Coefficients Of Parentage Research Articles

Partial dynamical symmetries in thej=9/2shell: Progress and puzzles

We present new results concerning the properties of solvable states of four particles in a $j=9/2$ shell which have seniority $v=4$ and angular momentum $I=4$ or 6. In particular, based on properties of certain coefficients of fractional parentage, we show that the number of pairs coupled to angular momentum $I$ is equal to one for these states. Similar results can be derived entirely analytically for four particles in a $j=7/2$ shell.

Genetic Diversity and Improvement of Contemporary Proprietary North American Dent Corn

Coefficient of parentage (CP) is useful to estimate genetic diversity (1 − CP) among a set of lines. Estimated diversity among 846 proprietary inbred corn (Zea mays L.) lines registered in the United States from 1976 to 2005 shows favorable diversity of 0.944. Less diversity (0.859) was found among 47 widely grown hybrids from 1995 to 2001. Cluster analysis of the 55 parental inbreds formulating these 47 hybrids found nine family clusters, four that were Iowa Stiff Stalk Synthetic (BSSS) and five that were non‐BSSS, with intergroup diversity of 0.99 between BSSS and non‐BSSS. There was less genetic diversity among BSSS (0.64) than among non‐BSSS (0.90) inbreds. Genetic diversity within the nine family clusters B73/B14, B73/B37, B73/Maiz Amargo, B37/B14/Maiz Amargo, Miscellaneous/Oh43, Mo17/LH123, LH82, Oh07/Midland/Female Composite, and Iodent were 0.238, 0.285, 0.285, 0.735, 0.817, 0.525, 0.346, 0.554, and 0.539, respectively. Evaluation of the lineage of 470 recently (1996–2005) registered proprietary inbreds found that 170 (36%) are direct descendents of the public inbred B73. Breeding progress was estimated using progeny to parent side‐by‐side comparisons. Significant increases per breeding cycle were found for inbred grain yield (6%), plant height (2.3%), ear height (2.2%), and kernel weight (3%), but ear length decreased 4%. Hybrid grain yield increased 2.2% per breeding cycle. A positive correlation (0.36) was found between inbred and hybrid grain yields.

Genetic Diversity of Contemporary North American Barley

Crop diversity has important implications for genetic vulnerability and potential for crop improvement. Genetic diversity was estimated by coefficient of parentage (CP) among 363 contemporary North American barley (Hordeum vulgare L.) cultivars registered during the era of 1970 through 2006. This was facilitated by using pedigree lineage derived from U.S. Plant Variety Protection Certificates and/or registration articles. Overall diversity, as measured through CP, was estimated at 0.023 for this era. Diversity was greater among feed (CP = 0.020) than among malt barley (0.111) cultivars. The estimate of genetic diversity was much lower (CP = 0.141) among 23 widely grown cultivars that constituted 87% of the U.S. harvested barley hectarage from 2001 through 2005. Within these 23 elite cultivars, diversity was substantially lower for six‐row malting barley (CP = 0.574) versus two‐row malting barley (CP = 0.237). Most prevalent types of breeding populations used for development of the 363 North American barley cultivars registered from 1970 through 2005 were two‐parent cross (used for 44% of new cultivars), complex cross (25%), and three‐parent cross (14%). Barley breeding progress for grain yield improvement was estimated at 4.4% per breeding cycle using yield comparison of progeny and parents across environments. Barley germplasm available is genetically diverse, recycling leading commercial cultivars predominates and this breeding strategy has been successful.

A computer program for two-particle generalized coefficients of fractional parentage

A computer program for two-particle generalized coefficients of fractional parentage

Systematic study of multi-quark states: Aqq−qq−q¯configuration

A group theoretic method for the systematic study of multiquark states is developed. The calculation of matrix elements of many-body Hamiltonians is simplified by transforming the physical bases (quark cluster bases) to symmetry bases (group chain classified bases), where the fractional parentage expansion method can be used. A five-quark system is taken as the example in this study. The Jaffe--Wilczek $\mathit{qq}\text{\ensuremath{-}}\mathit{qq}\text{\ensuremath{-}}\overline{q}$ configuration is chosen as one of the examples to construct the physical bases and the transformation coefficients between physical bases and symmetry ones are shown to be related to the ${\mathrm{SU}}_{\mathit{mn}}\ensuremath{\supset}{\mathrm{SU}}_{m}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}}_{n}$ isoscalar factors. A complete transformation coefficient table is obtained. The needed isoscalar factors and fractional parentage coefficients have been calculated with our new group representation theory and published before. Three quark models, the naive Glashow-Isgur model, the Salamanca chiral quark model, and quark delocalization color screening model, are used to show the general applicability of the new multiquark calculation method and general results of constituent quark models for five-quark states are given.

CIMMYT's use of synthetic hexaploid wheat in breeding for adaptation to rainfed environments globally.

The International Maize and Wheat Improvement Center (CIMMYT) has had significant impact on wheat production in rainfed regions of the developing world. During the last decade, yield potential has increased in drought-prone areas partly due to the use of synthetic hexaploid wheat (SHW), produced through interspecific hybridisation of Triticum turgidum spp. and Aegilops tauschii, followed by chromosome doubling. The objectives of this study were to document the use of SHW in wheat breeding at CIMMYT and quantify its potential effect on global wheat adaptation. The first SHW-derived lines targetted at rainfed conditions appeared in the 5th Semi-Arid Wheat Yield Trial (SAWYT) representing 8% of the lines, increasing to 46% by the 15th SAWYT. During the same period the average coefficient of parentage of SHW in all synthetically derived crosses decreased from 75 to 19%. Average yield rank of genotypes across locations and years was used as a performance indicator of the SHW-derived lines in SAWYT 5–12. In the 5th SAWYT the average rank of the SHW-derived lines was 30 (out of 50) increasing to 25 by the 12th SAWYT. SAWYT 11 was the first trial to include SHW-derived lines bred exclusively for rainfed environments, using directed selection for drought tolerance. International trial data from SAWYT 11 and 12 showed that the SHW-derived line Vorobey was a top-performing line. Vorobey performed well across all environments compared with the best locally adapted check cultivar at each location; trial means ranged from 1 to 8 t/ha. To further exploit genetic diversity for adaptation to drought, SHW has been produced using emmer wheat (T. turgidum L. subsp. dicoccon) as the tetraploid parent. Yield trial data from Mexico show that SHW derivatives based on emmer wheat improved yield performance under drought compared with their drought-tolerant recurrent parents. The use of SHW in wheat breeding for rainfed environments at CIMMYT has increased significantly over the past 10–15 years and the performance and effect of the derived lines have improved with time.

Genealogical analysis of the diversity of spring barley cultivars released in former Czechoslovakia and modern Czech Republic

Genealogical analysis was employed in studying the time course of changes in genetic diversity of spring barley cultivars released in former Czechoslovakia and the modem Czech Republic. Cultivars from different regions proved to significantly differ in the distribution of dominant ancestor contributions, suggesting a specificity of original ancestors to different cultivation conditions. A comparison of cultivar groups differing in end use showed that the genetic diversity of malting cultivars was significantly lower than that of feed cultivars, although modern malting and feed cultivars of Czechia and Slovakia have virtually the same genetic basis. Temporal analysis showed that diversity tended to increase through decades. While new original ancestors were introduced in pedigrees, especially in the past 30 years, the number of local landraces and old cultivars gradually decreased. The losses accounted for about two-thirds of the local germplasm. Thus, a substantial increase in genetic diversity was accompanied by genetic erosion of the local spring barley gene pool of former Czechoslovakia. A cluster structure was observed for the set of spring barley cultivars released in the postwar period. The coefficient of parentage averaged overall possible pairs of cultivars introduced in the Czech National List was estimated at 0.11. It was concluded that the genetic diversity of modern spring barley cultivars in the Czech Republic is at an acceptable level.

The grasp2K relativistic atomic structure package

This paper describes grasp2K, a general-purpose relativistic atomic structure package. It is a modification and extension of the GRASP92 package by [F.A. Parpia, C. Froese Fischer, I.P. Grant, Comput. Phys. Comm. 94 (1996) 249]. For the sake of continuity, two versions are included. Version 1 retains the GRASP92 formats for wave functions and expansion coefficients, but no longer requires preprocessing and more default options have been introduced. Modifications have eliminated some errors, improved the stability, and simplified interactive use. The transition code has been extended to cases where the initial and final states have different orbital sets. Several utility programs have been added. Whereas Version 1 constructs a single interaction matrix for all the J's and parities, Version 2 treats each J and parity as a separate matrix. This block structure results in a reduction of memory use and considerably shorter eigenvectors. Additional tools have been developed for this format. The CPU intensive parts of Version 2 have been parallelized using MPI. The package includes a “make” facility that relies on environment variables. These make it easier to port the application to different platforms. The present version supports the 32-bit Linux and ibmSP environments where the former is compatible with many Unix systems. Descriptions of the features and the program/data flow of the package will be given in some detail in this report.

Characteristic frequency of the magnetic radiation of spinor condensates

The magnetic radiation of the fully condensed states of spinor condensates has been studied. A narrow characteristic spectral line together with a strong background at its violet side have been found. For the condensate of $N={10}^{12}$ atoms of $^{23}\mathrm{Na}$ confined in an isotropic and harmonic trap with frequency ${\ensuremath{\omega}}_{o}=300\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, for instance, the photon energy of the characteristic line is $127.9\ensuremath{\hbar}{\ensuremath{\omega}}_{o}$ with width $<1.\ensuremath{\hbar}{\ensuremath{\omega}}_{o}$ and the probability of transition is $1.44\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}34}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The photon energy and probability have been found to be proportional to ${N}^{2∕5}$ and ${N}^{17∕5}$, respectively. It implies that magnetic radiations with higher photon energies and much larger probabilities can be obtained if numerous atoms are trapped. A technique developed by the authors, namely, the analytical forms of the fractional parentage coefficients, was used to calculate analytically the matrix elements between the spin states that conserve the total spin and its $Z$ component.

Relations between coefficients of fractional parentage

For each of the (9/2) (11/2), and (13/2) single j shells we have only one state with J=j v=3 for a five particle system. For four identical particles there can be more than one state of seniority four. We note some 'ratio' relations for the coefficients of fractional parentage for the four and five identical particle systems, which are found in the works of de Shalit and Talmi [Nuclear Shell Theory (Academic Press, New York, 1963)] and Talmi [Simple Models of Complex Nuclei (Harwood Academic, Reading, UK, 1993)] to be useful for explaining the vanishing of a five particle coefficients of fractional parentage (cfp). These relations are used to show that there is a special (g{sub 9/2}){sup 4} I=4 v=4 wave function that cannot be admixed with an I=4 v=2 wave function, even with seniority violating interactions.

Genetic base of tea (Camellia sinensis L.) cultivars in Sri Lanka as revealed by pedigree analysis

An understanding of genetic diversity and relationships among breeding materials is a prerequisite for crop improvement. Coefficient of parentage (COP) can be used to measure the genetic diversity among genotypes on the basis of pedigree information. In the present study, COP was estimated for 56 cultivars, including commercial tea cultivars developed by the Tea Research Institute of Sri Lanka and their parental lines. Mean COP of the 56 accessions studied was 0.097 and the value was raised up to 0.272 when non-related pair-wise comparisons were excluded. A single cultivar (Assam/Cambod introduction) was the nucleus of the commercial cultivars. Group mean COP of the cultivars derived from Assam/Cambod parentage was 0.17. Thirty-three percent of the pair-wise comparisons had 0.00 COP, highlighting that many cultivars were unrelated. Within the pedigree, 2 major COP clusters were identified: Assam/Cambod open-pollinated half-sib progenies, and full-sib progenies derived from crosses between Assam/Cambod and other parental lines. The elite groups within the pedigree, where Assam/Cambod parentage was concentrated, were also identified. Information generated in this study should be useful for effective utilization of available diversity in future breeding programmes as well as for proper conservation of genetic diversity in the adapted germplasm. This is the first report on estimates of genetic diversity based on COP in a woody perennial crop, such as tea.

Relationships among durum wheat accessions. II. A comparison of molecular and pedigree information

The study of direct ancestry relationships provides information with which to determine essential derivation. SSR profiles were used to determine the pattern of relatedness among 134 durum wheat accessions, representing the most important modern durum wheat gene pools. Simple sequence repeat (SSR)- and amplified fragment length polymorphism (AFLP)-based genetic similarities among cultivars with accurate pedigrees were compared with pedigree-based coefficients of parentage. Sizeable departures of molecular similarities from the expected ones were observed, indicating the unreliability of inferring the pattern of genetic relatedness from the coefficient of parentage. Case studies consisting of parent-progeny cultivar trios and pairs, identified on the basis of their registered pedigree, were studied to evaluate the probability of ancestry of each progeny cultivar, compared with all the remaining accessions. Rare alleles and haplotype sharing were also explored. When the results did not agree with the registered parentages, SSR markers provided information with which to identify the most probable parents (or the corresponding "breeding lineages") in the collection.

Genetic characterization of ninety elite soybean cultivars using coefficient of parentage

The objective of this work was to estimate the coefficient of parentage and to understand the genetic structure of 90 elite soybean cultivars, which are adapted to different Brazilian environments. A total of 4,005 coefficients of parentage (f) were obtained and used to group the cultivars by UPGMA method. The constructed dendrogram showed several related cultivar groups which shared similar ancestors and clearly showed the genetic structure of the main Brazilian cultivars. Effective population sizes (Ne) were also estimated for cultivars in different generations. The average f = 0.2124 value, obtained from cultivars classified into four decades according to the release year, suggested effective soybean population sizes of 11 and 13 calculated using arithmetic and weighted means, respectively. The relatively small Ne and the high parentage coefficient support the conclusion that there is a high similarity degree among the main soybean cultivars in Brazil.

The p-band of spin-1 87Rb BEC in an isotropic laser trap

The energy band of spin-1 87Rb Bose–Einstein condensate with orbital angular momentum L = 1 has been investigated by the fractional parentage coefficient method that deals with spin wavefunctions and associated matrix elements rigorously. A couple of generalized Gross–Pitaevskii equations for spatial wavefunctions have been deduced. The bottom level of the p-band and the top level of the s-band exhibit an interesting crossover.

Genealogical Analysis in the Czech Spring Wheat Collection and its Use for the Creation of Core Collection

A spring wheat collection of the Czech gene bank included altogether 3270 original accessions in 2005; among them 2123 accessions with pedigree were analyzed using the construction of genetic profiles and subsequent calculation of Renkonen similarity indexes. Genetic diversity was estimated by Shannon diversity index. Subsequently we calculated cluster analysis using coefficients of parentage and in addition, we selected representatives of particular clusters for a core collection. Accessions of the whole analysed set of spring wheat (2123) were progenies of 929 original ancestors and diversity index within the set was H = 4.17. In the selected core set we can trace 718 ancestors and the diversity index is H' = 4.82. The selected core set is composed of 645 accessions (i.e. 30.4% of the whole set) and it represents 77.3% of genetic diversity in the whole set. The diversity between clusters did not decrease in the core set, which shows the representativeness of selected core accessions. Genealogical analysis provided useful information for the choice of cultivars to a core collection. However, pedigree analysis has to be complemented by other generally applicable approaches such as the use of molecular markers, morphological and agronomical characters. The analysis can also provide valuable information for breeders and researchers.  

Genetic diversity among parental lines of Indica hybrid rice (Oryza sativa L.) in China based on coefficient of parentage

AbstractGenetic diversity constitutes the raw material for plant improvement, and provides protection against genetic vulnerability to biotic and abiotic stresses. Diversity of parental lines of indica hybrid rice in China is not well‐characterized. The major objective of this study was to quantify genetic diversity of Chinese parental lines of hybrid rice via coefficient of parentage (COP). All 100 parental lines of hybrid rice widely used in hybrid breeding and commercial production during 1976–2003 were studied by COP analysis. The mean COP for the 100 parental lines was low (0.056), indicating a potentially high degree of diversity in Chinese hybrid rice breeding. Forty‐nine percent of all pairs of parental lines were completely unrelated by pedigree data. The low mean COP for the parental lines was attributed to a continual incorporation of exotic germplasm (wild rice, japonica and javanica etc.) into the genetic base over time, to the introduction of foreign germplasm from the Philippines (International Rice Research Institute), Korea, the United States, Thailand, and Guyana as breeding stock. The mean COP from 1976 to 1990 was twice as much as that from 1990 to 2003. Cluster analysis was an effective method to discriminate diversity, ten clusters were identified, and maintainer lines, restorer lines and other parental lines with special genetic background were clearly grouped. In addition, restorer lines were further divided into 11 sub‐clusters, which basically was in agreement with hybrid rice breeding. Among ten provinces, Hunan, Sichuan and Fujian were outstanding for breeding 54 of 100 parental lines in hybrid rice production, and the genetic diversity of parental lines in Fujian, Sichuan,Guangxi, Hunan and Jiangsu were all narrower than that in Hubei, Guangdong, Zhejiang and Jiangxi. The result of coefficient of parentage analysis for 100 parental lines may promote the management of parental diversity and hybrid rice breeding in China.

SYMMETRIES AND STRUCTURE IN THE fp SHELL AND g9/2 SHELL

First in a single-j-shell calculation (j = f7/2) we discuss various symmetries, e.g., two to one in 44 Ti vs 43 Ti . We note that the wave function amplitudes for T(higher) states are coefficients of fractional parentage, and that orthogonality of T(higher) and T(lower) states leads to useful results. Then we consider what happens if T = 0 two-body matrix elements are set equal to zero. We find a partial dynamical symmetry with several interesting degeneracies. It is noted that some formulae developed for identical particles also apply to different (companion) problems involving mixed systems of protons and neutrons. In the g9/2 shell, where one can have for the first time seniority violation for identical particles, we find some interesting yet unproven results.

GRASP92: a package for large-scale relativistic atomic structure calculations

GRASP92: a package for large-scale relativistic atomic structure calculations

Dynamics of genetic diversity in winter common wheat Triticum aestivum L. cultivars released in Russia from 1929 to 2005

Genealogical analysis was used to study the dynamics of genetic diversity in Russian cultivars of winter common wheat from 1929 to 2005. The Shannon diversity index of the total set of released cultivars remained almost unchanged, although the number of original ancestors (landraces and genetic lines) increased almost tenfold in the period under study. This was explained in terms of the dependence of the modified Shannon diversity index on two parameters, the number of original ancestors and the mean coefficient of parentage. Significant direct effects were revealed: a positive effect of the former parameter and a negative of the latter. As a result, the increase in the number of original ancestors was compensated by the increase in relatedness of cultivars. Genetic erosion of realized diversity was observed, as a half of Russian landraces were lost. Although the mean coefficient of parentage did not reach its critical value (R = 0.25), cultivars of some regions (Central and Volga-Vyatka) proved to be closely related. A favorable gradual decrease in the mean coefficient of parentage was observed in the past 15 years. A set of modem winter wheat cultivars, which were introduced in the Russian State Catalog from 2002 to 2005, displayed a cluster structure. The overwhelming majority of cultivars formed two clusters originating from Bezostaya 1 (67% of cultivars) and Mironovskaya 808 (31%).

Genealogical analysis of resistance to fusarium head blight in Russian and Ukrainian cultivars of common wheat Triticum aestivum L.

The GRIS3.5 information analytical system of wheat genetic resources was used to track the possible ways of the transmission of fusarium head blight resistance from ancestors to progenies in extended pedigrees of 149 Russian and Ukrainian cultivaris of winter common wheat. Analysis of variance was performed for the coefficient of parentage computed for the cultivars under study and the putative sources of resistance and revealed that groups of resistant and susceptible cultivars differed in the distribution of contributions of the sources. In the resistant group, significant results were obtained for the contributions of Odesskaya 16, Gostianum 237, and Frontana. Pedigree analysis showed that fusarium head blight resistance was most commonly transmitted from Gostianum 237 through Odesskaya 16 and its derivatives. The landrace Khar'kovskaya probably served as a source of resistance in the case of Gostianum 237. In addition, the set of resistance sources included Kooperatorka, Hope, San Pastore, Triticum timopheevii Zhuk., and Secale cereale. Some well-known sources of fusarium head blight resistance varying in genetic determinants--Sumai 3, Wangshuibai, Wuhan 1, Nyubay (China), Nobeokabozukomugi, Shinchunaga (Japan), Arina (Switzerland), Fundulea-201R (Romania), and Renan (France)--have so far not being employed in breeding in Russia and provide an important reserve for breeding for resistance.