Genetic diversity and its relationship to hybrid performance in maize as revealed by RFLP and AFLP markers

 The challenge to maize breeders is to identify inbred lines that produce highly heterotic hybrids. In the present study we surveyed genetic divergence among 13 inbred lines of maize using DNA markers and assessed the relationship between genetic distance and hybrid performance in a diallel set of crosses between them. The parental lines were assayed for DNA polymorphism using 135 restriction fragment length polymorphisms (RFLPs) and 209 amplified-fragment polymorphisms (AFLPs). Considerable variation among inbreds was detected with RFLP and AFLP markers. Moreover AFLPs detect polymorphisms more efficiently in comparison to RFLPs, due to the larger number of loci assayed in a single PCR reaction. Genetic distances (GDs), calculated from RFLP and AFLP data, were greater among lines belonging to different heterotic groups compared to those calculated from lines of the same heterotic group. Cluster analysis based on GDs revealed associations among lines which agree with expectations based on pedigree information. The GD values of the 78 F₁ crosses were partioned into general (GGD) and specific (SGD) components. Correlations of GD with F₁ performance for grain yield were positive but too small to be of predictive value. The correlations of SGDs, particularly those based on AFLP data, with specific combining-ability effects for yield may have a practical utility in predicting hybrid performance. Received: 15 August 1997 / Accepted: 19 September 1997     

Deducing Hybrid Performance from Parental Metabolic Profiles of Young Primary Roots of Maize by Using a Multivariate Diallel Approach

Heterosis, the greater vigor of hybrids compared to their parents, has been exploited in maize breeding for more than 100 years to produce ever better performing elite hybrids of increased yield. Despite extensive research, the underlying mechanisms shaping the extent of heterosis are not well understood, rendering the process of selecting an optimal set of parental lines tedious. This study is based on a dataset consisting of 112 metabolite levels in young roots of four parental maize inbred lines and their corresponding twelve hybrids, along with the roots'' biomass as a heterotic trait. Because the parental biomass is a poor predictor for hybrid biomass, we established a model framework to deduce the biomass of the hybrid from metabolite profiles of its parental lines. In the proposed framework, the hybrid metabolite levels are expressed relative to the parental levels by incorporating the standard concept of additivity/dominance, which we name the Combined Relative Level (CRL). Our modeling strategy includes a feature selection step on the parental levels which are demonstrated to be predictive of CRL across many hybrid metabolites. We demonstrate that these selected parental metabolites are further predictive of hybrid biomass. Our approach directly employs the diallel structure in a multivariate fashion, whereby we attempt to not only predict macroscopic phenotype (biomass), but also molecular phenotype (metabolite profiles). Therefore, our study provides the first steps for further investigations of the genetic determinants to metabolism and, ultimately, growth. Finally, our success on the small-scale experiments implies a valid strategy for large-scale experiments, where parental metabolite profiles may be used together with profiles of selected hybrids as a training set to predict biomass of all possible hybrids.     

A general mixture model approach for mapping quantitative trait loci from diverse cross designs involving multiple inbred lines

Most current statistical methods developed for mapping quantitative trait loci (QTL) based on inbred line designs apply to crosses from two inbred lines. Analysis of QTL in these crosses is restricted by the parental genetic differences between lines. Crosses from multiple inbred lines or multiple families are common in plant and animal breeding programmes, and can be used to increase the efficiency of a QTL mapping study. A general statistical method using mixture model procedures and the EM algorithm is developed for mapping QTL from various cross designs of multiple inbred lines. The general procedure features three cross design matrices, W, that define the contribution of parental lines to a particular cross and a genetic design matrix, D, that specifies the genetic model used in multiple line crosses. By appropriately specifying W matrices, the statistical method can be applied to various cross designs, such as diallel, factorial, cyclic, parallel or arbitrary-pattern cross designs with two or multiple parental lines. Also, with appropriate specification for the D matrix, the method can be used to analyse different kinds of cross populations, such as F2 backcross, four-way cross and mixed crosses (e.g. combining backcross and F2). Simulation studies were conducted to explore the properties of the method, and confirmed its applicability to diverse experimental designs.     

Genetic diversity for RFLPs in European maize inbreds

Summary Restriction fragment length polymorphisms (RFLPs) have been proposed for the prediction of the yield potential of hybrids and the assignment of inbreds to heterotic groups. Such use was investigated in 66 diallel crosses among 6 flint and 6 dent inbreds from European maize (Zea mays L.) germ plasm. Inbreds and hybrids were evaluated for seven forage traits in four environments in the Federal Republic of Germany. Midparent heterosis (MPH) and specific combining ability (SCA) were calculated. Genetic distances (GD) between lines were calculated from RFLP data of 194 clone-enzyme combinations. GDs were greater for flint x dent than for flint x flint and dent x dent line combinations. Cluster analysis based on GDs showed separate groupings of flint and dent lines and agreed with pedigree information, except for 1 inbred. GDs of all line combinations in the diallel were partitioned into general (GGD) and specific (SGD) genetic distances; GGD explained approximately 20% of the variation among GD values. For the 62 diallel crosses (excluding 4 crosses of highly related lines), correlations of GD with F₁ performance, MPH, and SCA for dry matter yield (DMY) of stover, ear, and forage were positive but mostly of moderate size (0.09r0.60) compared with the higher correlations (0.39r0.77) of SGD with these traits. When separate calculations were performed for various subsets, correlations of GD and SGD with DMY traits were generally small (r<0.47) for the 36 flint x dent crosses, significantly positive (r<0.53) for the 14 flint x flint crosses, and inconclusive for the 12 dent x dent crosses because of the lack of significant genotypic variation. Results indicated that RFLPs can be used for assigning inbreds to heterotic groups. RFLP-based genetic distance measures seem to be useful for predicting forage yield of (1) crosses between lines from the same germ plasm group or (2) crosses including line combinations from the same as well as different heterotic groups. However, they are not indicative of the hybrid forage yield of crosses between unrelated lines from genetically divergent heterotic groups.     

Magnitude of hybrid vigor retained in double haploid lines of some heterotic rice hybrids

Sixty one double haploid (DH) lines were evaluated for yield components and yield and compared with the three corresponding hybrids from which they were derived through anther culture. Analysis of a 6×6 diallel experiment led to the selection of these hybrids based on their high heterosis and revealed the nature of gene action of the characters under evaluation. The DH lines along with the hybrids and parents were planted following a simple lattice design with two replications. The results show that in DH lines the values of the characters expressing predominantly additive genetic effects could reach the heterotic level of the hybrids. For characters including yield showing predominantly dominance effects, values in the DH lines were significantly lower than those of the corresponding hybrids. The promising DH lines, however, possess a higher yield potential than the better parents.     

RFLP Detection of Genetic Variation of Maize Inbred Lines

Genetic similarities of 13 inbred lines of maize (Zea mays L.) were analyzed by restriction fragment length polymorphisms (RFLPs). The objectives of the study were to detect genetic similarities among 13 inbreds and to assign them to heterotic groups. By means of 24 probe-enzyme combinations (PECs) selected for locus specificity, clear patterns and reproducibility, 85 alleles were found with an average of 3.3 alleles per locus. The allelic frequency data were used to estimate genetic similarities among lines, and as a result the diversity index of 0.499 was obtained. Genetic similarities between the pairs of 13 lines ranged from 0.523 up to 0.802 with an average of 0.649. The UPGMA clustering algorithm analysis classified the 13 lines into five groups, which generally corresponded to known maize heterotic groups based on pedigree information. The authors concluded that RFLP-based markers could be used for investigating genetic relationships between maize inbred lines and assigning them to heterotic groups, but it seemed that a large number of PECs were needed to obtain reliable estimates of genetic similarity.     

玉米自交系遗传变异的RFLP分析

利用ＲＦＬＰ标记研究了１３个玉米（Ｚｃａ ｎａｙｓ Ｌ．）自交系的遗传变异。从３０对探针／酶组合中筛选出杂交带型清晰、稳定、重复性好的２４对组合,在１３个自交系中获得８５个等位基因杂交片段,平均每个位点为３．３条,平均多态性指数为０．４９９。１３个自交系之间的遗传相似系数为０．５２３－０．８０２,平均为０．６４９。ＵＰＧＭＡ聚类分析表明,供试自交系共分为５个类群,分群结果与其系谱关系基本吻合;表明     

Combining ability of tropical maize lines for seed quality and agronomic traits

Studies of genetic effects of early selection of maize based on seed quality traits are rare, especially those that use materials from different heterotic groups. These studies are also useful in tropical environments and for the advancement of sustainable agriculture with cropping during seasons not commonly used for cultivation. We estimated, through diallel crosses, the predominant genetic effects on the expression of agronomic traits and seed quality and on the general combining ability of nine maize lines from commercial hybrids and the specific combining ability of hybrid combinations among them. In the evaluation of seed quality, seven tests were used: first count and final count of seed germination, seedling vigor classification, cold tolerance, seedling emergence rate in a sand seedbed, speed of emergence in a sand seedbed, and speed of emergence index. Plant height, first ear height and grain yield were the estimated agronomic traits. In the diallel analysis, method 3 (model I) proposed by Griffing was used. There was a greater significance of non-additive genetic effects in the genetic control of seed quality of the various lines. The Flash, Dekalb 350 and P 30F80 lines combined high seed quality and high grain yield. For growth during the normal planting season, the combinations CD 3121-1 x P 30F80, Speed x CD 3121-2, Dow 8330 x AG 8080 and Dekalb 350 x CD 3121-2 were the most promising for both seed quality and agronomic traits.     

The use of SSRs for predicting the hybrid yield and yield heterosis in 15 key inbred lines of Chinese maize

A challenge to maize breeders is to predict and identify inbred lines that can produce highly heterotic hybrids precisely. In the present study we surveyed the genetic diversity among 15 elite inbred lines of maize in China with SSR markers and assessed the relationship between SSR marker and hybrid yield/yield heterosis in a diallel set of 105 crosses. Forty-three SSR primers selected from all sixty-three primers gave stable profiles amplified in the sample of 15 inbred lines, which could clearly resolve on 4% metaphor agarose gel. The average number of alleles per SSR locus was 4.44 with a range from 2 to 9. The polymorphism information content (PIC) for the SSR loci varied from 0.28 to 0.81 with a mean of 0.6281. Genetic similarity (GS) among 15 lines was estimated with 191 alleles identified as raw data, the Nei's coefficient of GS ranged from 0.492 for 478 vs HZ4 up to 0.745 for E28 to ZH64 with a mean of 0.619. The cluster diagram based upon the SSR data grouped the 15 lines into families consistent with the yield heterotic response of these. Genetic distance (GD) based on SSR data was significantly correlated with hybrid yield/yield heterosis, the correlation coefficient (r) being 0.5432 and 0.4271 in 1999 and 0.4305 and 0.3614 in 1998 field test, respectively, whereas the determination coefficient (r2) was lower. The correlation between GD based on SSR data and hybrid yield/yield heterosis changed alone with the difference of number and pedigree relationship among parents that were used in this study. SSR makers showed high polymorphism and could be used to assess the relationship between inbred lines of maize, but it was difficult to predict the yield heterosis of maize.     

A general Bayesian approach to analyzing diallel crosses of inbred strains

The classic diallel takes a set of parents and produces offspring from all possible mating pairs. Phenotype values among the offspring can then be related back to their respective parentage. When the parents are diploid, sexed, and inbred, the diallel can characterize aggregate effects of genetic background on a phenotype, revealing effects of strain dosage, heterosis, parent of origin, epistasis, and sex-specific versions thereof. However, its analysis is traditionally intricate, unforgiving of unplanned missing information, and highly sensitive to imbalance, making the diallel unapproachable to many geneticists. Nonetheless, imbalanced and incomplete diallels arise frequently, albeit unintentionally, as by-products of larger-scale experiments that collect F(1) data, for example, pilot studies or multiparent breeding efforts such as the Collaborative Cross or the Arabidopsis MAGIC lines. We present a general Bayesian model for analyzing diallel data on dioecious diploid inbred strains that cleanly decomposes the observed patterns of variation into biologically intuitive components, simultaneously models and accommodates outliers, and provides shrinkage estimates of effects that automatically incorporate uncertainty due to imbalance, missing data, and small sample size. We further present a model selection procedure for weighing evidence for or against the inclusion of those components in a predictive model. We evaluate our method through simulation and apply it to incomplete diallel data on the founders and F(1)'s of the Collaborative Cross, robustly characterizing the genetic architecture of 48 phenotypes.     

Considerations of a method of analyzing diallel crosses of atlantic salmon.

Inferences derived from a proposed mixed model analysis of a diallel cross involving four stocks of Atlantic salmon (Salmo salar) are illustrated with growth data on weight and length. Variation between stocks was more apparent when samples represented dams as opposed to sires, thus stressing the relative importance of maternal effects. However, the ranking of stocks was not altered when either the means of sire sources or the means of dam sources were considered. No heterotic effects were found for the growth traits studied.     

Genome Properties and Prospects of Genomic Prediction of Hybrid Performance in a Breeding Program of Maize

Maize (Zea mays L.) serves as model plant for heterosis research and is the crop where hybrid breeding was pioneered. We analyzed genomic and phenotypic data of 1254 hybrids of a typical maize hybrid breeding program based on the important Dent × Flint heterotic pattern. Our main objectives were to investigate genome properties of the parental lines (e.g., allele frequencies, linkage disequilibrium, and phases) and examine the prospects of genomic prediction of hybrid performance. We found high consistency of linkage phases and large differences in allele frequencies between the Dent and Flint heterotic groups in pericentromeric regions. These results can be explained by the Hill–Robertson effect and support the hypothesis of differential fixation of alleles due to pseudo-overdominance in these regions. In pericentromeric regions we also found indications for consistent marker–QTL linkage between heterotic groups. With prediction methods GBLUP and BayesB, the cross-validation prediction accuracy ranged from 0.75 to 0.92 for grain yield and from 0.59 to 0.95 for grain moisture. The prediction accuracy of untested hybrids was highest, if both parents were parents of other hybrids in the training set, and lowest, if none of them were involved in any training set hybrid. Optimizing the composition of the training set in terms of number of lines and hybrids per line could further increase prediction accuracy. We conclude that genomic prediction facilitates a paradigm shift in hybrid breeding by focusing on the performance of experimental hybrids rather than the performance of parental lines in testcrosses.     

Heterotic trait locus (HTL) mapping identifies intra-locus interactions that underlie reproductive hybrid vigor in Sorghum bicolor

Identifying intra-locus interactions underlying heterotic variation among whole-genome hybrids is a key to understanding mechanisms of heterosis and exploiting it for crop and livestock improvement. In this study, we present the development and first use of the heterotic trait locus (HTL) mapping approach to associate specific intra-locus interactions with an overdominant heterotic mode of inheritance in a diallel population using Sorghum bicolor as the model. This method combines the advantages of ample genetic diversity and the possibility of studying non-additive inheritance. Furthermore, this design enables dissecting the latter to identify specific intra-locus interactions. We identified three HTLs (3.5% of loci tested) with synergistic intra-locus effects on overdominant grain yield heterosis in 2 years of field trials. These loci account for 19.0% of the heterotic variation, including a significant interaction found between two of them. Moreover, analysis of one of these loci (hDPW4.1) in a consecutive F2 population confirmed a significant 21% increase in grain yield of heterozygous vs. homozygous plants in this locus. Notably, two of the three HTLs for grain yield are in synteny with previously reported overdominant quantitative trait loci for grain yield in maize. A mechanism for the reproductive heterosis found in this study is suggested, in which grain yield increase is achieved by releasing the compensatory tradeoffs between biomass and reproductive output, and between seed number and weight. These results highlight the power of analyzing a diverse set of inbreds and their hybrids for unraveling hitherto unknown allelic interactions mediating heterosis.     

Genetic diversity for restriction fragment length polymorphisms and heterosis for two diallel sets of maize inbreds

Summary Changes that may have occurred over the past 50 years of hybrid breeding in maize (Zea maize L.) with respect to heterosis for yield and heterozygosity at the molecular level are of interest to both maize breeders and quantitative geneticists. The objectives of this study were twofold: The first, to compare two diallels produced from six older maize inbreds released in the 1950's and earlier and six newer inbreds released during the 1970's with respect to (a) genetic variation for restriction fragment length polymorphisms (RFLPs) and (b) the size of heterosis and epistatic effects, and the second, to evaluate the usefulness of RFLP-based genetic distance measures in predicting heterosis and performance of single-cross hybrids. Five generations (parents, F₁; F₂, and backcrosses) from the 15 crosses in each diallel were evaluated for grain yield and yield components in four Iowa environments. Genetic effects were estimated from generation means by ordinary diallel analyses and by the Eberhart-Gardner model. Newer lines showed significantly greater yield for inbred generations than did older lines but smaller heterosis estimates. In most cases, estimates of additive x additive epistatic effects for yield and yield components were significantly positive for both groups of lines. RFLP analyses of inbred lines included two restriction enzymes and 82 genomic DNA clones distributed over the maize genome. Eighty-one clones revealed polymorphisms with at least one enzyme. In each set, about three different RFLP variants were typically found per RFLP locus. Genetic distances between inbred lines were estimated from RFLP data as Rogers' distance (RD), which was subdivided into general (GRD) and specific (SRD) Rogers' distances within each diallel. The mean and range of RDs were similar for the older and newer lines, suggesting that the level of heterozygosity at the molecular level had not changed. GRD explained about 50% of the variation among RD values in both sets. Cluster analyses, based on modified Rogers' distances, revealed associations among lines that were generally consistent with expectations based on known pedigree and on previous research. Correlations of RD and SRD with f₁ performance, specific combining ability, and heterosis for yield and yield components, were generally positive, but too small to be of predictive value. In agreement with previous studies, our results suggest that RFLPs can be used to investigate relationships among maize inbreds, but that they are of limited usefulness for predicting the heterotic performance of single crosses between unrelated lines.Joint contribution from Cereal and Soybean Research Unit, USDA, Agricultural Research Service and Journal Paper no. J-13929 of the Iowa Agric and Home Economics Exp Stn, Ames, IA 50011. Projects no. 2818 and 2778A.E.M. is presently at the Iowa State University on leave from University of Hohenheim, D-7000 Stuttgart 70, Federal Republic of Germany     

Can spelt wheat be used as heterotic group for hybrid wheat breeding?

Key message

Spelt wheat is a distinct genetic group to elite bread wheat, but heterosis for yield and protein quality is too low for spelt to be recommended as heterotic group for hybrid breeding in wheat.

Abstract

The feasibility to switch from line to hybrid breeding is currently a hot topic in the wheat community. One limitation seems to be the lack of divergent heterotic groups within wheat adapted to a certain region. Spelt wheat is a hexaploid wheat that can easily be crossed with bread wheat and that forms a divergent genetic group when compared to elite bread wheat. The aim of this study was to investigate the potential of Central European spelt as a heterotic group for Central European bread wheat. We performed two large experimental field studies comprising in total 43 spelt lines, 14 wheat lines, and 273 wheat–spelt hybrids, and determined yield, heading time, plant height, resistance against yellow rust, leaf rust, and powdery mildew, as well as protein content and sedimentation volume. Heterosis of yield was found to be lower than that of hybrids made between elite wheat lines. Moreover, heterosis of the quality trait sedimentation volume was negative. Consequently, spelt wheat does not appear suited to be used as heterotic group in hybrid wheat breeding. Nevertheless, high combining abilities of a few spelt lines with elite bread wheat lines make them interesting resources for pre-breeding in bread wheat. Thereby, the low correlation between line per se performance and combining ability of these spelt lines shows the potential to unravel the breeding value of genetic resources by crossing them to an elite tester.

     

Epistasis in maize (Zea mays L.)

Summary Three flint and three dent maize (Zea mays L.) inbred lines, their possible F₁ crosses, F₂ and backcross progenies, and all possible three-way crosses were evaluated in a three-year experiment for yield, ear moisture, and plant height. The purpose was to estimate genetic parameters in European breeding materials from (i) generation means analysis, (ii) diallel analysis of generation means, and (iii) analysis of F₁ and three-way cross hybrids. Method (i) was based on the F-metric model and methods (ii) and (iii) on the Eberhart-Gardner (1966) genetic model; both models extended for heterotic maternal effects.Differences among generation means for yield and plant height were mainly attributable to dominance effects. Epistatic effects were significantly different from zero in a few crosses and considerably reduced heterosis in both traits. Additive x additive and domiance x dominance effects for yield were consistently positive and negative, respectively. Significant maternal effects were established to the advantage of generations with a heterozygous seed parent. In the diallel analysis, mean squares for dominance effects were greater than for additive effects for yield and plant height but smaller for ear moisture. Though significant for yield and plant height, epistatic variation was small compared to additive and dominance variation. Estimates of additive x additive epistasis for yield were significantly negative in 11 of 15 crosses, suggesting that advantageous gene combinations in the lines had been disrupted by recombination in the segregating generations. The analysis of hybrids supported the above findings regarding the analysis of variance. However, the estimates of additive x additive epistasis for yield were considerably smaller and only minimally correlated with those from the diallel analysis. Use of noninbred materials as opposed to materials with different levels of inbreeding is considered the main reason for the discrepancies in the results.     

Performance of recombinant inbred lines in Brussels sprouts (Brassica oleracea var. gemmifera)

Summary Performance of a random array of recombinant inbred lines derived by single seed descent from five different source populations of Brussels sprouts (Brassica oleracea var. gemmifera) is presented. A total of 2,356 lines were tested in trials during 1985 and 1986. Three of the source populations were derived from double crosses between F₁ hybrids. These hybrids show a considerable heterotic advantage over their inbred parents for the most important agronomic traits. The recombinant inbred lines performed, on average, less well than the parental inbred material, indicating that additive x additive genie interactions may make a significant contribution to the performance of current inbred material. Nevertheless, the very large variation among the recombinant inbred lines permitted many lines to be identified which outperformed the best parental inbred for all traits. Two lines outperformed the reference F₁ hybrid, Gower, for an index that included marketable yield and quality. Consideration was also given to the dangers of misinterpreting phenotypically based proportions. Accordingly, response equations were used to ascertain the real genetic progress that was made. Advance seemed small when compared with the large heterotic effect, which is consistent with the segregation of a large number of loci. The distribution of the recombinant inbred lines was compared to predictions made from early generation trials. There was broad agreement but significant discrepancies existed which, it is suggested, may arise from the effects of genotype-environment interactions.     

Grouping of tropical mid-altitude maize inbred lines on the basis of yield data and molecular markers

The classification of maize inbred lines into heterotic groups is an important undertaking in hybrid breeding. The objectives of our research were to: (1) separate selected tropical mid-altitude maize inbred lines into heterotic groups based on grain yield data; (2) assess the genetic relationships among these inbred lines using amplified fragment length polymorphism (AFLP) and simple sequence repeat (SSR) markers; (3) examine the consistency between yield-based and marker-based groupings of the inbred lines. Thirty-eight tropical mid-altitude maize inbred lines were crossed to two inbred line testers representing the flint and dent heterotic pattern, respectively. The resulting testcrosses were evaluated in a trial at three locations for 2 years. Significant general combining ability (GCA) and specific combining ability (SCA) effects for grain yield were detected among the inbred lines. The tester inbred lines classified 23 of the 38 tested inbred lines into two heterotic groups based on SCA effects and testcross mean grain yields. This grouping was not related to endosperm type of the inbred lines. The outstanding performance of testcrosses of the remaining 15 inbred lines indicates the presence of significant genetic diversity that may allow the assignment of the lines into more than two heterotic groups. Diversity analysis of the 40 maize inbred lines using AFLP and SSR markers found high levels of genetic diversity among these lines and subdivided them into two main groups with subdivision into sub-groups consistent with breeding history, origin and parentage of the lines. However, heterotic groups formed using yield-based combining ability were different from the groups established on the basis of molecular markers. Considering the diversity of the genetic backgrounds of the mid-altitude inbred lines, the marker-based grouping may serve as the basis to design and carry out combining ability studies in the field to establish clearly defined heterotic groups with a greater genetic similarity within groups.Communicated by H.H. Geiger     

Genetically based differences in photochemical activities of isolated maize (Zea mays L.) mesophyll chloroplasts

Photochemical activity of isolated mesophyll chloroplasts was measured as Hill reaction activity (HRA) and photosystem 1 (PS1) activity in three diallel crosses of maize (Zea mays L.) inbred lines and F₁ hybrids. Statistically significant differences between genotypes together with positive heterotic effect in F₁ generation were found for both traits studied. These differences were more pronounced when HRA or PS1 activity was expressed per leaf area unit or dry matter unit compared to the expression per chlorophyll content unit. Analysis of variance showed that both the genetic and non-genetic components of variation in the photochemical activity of isolated mesophyll chloroplasts are present in all three diallel crosses examined. The positive heterosis in F₁ hybrids probably arises from non-additive genetic effects of a positive dominance type. Additive genetic effects were also statistically highly significant. We found no differences between reciprocal crosses. This revised version was published online in September 2006 with corrections to the Cover Date.