Genetic diversity of the azuki bean (Vigna angularis (Willd.) Ohwi & Ohashi) gene pool as assessed by SSR markers

To facilitate the wider use of genetic resources including newly collected cultivated and wild azuki bean germplasm, the genetic diversity of the azuki bean complex, based on 13 simple sequence repeat (SSR) primers, was evaluated and a core collection was developed using 616 accessions originating from 8 Asian countries. Wild germplasm from Japan was highly diverse and represented much of the allelic variation found in cultivated germplasm. The SSR results together with recent archaeobotanical evidence support the view that Japan is one center of domestication of azuki bean, at least for the northeast Asian azuki bean. Cultivated azuki beans from China, Korea, and Japan were the most diverse and were genetically distinct from each other, suggesting a long and relatively isolated history of cultivation in each country. Cultivated azuki beans from eastern Nepal and Bhutan were similar to each other and quite distinct from others. For two primers, most eastern Nepalese and Bhutanese cultivated accessions had null alleles. In addition, wild accessions from the Yangtze River region of China and the Himalayan region had a null allele for one or the other of these primers. Whether the distinct diversity of azuki bean in the Himalayan region is due to introgression or separate domestication events requires further study. In contrast, western Nepalese azuki beans showed an SSR profile similar to that of Chinese azuki beans. The genetic distinctness of cultivated azuki beans from Vietnam has been revealed for the first time. The specific alleles indicate that Vietnamese azuki beans have been cultivated in isolation from Chinese azuki beans for a long time. Wild germplasm from the Himalayan region showed the highest level of variation. Based on the results, Himalayan germplasm could be considered a novel gene source for azuki bean breeding. A comparison with mungbean SSR analysis revealed that the mean gene diversity of cultivated azuki bean (0.74) was much higher than that of cultivated mungbean (0.41). The reduction in gene diversity due to domestication, the domestication bottleneck, in azuki bean is not strong compared with that in mungbean.     

Genetic diversity in Bambara groundnut (Vigna subterranea L.) germplasm revealed by RAPD markers.

Random amplified polymorphic DNA (RAPD) markers were used to assess genetic diversity in Bambara groundnut (Vigna subterranea L.) germplasm using 25 African accessions from the collection in the International Institute for Tropical Agriculture, Ibadan, Nigeria. Fifty random decamer primers were screened to assess their ability to detect polymorphism in bambara; 17 of them were selected for this study. Considerable genetic diversity was found among the V. subterranea accessions studied. The relationships among the 25 accessions were studied by cluster analysis. The dendrograms showed two main groups of accessions mainly along the lines of their geographic origin. It is concluded that RAPD can be used for germplasm classification in bambara groundnut and hence for improving this crop.     

用于绿豆种质资源遗传多样性分析的SSR及STS引物的筛选

目前能够用于绿豆(Vigna radiate)种质资源遗传多样性分析的PCR引物极其有限。通过12份农艺性状差异较大的绿豆种质对绿豆以及小豆(Vigna angularis)、豇豆(Vigna unguiculata)、菜豆(Phaseolus vulgaris)等近缘食用豆中的PCR引物进行筛选,结果表明41对绿豆SSR引物中能够有效扩增的有35对,6对有多态性;28对绿豆STS引物中有23对能够有效扩增,2对有多态性;8对小豆SSR引物能够有效扩增的有6对,但均无多态性;27对豇豆SSR引物能够有效扩增的有17对,1对有多态性;24对菜豆SSR引物能够有效扩增的有9对,1对有多态性。这些多态性引物的获得将有助于中国绿豆种质资源的遗传多样性分析。     

绿豆基因组研究进展

绿豆是亚洲国家重要的经济作物。绿豆基因组的研究工作已开展多年,至今已经发布了6张遗传连锁图谱,然而还未有一张图谱的连锁群数与绿豆(2n=2x=22,n=11)的染色体基数一致。近年来,豆科植物比较基因组学的研究成果,为绿豆遗传连锁图谱的发展提供了新的思路。通过将绿豆遗传连锁图与其他豆类连锁图比较发现,绿豆与小豆、豇豆、普通菜豆、大豆、藊豆以及豆科模式植物—蒺藜苜蓿的基因组间有不同程度的保守性,其中尤以绿豆与普通菜豆基因组间共线性水平高。本文分别从绿豆遗传连锁图谱构建、比较基因组作图以及抗豆象基因定位等方面进行了综述,以期为绿豆遗传研究工作者提供参考。     

A genetic linkage map for azuki bean [Vigna angularis (Willd.) Ohwi & Ohashi]

To make progress in genome analysis of azuki bean (Vigna angularis) a genetic linkage map was constructed from a backcross population of (V. nepalensis x V. angularis) x V.angularis consisting of 187 individuals. A total of 486 markers—205 simple sequence repeats (SSRs), 187 amplified fragment length polymorphisms (AFLPs) and 94 restriction fragment length polymorphisms (RFLPs) —were mapped onto 11 linkage groups corresponding to the haploid chromosome number of azuki bean. This map spans a total length of 832.1 cM with an average marker distance of 1.85 cM and is the most saturated map for a Vigna species to date. In addition, RFLP markers from other legumes facilitated finding several orthologous linkage groups based on previously published RFLP linkage maps. Most SSR primers that have been developed from SSR-enriched libraries detected a single locus. The SSR loci identified are distributed throughout the azuki bean genome. This moderately dense linkage map equipped with many SSR markers will be useful for mapping a range of useful traits such as those related to domestication and stress resistance. The mapping population will be used to develop advanced backcross lines for high resolution QTL mapping of these traits. O.K. Han, A. Kaga, T. Isemura have contributed equally to this paper.     

The genetic diversity of the Vigna angularis complex in Asia.

A selected set of accessions of components of the azuki bean (Vigna angularis) complex comprising 123 cultivated accessions and 23 wild or weedy accessions from Bhutan, China (including Taiwan), India, Japan, Korea, and Nepal was analyzed using amplified fragment length polymorphism (AFLP) methodology. Using 12 AFLP primer pairs, 580 unambiguous bands were generated, 313 (53.9%) of which were polymorphic among azuki bean accessions. All 580 bands were used to assess phenotypic (band) and genetic (nucleotide) diversity among the 146 azuki bean accessions. The results indicate five major groups of azuki bean germplasm primarily associated with geographic origin of accessions and their status: wild, weedy, or cultivated. These five groups are (i) Himalayan wild, (ii) Nepal-Bhutan cultivated, (iii) Chinese wild, (iv) Taiwan wild - Bhutan cultivated, and (v) northeast Asian accessions. Within the northeast Asian accessions, three subgroups are present. These consist of (v1) Japanese complex - Korean cultivated, (v2) Japanese cultivated, and (v3) Chinese cultivated accessions. The results suggest domestication of azuki bean occurred at least twice, once in the Himalayan region of southern Asia and once in northeast Asia. The remarkable diversity of azuki bean germplasm in the Himalayan region compared with other regions suggests this is a rich source of germplasm for plant breeding. The results suggest there are important gaps in the germplasm collections of azuki bean and its close relatives from various parts of Asia and that specific collecting missions for Vigna germplasm related to azuki bean in the highlands of subtropical Asia are needed.     

Expanding the repertoire of microsatellite markers for polymorphism studies in Indian accessions of mung bean (Vigna radiata L. Wilczek)

Limited availability of validated, polymorphic microsatellite markers in mung bean (Vigna radiata), an important food legume of India, has been a major hurdle towards its improvement and higher yield. The present study was undertaken in order to develop a new set of microsatellite markers and utilize them for the analysis of genetic diversity within mung bean accessions from India. A GA/CT enriched library was constructed from V. radiata which resulted in 1,250 putative recombinant clones of which 850 were sequenced. SSR motifs were identified and their flanking sequences were utilized to design 328 SSR primer pairs. Of these, 48 SSR markers were employed for assessing genetic diversity among 76 mung bean accessions from various geographical locations in India. Two hundred and thirty four alleles with an average of 4.85 alleles per locus were detected at 48 loci. The polymorphic information content (PIC) per locus varied from 0.1 to 0.88 (average: 0.49 per locus). The observed and expected heterozygosities ranged from 0.40 to 0.95 and 0.40 to 0.81 respectively. Based on Jaccard’s similarity matrix, a dendrogram was constructed using the unweighted pair-group method with arithmetic averages (UPGMA) analysis which revealed that one accession from Bundi, Rajasthan was clustered out separately while remaining accessions were grouped into two major clusters. The markers generated in this study will help in expanding the repertoire of the available SSR markers thereby facilitating analysis of genetic diversity, molecular mapping and ultimately broadening the scope for genetic improvement of this legume.     

Nodule Function in Symbiotic Bambara Groundnut (Vigna subterraneaL.) and Kersting's Bean (Macrotyloma geocarpumL.) is Tolerant of Nitrate in the Root Medium

Nitrogen-fixing activity in two nodulated African legumes, Bambaragroundnut (Vigna subterraneaL.) and Kersting's bean (MacrotylomageocarpumL.), was assessed in the presence of nitrate (NO₃^-)ions in the rooting medium. Nitrogenase activity was unimpairedby the supply of 5 mol m^-3NO₃to both species. Also, large concentrationsof ureides dominated the transpiration stream of NO₃-fed plants.Compared to other symbiotic legumes cultured with similar NO₃concentrations,nodule functioning in the tested landraces of Bambara groundnutand Kersting's bean is tolerant of NO₃ions in the rhizosphere.The potential benefits of such naturally occurring NO₃-tolerantsymbioses are substantial, as they would permit inorganic Nfertilizer application in intercropping systems without inhibitingN₂fixation in the associated legumes.Copyright 1998 Annals ofBotany Company NO₃tolerance, Bambara groundnut, Kersting's bean, nitrogenase activity, xylem ureides.     

Molecular studies on mungbean (Vigna radiata (L.) Wilczek) and ricebean (Vigna umbellata (Thunb.)) interspecific hybridisation for Mungbean yellow mosaic virus resistance and development of species-specific SCAR marker for ricebean

The aim of this study was to identify the molecular markers (SSR, RAPD and SCAR) associated with Mungbean yellow mosaic virus resistance in an interspecific cross between a mungbean variety, VRM (Gg) 1 X a ricebean variety, TNAU RED. The parental survey was carried out by using 118 markers (including 106 azuki bean primers, seven mungbean primers and five ricebean primers). This study revealed that 42 azuki bean markers (39.62%) and four mungbean markers (54.07%) showed parental polymorphism. These polymorphic markers were surveyed among the 187 F₂ plants and the results showed distorted segregation or chromosomal elimination at all the marker loci (thus, deviating from the expected 1:2:1 segregation). None of the plants harboured the homozygous ricebean allele for the markers surveyed and all of them were skewed towards mungbean, VRM (Gg) 1, allele, except a few plants which were found to be heterozygous for few markers. Among the 42 azuki bean SSR markers surveyed, only 10 markers produced heterozygotic pattern in six F₂ lines viz. 3, 121, 122, 123, 185 and 186. These markers were surveyed in the corresponding F₃ individuals, which too skewed towards the mungbean allele. In this study, one species-specific SCAR marker was developed for ricebean by designing primers from the sequenced putatively species-specific RAPD bands. A single, distinct and brightly resolved band of 400?bp was found amplified only in the resistant parent, TNAU RED, and not in any other six species or in the resistant or the susceptible bulks of the mapping population clearly indicated the identification of SCAR marker specific to the ricebean.     

Assessing host range,symbiotic effectiveness,and photosynthetic rates induced by native soybean rhizobia isolated from Mozambican and South African soils

Host range and cross-infectivity studies are important for identifying rhizobial strains with potential for use as inoculants. In this study, 10 native soybean rhizobia isolated from Mozambican and South African soils were evaluated for host range, symbiotic effectiveness and ability to induce high rates of photosynthesis leading to enhanced plant growth in cowpea (Vigna unguiculata L. Walp.), Bambara groundnut (Vigna subterranean L. Verdc.), Kersting’s groundnut (Macrotyloma geocarpum Harm) and soybean (Glycine max L. Merr). The test isolates had different growth rates and colony sizes. Molecular analysis based on enterobacterial repetitive intergenic consensus (ERIC)-PCR revealed high genetic diversity among the test isolates. The results further showed that isolate TUTLBC2B failed to elicit nodulation in all test plants, just as TUTNSN2A and TUTDAIAP3B were also unable to nodulate cowpea, Kersting’s bean and Bambara groundnut. Although the remaining strains formed ineffective nodules on cowpea and Kersting’s bean, they induced effective nodules on Bambara groundnut and the two soybean genotypes. Bacterial stimulation of nodule numbers, nodule dry weights and photosynthetic rates was generally greater with isolates TUTRSRH3A, TUTM19373A, TUTMCJ7B, TUTRLR3B and TUTRJN5A. As a result, these isolates elicited significantly increased accumulation of biomass in shoots and whole plants of Bambara groundnut and the two soybean genotypes. Whole-plant symbiotic nitrogen (N) of soybean and Bambara groundnut was highest for the commercial strains CB756 and WB74, as well as for TUTRLR3B, TUTMCJ7B and TUTRSRH3A, suggesting that the three native rhizobial isolates have potential for use as inoculants.     

Comparative molecular mapping in Ceratotropis species using an interspecific cross between azuki bean (Vigna angularis) and rice bean (V. umbellata)

A genetic linkage map was developed with 86 F₂ plants derived from an interspecific cross between azuki bean (Vigna angularis, 2n=2x=22) and rice bean (V. umbellata, 2n=2x=22). In total, 14 linkage groups, each containing more than 4 markers, were constructed with one phenotypic, 114 RFLP and 74 RAPD markers. The total map size was 1702 cM, and the average distance between markers was 9.7 cM. The loci showing significant deviation from the expected ratio clustered in several linkage groups. Most of the skewed loci were due to the predominance of rice bean alleles. The azuki-rice bean linkage map was compared with other available maps of Vigna species in subgenus Ceratotropis. Based on the lineage of the common mapped markers, 7 and 16 conserved linkage blocks were found in the interspecific map of azuki bean ×V. nakashimae and mungbean map, respectively. Although the present map is not fully saturated, it may facilitate gene tagging, QTL mapping and further useful gene transfer for azuki bean breeding. Received: 20 March 1999 / Accepted: 29 April 1999     

New microsatellite markers isolated from mungbean (Vigna radiata (L.) Wilczek)

In this study, we reported the isolation and analysis of new polymorphic microsatellites in mungbean (Vigna radiata (L.) Wilczek). Twelve out of 210 primer pairs screened in 30 mungbean accessions gave polymorphism. The polymorphic markers detected two to three alleles per locus with an average of 2.08. Observed heterozygosity varied from 0 to 0.133, while expected heterozygosity ranged from 0.095 to 0.498. Tests for Hardy-Weinberg equilibrium (HWE) and pairwise linkage disequilibrium of the polymorphic loci revealed that all loci except MB-SSR14 significantly departed from HWE and four pairwise combinations, viz. MB-SSR14 vs. MB-SSR42, MB-SSR42 vs. MB-SSR87, MB-SSR114 vs. MB-SSR121, and MB-SSR175 vs. MB-SSR231 significantly deviated from linkage disequilibrium. The markers are being used to study genetic diversity and genome mapping of mungbean.     

基于SSR标记分析小豆及其近缘植物的遗传关系

本研究利用87对SSR引物分析了80份栽培小豆(Vigna angularis)、22份野生小豆(V.angularis var.nipponensis)以及10份豇豆属(共7个种)近缘植物,旨在比较豇豆属不同种的遗传多样性,并分析种间的遗传关系.结果显示87对SSR引物在112份小豆及其近缘植物资源中共检测到667个等位变异.其中有75个、71个和82个SSR位点分别在栽培小豆、野生小豆和近缘植物中表现为多态.随机抽样分析发现,平均每SSR位点检测到的等位变异数目为近缘植物>野生小豆>栽培小豆,与多态信息含量(PIC)值一致,说明近缘植物及野生小豆中蕴含着丰富的遗传变异,是栽培小豆育种的重要基因来源.聚类分析显示,栽培小豆、野生小豆和近缘植物间的遗传分化比较明显,分别聚为三大类,其中栽培小豆的遗传背景与其生态环境相对应;近缘植物又可以分为三个亚类,亚类间的遗传距离与其亲缘关系相对应.本研究结果也说明利用SSR标记辅助豇豆属的种间分类是可行的.     

Assessment of genetic diversity in Ethiopian cowpea [<Emphasis Type="Italic">Vigna unguiculata</Emphasis> (L.) Walp.] germplasm using simple sequence repeat markers

The genetic diversity of cowpea (Vigna unguiculata L. Walp.) in Ethiopia was analyzed using 19 uniform accessions, 62 variable accessions (yielding 185 sub-types), and two mungbean (Vigna radiata) accessions (four subtypes) as outgroup. A set of 23 polymorphic simple sequence repeat (SSR) markers was identified, and polymorphism in the various accessions was scored by determining amplicon variability. Allele frequency, genetic diversity, and polymorphism information content (PIC) were determined for each SSR marker, and a neighbor joining dendrogram was generated to show the genetic relationship among the individual accessions. A total of 75 allelic variants was defined, with the average number of alleles per locus calculated to be three. The average genetic diversity (D) was 0.47, and PIC was 0.4. Three main clusters were identified by phylogenetic analysis, and the clusters and sub-grouping were supported by STRUCTURE and principal component analysis. This grouping had a moderate fixation index value of 0.075 and gene flow (Nm) of 3.176, indicating that the accessions possess wide diversity within individuals and populations. The accessions showed no clustering by geographical origins. Three well-characterized molecular markers (SSR1, C42-2B, and 61RM2) for race specific resistance to Striga gesnerioides in the cowpea cultivar B301 were used to evaluate the accessions for their potential for use in genetic improvement against this pest. Based on this analysis, only two accessions, 222890–2 from Gambela and 286–2 from the Southern Nations, Nationalities, and Peoples (SNNP) region, were found to cluster with B301 and contain the SSR1 resistance allele. These findings will assist in germplasm conservation efforts by the Institute of Biodiversity and Conservation of Ethiopia, and contribute to future studies aimed at the genetic improvement of local germplasm for improved overall agronomic performance as well as Striga resistance in particular.     

Characterization of new microsatellite markers in mung bean,Vigna radiata (L.)

The present work reports the isolation and characterization of new polymorphic microsatellites in mung bean (Vigna radiata L.). Of 93 designed primer pairs, seven were found to amplify polymorphic microsatellite loci, which were then characterized using 34 mung bean accessions. The number of alleles ranged from two to five alleles per locus with an average of three alleles. Observed and expected heterozygosity values ranged from 0 to 0.088 and from 0.275 to 0.683, respectively. All seven loci showed significant deviations from Hardy–Weinberg equilibrium, whereas only one pairwise combination (GBssr‐MB77 and GBssr‐MB91) exhibited significant departure from linkage disequilibrium. These newly developed markers are currently being utilized for diversity assessment within the mung bean germplasm collection of the Korean Gene Bank.     

Genetic diversity in bambara groundnut (Vigna subterranea (L.) Verdc) landraces revealed by AFLP markers.

Bambara groundnut (Vigna subterranea (L.) Verdc), an African indigenous legume, is popular in most parts of Africa. The present study was undertaken to establish genetic relationships among 16 cultivated bambara groundnut landraces using fluorescence-based amplified fragment length polymorphism (AFLP) markers. Seven selective primer combinations generated 504 amplification products, ranging from 50 to 400 bp. Several landrace-specific products were identified that could be effectively used to produce landrace-specific markers for identification purposes. On average, each primer combination generated 72 amplified products that were detectable by an ABI Prism 310 DNA sequencer. The polymorphisms obtained ranged from 68.0 to 98.0%, with an average of 84.0%. The primer pairs M-ACA + P-GCC and M-ACA + P-GGA produced more polymorphic fragments than any other primer pairs and were better at differentiating landraces. The dendrogram generated by the UPGMA (unweighted pair-group method with arithmetic averaging) grouped 16 landraces into 3 clusters, mainly according to their place of collection or geographic origin. DipC1995 and Malawi5 were the most genetically related landraces. AFLP analysis provided sufficient polymorphism to determine the amount of genetic diversity and to establish genetic relationships in bambara groundnut landraces. The results will help in the formulation of marker-assisted breeding in bambara groundnut.     

Use of genomic and genic SSR markers for assessing genetic diversity and population structure in Indian and African finger millet (Eleusine coracana (L.) Gaertn.) germplasm

Genetic diversity and population structure were analyzed in 67 diverse finger millet accessions of African and Indian origin. A total of 69 alleles were generated with a mean of 4.0 alleles per locus and with an average gene diversity of 0.471. Molecular diversity parameters showed higher values in African accessions. Nineteen rare and nine unique alleles were observed and the identified accessions can be a potential source for further improvement of finger millet. Clustering of south Indian accessions with African lowland types and north/highland Indian accessions with that of African highlands was also observed. Structure analysis revealed the distinctness of Ugandan accessions compared to other African accessions and five major sub-populations useful for parental selection, conservation, and utilization of finger millet.     

Molecular characterization and genetic diversity analysis of soybean (Glycine max (L.) Merr.) germplasm accessions in India

Molecular characterization and genetic diversity among 82 soybean accessions was carried out by using 44 simple sequence repeat (SSR) markers. Of the 44 SSR markers used, 40 markers were found polymorphic among 82 soybean accessions. These 40 polymorphic markers produced a total of 119 alleles, of which five were unique alleles and four alleles were rare. The allele number for each SSR locus varied between two to four with an average of 2.97 alleles per marker. Polymorphic information content values of SSRs ranged from 0.101 to 0.742 with an average of 0.477. Jaccard’s similarity coefficient was employed to study the molecular diversity of 82 soybean accessions. The pairwise genetic similarity among 82 soybean accessions varied from 0.28 to 0.90. The dendrogram constructed based on genetic similarities among 82 soybean accessions identified three major clusters. The majority of genotypes including four improved cultivars were grouped in a single subcluster IIIa of cluster III, indicating high genetic resemblance among soybean germplasm collection in India.

Electronic supplementary material

The online version of this article (doi:10.1007/s12298-014-0266-y) contains supplementary material, which is available to authorized users.     

Development of a black gram [Vigna mungo (L.) Hepper] linkage map and its comparison with an azuki bean [Vigna angularis (Willd.) Ohwi and Ohashi] linkage map

The Asian Vigna group of grain legumes consists of six domesticated species, among them black gram is widely grown in South Asia and to a lesser extent in Southeast Asia. We report the first genetic linkage map of black gram [Vigna mungo (L.) Hepper], constructed using a BC₁F₁ population consisting of 180 individuals. The BC₁F₁ population was analyzed in 61 SSR primer pairs, 56 RFLP probes, 27 AFLP loci and 1 morphological marker. About 148 marker loci could be assigned to the 11 linkage groups, which correspond to the haploid chromosome number of black gram. The linkage groups cover a total of 783 cM of the black gram genome. The number of markers per linkage group ranges from 6 to 23. The average distance between adjacent markers varied from 3.5 to 9.3 cM. The results of comparative genome mapping between black gram and azuki bean show that the linkage order of markers is highly conserved. However, inversions, insertions, deletions/duplications and a translocation were detected between the black gram and azuki bean linkage maps. The marker order on parts of linkage groups 1, 2 and 5 is reversed between the two species. One region on black gram linkage group 10 appears to correspond to part of azuki bean linkage group 1. The present study suggests that the azuki bean SSR markers can be widely used for Asian Vigna species and the black gram genetic linkage map will assist in improvement of this crop.Electronic Supplementary Material Supplementary material is available in the online version of this article at and is accessible for authorized users.The first three authors contributed equally to this research     

High SSR diversity but little differentiation between accessions of Nordic timothy (Phleum pratense L.)

A large collection of genebank accessions of the hexaploid outcrossing forage grass species timothy (Phleum pratense L.) was for the first time analysed for SSR diversity on individual, population and regional level. Timothy is the most important forage grass species in the Nordic countries. Eighty-eight timothy accessions from Nordic countries and eight accessions around Europe were analysed with recently developed simple sequence repeat (SSR) markers. Timothy proved to be very polymorphic: the 13 selected SSRs amplified a total of 499 polymorphic alleles, the number of alleles per SSR locus varying from 15 to 74. Taking all SSR alleles together, the observed number in each accession ranged from 95 to 203. Levels of diversity were found to be significantly different between countries, vegetation zones and different cultivar types. However, the differentiation between accessions was low: most of the variation (94%) in the studied timothy material was due to variation within accessions and only 5% was between accessions and 1% between countries. Lack of geographical differentiation may reflect the outcrossing and hexaploid nature of timothy. Our results showed that neutral SSR markers are suitable for demonstrating levels of diversity but not alone adequate to resolve population structure in timothy. Nordic timothy material seems to be diverse enough for breeding purposes and no decline in the level of diversity was observed in varieties compared to wild timothy populations. Challenges in analysing SSR marker data in a hexaploid outcrosser were discussed.