crassostrea gigas).A total of 88 wild and 96 cultured individuals were selected to assess the level of genome-wide LD with 53 microsatellites,respectively.For syntenic marker pairs,no significant association was observed in the wild population;however,three significant associations occurred in the cultured population,and the significant LD extended up to 12.7 c M,indicating that strong artificial selection is a key force for substantial increase of genome-wide LD in cultured population.The difference of LD between wild and cultured populations showed that association studies in Pacific oyster can be achieved with reasonable marker densities at a relatively low cost by choosing an association mapping population.Furthermore,the frequent occurrence of LD between non-syntenic loci and rare alleles encourages the joint application of linkage analysis and LD mapping when mapping genes in oyster.The information on the linkage disequilibrium in the cultured population is useful for future association mapping in oyster.

Detection of QTL(quantitative trait loci) associated with wood density by evaluating genetic structure and linkage disequilibrium of teak

To find the quantitative trait loci associated with wood density in teak(Tectona grandis L.f.), 21 co-dominant markers including 13 site specific recombinase and 8 EST-based co-dominant markers designed from lignin biosynthesis genes were applied to 174 teak plus tree clones at the National Germplasm Bank, Chandrapur,India. The germplasm bank exhibited 10.6% coefficient of variation for wood densities with 84.5 ± 31.3 genetic polymorphism(%). The highly panmictic set of genotypes(FST= 0.035 ± 0.004) harbored 96.47 ± 0.40 genetic variability(%). The average allelic frequency of the 21 codominant markers was 0.65 ± 0.11 with 12.9% pairs of loci in significant LD(p\0.05, R^2 values [ 0.1), confirming their suitability for a strong marker-trait association study. The marker CCoAMT-1 was significantly(p\0.01) associated with wood density showing stability by both GLM and MLM models and explained 4.3% of the phenotypic effect. The marker from the EST representing CCoAMT can be further developed for gene-assisted selection of elite genotypes of teak with greater wood density. Therefore, we believe that the report will help accelerate the genetic improvement and advance the breeding program of the species.

Decentralization,spatial disequilibrium,and restructuring of coastal tourist destination-Empirical research from Sanya,China

The objective of this article is to speculate on resort restructuring in the market-oriented reform process in China.Previous studies show that spatial disequilibrium was aggravated by decentralization,which leads to the difference in tourism policy and investment,public goods,and service;a profound analytical framework is much needed for further empirical studies.This article has reviewed the relevant studies on links between decentralization and restructuring,spatial influences of decentralization on tourism,based on which we put forward the theoretical framework of resort spatial restructuring from the view of political economy analysis,then we elaborate on and discuss it based on the example of Sanya,China.In short,the article suggests that decentralization of fiscal responsibilities and institutional power contributes to the spatial disequilibrium of tourism industrial structure,land use,public infrastructure and service facilities,and to community inequality.Interests of government,investors,and community should be comprehensively coordinated in the resort spatial restructuring process from three aspects:restructuring government,optimizing space structure,and tourism industry.Furthermore,we argue that resort restructuring in the context of Sanya requires coordination of various interest groups through four ways:restructure the government power under administrative division adjustment,optimizing spatial structure,expanding industrial space to diversified tourism products,and building resort management services organization.Finally,we discussed some policy requirements for resort sustainable development.

Particulate organic carbon export flux by ^(234)Th/^(238)U disequilibrium in the continental slope of the East China Sea

234Th is widely used to quantify the magnitude of upper ocean particulate organic carbon （POC） export in oceans. In the present work, the rates of particulate organic carbon export were measured based on the distribution patterns of 234Th/238U disequilibrium in the water column within the continental slope of the East China Sea （ECS） during May 2011. The profiles of particulate and dissolved 234Th activities at all three stations showed a relative deficit with respect to 238U in the upper 100 m of the water column. The dissolved 234Th scavenging rates and the particulate 234Th removal rates and their residence times were calculated by a one-dimensional steady state model. The results showed that the dissolved a34Th scavenging rates and the particulate 234Th removal rates ranged from 12.4-61.4 dpm/（m3.d） and from 3.8-21.8 dpm/（m3.d）, respectively. The residence times of dissolved and particulate 234Th were in the range of 3.4-158 d and 63.7- 96.5 d, respectively. Combined with the measurement of POC/Z34Th ratios of suspended particles, POC export flux （calculated by carbon） from the euphotic zone was estimated in the study region, which ranged from 4.14-14.7 mmol/（m2 .d）, with an average of 8.21 mmol/（m3.d）, occupying 35% of the prime productivity in the study area. The results of this study can provide new information for better understanding the carbon biogeochemical cycle within the continental slope of the ECS.

Particulate organic carbon export fluxes on Chukchi Shelf,western Arctic Ocean,derived from ^(210)Po/^(210)Pb disequilibrium

Fluxes of particulate organic carbon （POC） were derived from ^210Po/^210Pb disequilibrium during the 4th Chinese National Arctic Research Expedition （CHINARE-4） from July 1 to September 28, 2010. Average residence times of particulate ^210Po in the euphotic zone were -16.00 a to 1.54 a, which are higher than those of dissolved ^210^Po （-6.89 a to -0.70 a）. Great excesses of dissolved ^210Po were observed at all stations, with an average 210^Po/^210^Pb ratio of 1.91±0.20, resulting from 210^Pb atmospheric deposition after sea ice melt. POC fluxes from the euphoric zone were estimated by two methods （E and B） in the irreversible scavenging model. Estimated POC fluxes were 945-126 mmol C/（m^2·a）and 1 848-109 mmol C/（m^2·a） by methods E and B, respectively, both decreasing from low to high latitude. The results are comparable to previous works for the same region, indicating efficient biological pumping in the Chukchi Sea. The results can improve understanding of the carbon cycle in the western Arctic Ocean.

Equilibrium vs.disequilibrium melting relations in the Higher Himalayan Crystalline(HHC) pelitic migmatites,Sikkim Himalaya

Higher Himalayan Crystalline（HHC） complex of the Sikkim Himalaya predominantly consists of high-grade pelitic migmatites.In this study,reaction textures,mineral/bulk rare earth elements （REE）,trace element partition coefficients and trace element zoning profiles in garnet are used to demonstrate a complex petrogenetic process during crustal anatexis.With the help of equilibrium REE and trace element partitioning model,it is shown that strong enrichment of Effective Bulk Composition（EBC） is responsible for the zoning in garnet in these rocks.The data strongly support disequilibrium element partitioning and suggest that the anatectic melts associated with mafic selvedges are likely produced by disequilibrium melting because of fast melt segregation process.

Haplotype phasing after joint estimation of recombination and linkage disequilibrium in breeding populations

A novel method for haplotype phasing in families after joint estimation of recombination fraction and linkage disequilibrium is developed. Results from Monte Carlo computer simulations show that the newly developed E.M. algorithm is accurate if true recombination fraction is 0 even for single families of relatively small sizes. Estimates of recombination fraction and linkage disequilibrium were 0.00 （SD 0.00） and 0.19 （SD 0.03） for simulated recombination fraction and linkage disequilibrium of 0.00 and 0.20, respectively. A genome fragmentation phasing strategy was developed and used for phasing haplotypes in a sire and 36 progeny using the 50 k Illumina BeadChip by： a） estimation of the recombination fraction and LD in consecutive SNPs using family information, b） linkage analyses between fragments, c） phasing of haplotypes in parents and progeny and in following generations. Homozygous SNPs in progeny allowed determination of paternal fragment inheritance, and deduction of SNP sequence information of haplotypes from dams. The strategy also allowed detection of genotyping errors. A total of 613 recombination events were detected after linkage analysis was carried out between fragments. Hot and cold spots were identified at the individual （sire level）. SNPs for which the sire and calf were heterozygotes became informative （over 90%） after the phasing of haplotypes. Average of regions of identity between half-sibs when comparing its maternal inherited haplotypes （with at least 20 SNP） in common was 0.11 with a maximum of 0.29 and a minimum of 0.05. A Monte-Carlo simulation of BTA1 with the same linkage disequilibrium structure and genetic linkage as the cattle family yielded a 99.98 and 99.94% of correct phases for informative SNPs in sire and calves, respectively.

An Analysis of Disequilibrium Consumption and Inflation in China

The rapid economic growth in China has attracted the attention all over the world since 1980s. At the same time Chinese economists and government are perplexed by high rate of inflation. The high rate of inflation in China’s economy is shown by the coexistance of investment expansion and consumption expansion. It is difficult, with recent research results, to distinguish quantitatively the influence degree and the causes of formation of the consumption expansion and investment expansion in such a high rate of inflation. Based on disequilibrium economic theory and the method of disequilibrium econometric analysis, a disequilibrium model of consumption goods market in China is proposed. The relationship between the disequilibrium consumption and inflation in China’s macroeconomy is analyzed. It is pointed out that the part of high rate of inflation caused by the increase in consumer demand only takes up a comparatively small proportion in the whole inflation, and the main cause is not merely the rapid increase in people’s income.

Identification of Single Nucleotide Polymorphisms and Analysis of Linkage Disequilibrium in Different Bamboo Species Using the Candidate Gene Approach

Bamboos are one of the most beautiful and useful plants on Earth.The genetic background and population structure of bamboos are well known,which helps accelerate the process of artificial domestication of bamboo.Partial sequences of six genes involved in nitrogen use efficiency in 32 different bamboo species were analyzed for occurrence of single nucleotide polymorphisms(SNPs).The nucleotide diversityθw and total nucleotide polymorphismsπT of the sequenced DNA regions was 0.05137 and 0.03332,respectively.Bothπnonsyn/πsyn and Ka/Ks values were<1.The nucleotide sequences of these six genes were inferred to be relatively conserved,and the haplotype diversity was relatively high.The results of evolutionary neutrality tests showed that the six genes were in line with neutral evolution,and that the NRT2.1 and AMT2.1 gene sequences may have experienced negative selection.An inter-SNP recombination event at the NRT2.1 gene in the all pooled sample,of all 32 bamboo species was the lowest at 0.0645,whereas the AMT gene recombination events were all>0.1.Estimation and analysis of linkage disequilibrium of five genes revealed that with the increase in nucleotide sequence length,the degree of SNP linkage disequilibrium decreased rapidly.We inferred the population genetic structure of 32 bamboo species based on the SNP loci of six genes with frequencies>18%.32 bamboo species were divided into five categories,which indicated that the combined population of all bamboo species had obvious multivariate characteristics and was heterogeneous;red(Group 1)and green(Group 2)were the main groups.

Testing for Homogeneity of Linkage Disequilibrium Across Strata

In this article, using the likelihood score theory extended to nuisance parameters we derive a new homogeneity score test for comparing linkage disequilibrium across several strata. Power and sample size formulae are also obtained.

Fine mapping of multiple interacting quantitative trait loci using combined linkage disequilibrium and linkage information

Quantitative trait loci (QTL) and their additive, dominance and epistatic effects play a critical role in complex trait variation. It is often infeasible to detect multiple interacting QTL due to main effects often being confounded by interaction effects. Positioning interacting QTL within a small region is even more difficult. We present a variance component approach nested in an empirical Bayesian method, which simultaneously takes into account additive, dominance and epistatic effects due to multiple interacting QTL. The covariance structure used in the variance component approach is based on combined linkage disequilibrium and linkage (LDL) information. In a simulation study where there are complex epistatic interactions between QTL, it is possible to simultaneously fine map interacting QTL using the proposed approach. The present method combined with LDL information can efficiently detect QTL and their dominance and epistatic effects, making it possible to simultaneously fine map main and epistatic QTL.

Use of Observed Genomic Information to Infer Linkage Disequilibrium between Markers and QTLs

Conducting genomic selection in admixed populations is challenging and its accuracy in this case largely depends on the persistence of linkage disequilibrium between single nucleotide polymorphisms (SNP) and quantitative trait loci (QTL). Inferring linkage disequilibrium (LD) between SNP markers and QTLs could be important in understanding the change of SNP marker effects across different breeds. Predicting the change in linkage disequilibrium between markers and QTLs across two divergent breeds was explored using information from the genotype data. Two different models (M1, M2) that differ in the definition of the explanatory variables were used to infer the level of LD between SNP markers and QTLs using all markers in the panel or windows of fixed number of markers. Three simulation scenarios were conducted using different number of SNPs and QTLs. In the first scenario, the resulting coefficient of determination (R2) was 0.65 and 0.52 using M1 and M2, respectively. In the second scenario, average R2 equaled 0.12 using all markers in the panel and 0.25 using 100 marker windows. Across the three simulation scenarios, it was clear that a significant portion of the variation in the change in LD between SNP markers and QTLs could be explained by information already available in the observed SNP marker data.

Disequilibrium Analysis of Money Market in China

By the disequilibrium economic theory,this paper first investigates the disequilibrium mathematical economic model of the money market in China.Then,we study the disequilibrium transition of Chinese money market from 1954 to 1993 using a non parametric local fitting technique.Without assuming explicit functional forms,the method of locally weighted maximum likelihood is applied to estimate and test the variations in demand and supply during the period between 1954 to 1993.Furthermore,the disequilibrium state and mechanism of Chinese money market are inspected and the direction,the strength and the fluctuation of the disequilibrium are discussed respectively.Finally the policy suggestions are given about adjusting effectively money demand and supply under the condition of co existing of plan and market economy.In this paper,a brief review on the disequilibrium researches on money market in foreign countries is also given.