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1.
Soil chemistry can play an important role in determining plant diversity. Serpentine soils are usually toxic to many plant taxa, which limits plant diversity compared to that on adjacent non-serpentine soils. The usually high concentrations of toxic metals in serpentine soils are considered to be the edaphic factors that cause low diversity and high endemism. This paper aimed primarily to determine whether there is a relationship between serpentine soil chemistry and species richness on the Witwatersrand and to compare species richness of the serpentine areas with that of adjacent non-serpentine areas as well as with the species richness of the serpentine areas in the Barberton Greenstone Belt. The alpha- and beta-diversity of the Witwatersrand serpentine and non-serpentine areas was also investigated. A secondary aim of this study was to determine which of the non-serpentine taxa were more common on the serpentine than off the serpentine, which taxa were more common off the serpentine than on the serpentine and which taxa were equally common on and off serpentine soils. There was no significant difference in alpha-diversity between the serpentine and the adjacent non-serpentine areas, but beta-diversity is higher between serpentine plots than between non-serpentine plots. Although soil factors do affect species richness and diversity of plants on the Witwatersrand to a limited extent, the concentrations of soil chemicals in serpentine soils are not sufficiently different from those in non-serpentine soils to significantly influence the species richness and diversity of the serpentine soils. The high, but similar, diversity on serpentine and non-serpentine soils on the Witwatersrand indicates that soil factors do not play a significant role in determining diversity on potentially toxic soils in the area.  相似文献   

2.
The presence of such a large number of terrestrial orchid species in a small area (ca. 1 km2) of the Huanglong valley in southwestern China is uncommon for this country. Studying the relationship between the distribution patterns of these orchid species and their microenvironments may help us understand this uncommon phenomenon. We established 662 1 m × 1 m plots, measured the cover of each species and found that there were 33 orchid species distributed mainly in two different habitats, i.e. travertine areas and forest. In the travertine areas, 30 orchid species were found; the six most common ones being Cypripedium bardolphianum, Cypripedium flavum, Cypripedium tibeticum, Galearis diantha, Ponerorchis chusua and Phaius delavayi. However in the forested habitat, we found 21 orchid species; the most common ones being Tipularia szechuanica and Goodyera repens. Travertine areas had a higher number of orchid species as well as higher numbers of orchid species per plot as compared to forest. Light availability seems critical to the performance and distribution of orchid species. Stream flow through the travertine area during the orchids growing season appears to be an important factor in shaping and maintaining stable microenvironments favorable to the growth and reproduction of orchids. The results presented in this study suggest that some orchid species in the travertine area might be threatened if the travertine stream flows were to change or be disrupted.  相似文献   

3.
The loss of orchid habitats has increased the investment on orchid conservation efforts to reduce the risk of extinction of rare species. In northwestern Italy, orchids are among the most threatened of all plant groups in the region, but little is known about the biology of most of the less abundant taxa. In this study, we used light and scanning electron microscopy to characterize the morphology of the seeds of the threatened Orchis patens Desf., a declining species present in semi-natural habitats. We found a marked positive relationship between seed size and embryo size that may be not restricted to O. patens but also occur in other orchid species. The comparative analysis of the observed seed traits revealed hidden morphological affinities at the reproductive level among O. patens and the three subspecies of O. mascula, showing the potential of this approach to test the taxonomic relationships among the different taxa included in the genus Orchis.  相似文献   

4.
Mycorrhizal association is a common characteristic in a majority of land plants, and the survival and distribution of a species can depend on the distribution of suitable fungi in its habitat. Orchidaceae is one of the most species‐rich angiosperm families, and all orchids are fully dependent on fungi for their seed germination and some also for subsequent growth and survival. Given this obligate dependence, at least in the early growth stages, elucidating the patterns of orchid–mycorrhizal relationships is critical to orchid biology, ecology and conservation. To assess whether rarity of an orchid is determined by its specificity towards its fungal hosts, we studied the spatial and temporal variability in the host fungi associated with one of the rarest North American terrestrial orchids, Piperia yadonii. The fungal internal transcribed spacer region was amplified and sequenced by sampling roots from eight populations of P. yadonii distributed across two habitats, Pinus radiata forest and maritime chaparral, in California. Across populations and sampling years, 26 operational taxonomic units representing three fungal families, the Ceratobasidiaceae, Sebacinaceae and Tulasnellaceae, were identified. Fungi belonging to the Sebacinaceae were documented in orchid roots only at P. radiata forest sites, while those from the Ceratobasidiaceae and Tulasnellaceae occurred in both habitats. Our results indicate that orchid rarity can be unrelated to the breadth of mycorrhizal associations. Our data also show that the dominance of various fungal families in mycorrhizal plants can be influenced by habitat preferences of mycorrhizal partners.  相似文献   

5.
《Nordic Journal of Botany》2007,25(3-4):227-237
The orchid flora of the Iberian Peninsula is relatively well known, but its biogeographical and diversity patterns have until now remained unanalysed. This work compares the richness of this flora with that of 27 other territories in different continents and at different latitudes, with the aim of establishing whether it is richer or poorer than might be expected. Latitude was found to be an excellent predictor of regional orchid species richness. With 122 taxa, the orchid flora of the Iberian Peninsula is more or less as diverse as that of other Mediterranean areas of similar latitude (e.g. France, Greece or Italy), but more diverse than other European or indeed North African orchid floras. In this study, the Iberian orchid species were assigned to eight monophyletic clades and the global distribution of these are mapped to establish continental affinities between the floras. A recent floristic account on the Iberian orchids was also used to assign the orchid taxa to habitats, and the relationship between the number of endemisms and their habitats was analysed. The patterns of endemism differed in different habitats. Very high levels of endemism were found in habitats peculiar to the Mediterranean Basin, indicating the relict status of its orchid flora.  相似文献   

6.
四川黄龙沟草本植物群落在所调查样方中(N=662)共出现维管植物124种,分属于37科91属,有54个中国特有种:其中兰科植物多达21属33种,中国特有种有12个,新种一个。如此众多的地生兰科植物聚集在面积不到1公里的沟内,而且部分兰科植物种类在沟内形成优势草本群落,这在中国地生兰的分布区域中是不多见的。大多数物种,包括兰科植物在内,出现的频率都较小,并且分布不均匀。黄龙沟兰科植物主要分布在两种生境中,即钙化滩流地和森林中。在这两种生境中微环境条件以及兰科植物的种类组成、数量特征和分布格局的差异都很大。钙化滩流地的兰科植物种类数目和每个样方中包含的兰科植物种类数目都比森林生境中的高。钙化滩流地中发现有30种兰科植物,最为常见的是无苞杓兰、黄花杓兰、西藏杓兰、广布小碟兰、二叶根茎兰和少花鹤顶兰。森林生境中有21种兰科植物分布,其中筒距兰和斑叶兰出现最多,光照强度可能对兰科植物的分布起到重要的决定作用。钙化滩流地中的溪流对建立和维持兰科植物生存所必须的稳定环境条件起到至关重要的作用,如果随意改变水流的方向或减少水流的流量,将给某些兰科植物带来灾难性的后果。  相似文献   

7.
We compared the nutritional modes and habitats of orchids (e.g., autotrophic, partially or fully mycoheterotrophic) of the Mediterranean region and adjacent islands of Macaronesia. We hypothesized that ecological factors (e.g., relative light availability, surrounding vegetation) determine the nutritional modes of orchids and thus impose restrictions upon orchid distribution. Covering habitats from dark forests to open sites, orchid samples of 35 species from 14 genera were collected from 20 locations in the Mediterranean and Macaronesia to test for mycoheterotrophy. Mycorrhizal fungi were identified via molecular analyses, and stable isotope analyses were applied to test whether organic nutrients are gained from the fungal associates. Our results show that orchids with partial or full mycoheterotrophy among the investigated species are found exclusively in Neottieae thriving in light-limited forests. Neottioid orchids are missing in Macaronesia, possibly because mycoheterotrophy is constrained by the lack of suitable ectomycorrhizal fungi. Furthermore, most adult orchids of open habitats in the Mediterranean and Macaronesia show weak or no N gains from fungi and no C gain through mycoheterotrophy. Instead isotope signatures of some of these species indicate net plant-to-fungus C transfer.  相似文献   

8.
9.
In the mycorrhizal symbiosis, plants exchange photosynthates for mineral nutrients acquired by fungi from the soil. This mutualistic arrangement has been subverted by hundreds of mycorrhizal plant species that lack the ability to photosynthesize. The most numerous examples of this behaviour are found in the largest plant family, the Orchidaceae. Although these non-photosynthetic orchid species are known to be highly specialized exploiters of the ectomycorrhizal symbiosis, photosynthetic orchids are thought to use free-living saprophytic, or pathogenic, fungal lineages. However, we present evidence that putatively photosynthetic orchids from five species which grow in the understorey of forests: (i) form mycorrhizas with ectomycorrhizal fungi of forest trees; and (ii) have stable isotope signatures indicating distinctive pathways for nitrogen and carbon acquisition approaching those of non-photosynthetic orchids that associate with ectomycorrhizal fungi of forest trees. These findings represent a major shift in our understanding of both orchid ecology and evolution because they explain how orchids can thrive in low-irradiance niches and they show that a shift to exploiting ectomycorrhizal fungi precedes viable losses of photosynthetic ability in orchid lineages.  相似文献   

10.
Harvest of orchid tubers for salep production is widespread in southwestern Asia and the Balkans and constitutes a major conservation risk for wild orchid populations. Synanthropic habitats, such as graveyards, are important refuges for orchids and other organisms and could offer protection from salep harvesting because of their special cultural role. However, little is known about the occurrence and factors influencing harvesting of salep in graveyards. During field surveys of 474 graveyards throughout Turkey, we observed 333 graveyards with orchids, 311 graveyards with tuberous orchids, and salep harvest in 14 graveyards. Altogether, 530 individuals of 17 orchid species were collected, representing 9% of the individuals recorded. Harvesting intensity was relatively low, and populations were usually not wholly destroyed. However, some species were clearly more affected than others. Salep harvesting risk of orchid species was significantly associated with flowering time, with early‐flowering species being more affected. A marginally significant positive relationship between harvesting risk and species‐specific tuber size was also detected. Our data suggest that graveyards might offer some protection against salep harvesting in Turkey, but they also show that some orchid taxa are much more affected than others. Overall, our observations add more weight to the conservation value of these special habitats.  相似文献   

11.
Aim The Southern African orchid flora is taxonomically well known, but the biogeographical and diversity patterns have not yet been analysed. In particular, we want to establish whether (a) it is, like the Southern African flora in general, more diverse than would be expected from its latitude and area; (b) it is an African flora, or whether it contains palaeoendemic relicts of a Gondwanan orchid flora; (c) the diversity and endemism in the orchid flora is concentrated in particular biomes and habitat types; and (d) the patterns of endemism in the flora can be accounted for by current environmental parameters, or whether we need to invoke historical explanations. Location Southern Africa. Methods We used the recent floristic account of the Southern African orchids, in conjunction with a data base of over 14,642 herbarium records, to assign the species and subspecies of Southern African orchids to biomes, habitats, and clades. We explored the relationship between the number and endemism of entities (species, subspecies and varieties) and the biomes and habitats. We compared the richness of this flora with that of 31 other regions from all continents and latitudes, to establish whether the Southern African orchid flora is richer or poorer than expected. We assigned the Southern African orchid species to 16 monophyletic clades and mapped the global distribution of these clades to establish the continental affinities of the flora. Main conclusions The Southern African orchid flora is not any more diverse than could be expected from its latitude or area, while the two tropical African floras included were less diverse than expected. Latitude is an excellent predictor of regional orchid species richness; this might indicate that available habitat is more important for orchid diversity than gross area available, since latitude is probably correlated with the extent of suitable habitat. The Southern African orchid flora is clearly an African flora, since all clades are also found in tropical Africa, while many of them are absent from the Americas or Asia. Conversely, while most African orchid clades are also found in Southern Africa, both the Americas and Asia contain many clades absent from Africa. The distribution of orchid entities among the biomes in Southern Africa is very uneven, with two of the seven biomes totally devoid of orchids. Habitats and biomes that have no equivalent in tropical Africa are high in endemism, and habitats and biomes which are also well developed in tropical Africa are low in endemism. Endemism appears largely explained in terms of modern habitats. However, two patterns (the high endemism in the Succulent Karoo and the lack of endemism in the southern Cape among epiphytic orchids) may also be explained in terms of Quaternary climatic changes.  相似文献   

12.
Mycorrhizal association is known to be important to orchid species, and a complete understanding of the fungi that form mycorrhizas is required for orchid ecology and conservation. Liparis japonica (Orchidaceae) is a widespread terrestrial photosynthetic orchid in Northeast China. Previously, we found the genetic diversity of this species has been reduced recent years due to habitat destruction and fragmentation, but little was known about the relationship between this orchid species and the mycorrhizal fungi. The Rhizoctonia-like fungi are the commonly accepted mycorrhizal fungi associated with orchids. In this study, the distribution, diversity and specificity of culturable Rhizoctonia-like fungi associated with L. japonica species were investigated from seven populations in Northeast China. Among the 201 endophytic fungal isolates obtained, 86 Rhizoctonia-like fungi were identified based on morphological characters and molecular methods, and the ITS sequences and phylogenetic analysis revealed that all these Rhizoctonia-like fungi fell in the same main clade and were closely related to those of Tulasnella calospora species group. These findings indicated the high mycorrhizal specificity existed in L. japonica species regardless of habitats at least in Northeast China. Our results also supported the wide distribution of this fungal partner, and implied that the decline of L. japonica in Northeast China did not result from high mycorrhizal specificity. Using culture-dependent technology, these mycorrhizal fungal isolates might be important sources for the further utilizing in orchids conservation.  相似文献   

13.
Understanding the processes that determine the architecture of interaction networks represents a major challenge in ecology and evolutionary biology. One of the most important interactions involving plants is the interaction between plants and mycorrhizal fungi. While there is a mounting body of research that has studied the architecture of plant–fungus interaction networks, less is known about the potential factors that drive network architecture. In this study, we described the architecture of the network of interactions between mycorrhizal fungi and 44 orchid species that represented different life forms and co‐occurred in tropical forest and assessed the relative importance of ecological, evolutionary and co‐evolutionary mechanisms determining network architecture. We found 87 different fungal operational taxonomic units (OTUs), most of which were members of the Tulasnellaceae. Most orchid species associated with multiple fungi simultaneously, indicating that extreme host selectivity was rare. However, an increasing specificity towards Tulasnellaceae fungal associates from terrestrial to epiphytic and lithophytic orchids was observed. The network of interactions showed an association pattern that was significantly modular (M = 0.7389, Mrandom = 0.6998) and nested (NODF = 5.53, p < 0.05). Terrestrial orchids had almost no links to modules containing epiphytic or lithophytic orchids, while modules containing epiphytic orchids also contained lithophytic orchids. Within each life form several modules were observed, suggesting that the processes that organize orchid–fungus interactions are independent of life form. The overall phylogenetic signal for both partners in the interaction network was very weak. Overall, these results indicate that tropical orchids associate with a wide number of mycorrhizal fungi and that ecological rather than phylogenetic constraints determine network architecture.  相似文献   

14.
A current key issue in ecology is the role of spatial effects on population and community dynamics. In this paper, we test several hypotheses related to spatial structures and coexistence of epiphytic tropical orchid species with special emphasis on the endemic species Broughtonia cubensis. More specifically, we explored the spatial structure of orchid–host plant communities at three different levels of organization (occupied vs. nonoccupied host trees, trees with B. cubensis vs. other orchids, and reproductive vs. nonreproductive B. cubensis plants). We mapped all potential host trees and orchids at three 20 × 20 m plots and applied techniques of spatial point pattern analysis such as mark connection and mark correlation functions to evaluate departures from randomized communities. We found spatial aggregation of trees with epiphytic orchids and segregation between trees with and without epiphytic orchids, and that there was an intraspecific spatial aggregation of B. cubensis in relation to the other seven epiphytic orchid species. Furthermore, we found spatial aggregation of reproductive B. cubensis individuals and segregation between reproductive and nonreproductive individuals on their phorophytes. Thus, orchid–host plant communities show hierarchical spatial structuring with aggregation and segregation at different levels of organization. Our results point to an enhancement of local species in the coexistence of tropical epiphytic orchid communities, by reducing competition through niche differentiation.  相似文献   

15.
Biotic interactions play an important role in the assembly and stability of communities. All orchids depend on mycobionts for early establishment, but whether individual orchid species depend on a specific or broad spectrum of mycobionts is still a matter of debate. Tulasnellaceae (Basidiomycota) is the richest and most widespread mycobiont worldwide. We assessed Tulasnellaceae richness in epiphytic and terrestrial orchids in different habitats, and evaluated the degree of generalism in orchid-Tulasnellaceae interactions and the robustness of this mutualistic system to the extinction of mycobiont partners. We sampled 114 orchid individuals including all common and rare species in 56 plots of 1 m2 in 3 habitats: pristine forest, regenerating forest and a landslide site in a tropical montane rainforest in Southern Ecuador. We found 52 orchid and 29 Tulasnellaceae species. The composition of Tulasnellaceae OTUs was moderately to highly similar across habitats and between orchid growth forms. A significantly nested network architecture indicated the existence of a core of generalist Tulasnellaceae OTUs interacting with both rare and common orchids. Terrestrial and epiphytic orchids showed significant differences in robustness to the extinction of their Tulasnellaceae mycobionts. Thus, generalist mycobionts may be relevant for the preservation of hyperdiverse orchid communities in the tropics.  相似文献   

16.
We studied the influence of site conditions on epiphytic orchids under a subtropical climate in the Kathmandu Valley, Nepal. We analysed 96 systematically distributed grid points situated in Kathmandu Valley across a land-use intensity gradient (national park to urbanised city area). Geographical Information System (GIS) and remote sensing were used for classification of land-use types. We identified 23 species of epiphytic orchids, within 13 genera, from 42 different host tree species. Host preference is obvious for some orchid species (e.g., Dendrobium nobile), with certain tree species (e.g., Schima wallichii, Ficus religiosa) hosting more orchid species than others. The orchid Rhynchostylis retusa was the most common species found on many different host tree species across the land-use intensity gradient. Host species and host bark characteristics (e.g., rugosity, pH and exposure to wind) played a vital role for orchid distribution, with lower abundance in areas of higher impact. Under strong human impact (urban city area), F. religiosa was the dominant host tree, with large individual trees (mean diameter in breast height, dbh?=?1.3?m) providing the habitat for considerable populations of R. retusa individuals. In general, epiphytic orchids were found on larger host trees in urban areas than in areas of lower human impact. We found that some hosts are more likely to harbour orchid species, especially native host species. Older larger trees with rougher bark, low pH, exposed to wind and reduced human impact provided better habitats for orchids. We suggest these characteristics should be considered in urban planning to reduce human impact on the associated orchid epiphytic community.  相似文献   

17.
  • Orchids are distributed around the world, however, the factors shaping their specific distribution and habitat preferences are largely unknown. Moreover, many orchids are at risk of becoming threatened as landscapes change, sometimes declining without apparent reason. One important factor affecting plant distribution is nutrient levels in the environment. Nitrates can inhibit not only orchid growth and persistence, but also seed germination.
  • We used in vitro axenic cultures to exactly determine the germination sensitivity of seven orchid species to nitrates and correlated this with soil properties of the natural sites and with the species’ habitat preferences.
  • We found high variation in response to nitrate between species. Orchids from oligotrophic habitats were highly sensitive, while orchids from more eutrophic habitats were almost insensitive. Sensitivity to nitrate was also associated with soil parameters that indicated a higher nitrification rate.
  • Our results indicate that nitrate can affect orchid distribution via direct inhibition of seed germination. Nitrate levels in soils are increasing rapidly due to intensification of agricultural processes and concurrent soil pollution, and we propose this increase could cause a decline in some orchid species.
  相似文献   

18.
Several important habitats have become threatened in the last few centuries in the Mediterranean Basin due to major changes adopted in land‐use practices. The consequent loss of natural and seminatural orchid habitats leads to the appreciation of small anthropogenic habitats, such as cemeteries and roadside verges. Colonization of cemeteries and roadside verges by orchids has long been known, but no study to date compared the suitability of these two anthropogenic habitats for orchids. Therefore, in this paper our aim was to survey cemeteries and roadside verges and to compare these two habitats regarding their role in conserving Mediterranean terrestrial orchids. We conducted field surveys in three Mediterranean islands, Cyprus, Crete, and Lesbos, where both cemeteries and roadside verges were sampled on a geographically representative scale. We found a total of almost 7,000 orchid individuals, belonging to 77 species in the two anthropogenic habitat types. Roadside verges hosted significantly more individuals than cemeteries in Crete and Lesbos, and significantly more species across all three islands. Our results suggest that although cemeteries have a great potential conservation value in other parts of the world, intensive maintenance practices that characterized cemeteries in these three islands renders them unable to sustain valuable plant communities. On the other hand, roadside verges play a prominent role in the conservation of Mediterranean orchids in Cyprus and Greece. The pioneer status of roadside verges facilitates their fast colonization, while roads serve as ecological corridors in fragmented landscapes.  相似文献   

19.
A soil Ca/Mg quotient greater than unity is generally considered necessary for normal plant growth but some serpentine plants are adapted to much lower Ca/Mg quotients, resulting from a major cation imbalance in their substrata. In order to investigate the growth and tolerance responses of serpentine and non-serpentine species to varied Ca/Mg quotients, controlled nutrient solution experiments were performed using an a newly reported Iranian endemic serpentine plant, Cleome heratensis Bunge et Bien. Ex Boiss. and a related non-serpentine species Cleome foliolosa DC. and a Eurasian Ni-hyperaccumulating species Alyssum murale Waldst. and Kit. Seedlings were grown in modified Hoagland’s solutions with varying Ca and Mg concentrations (0.2–2.5 and 0.5–10 mM, respectively) in a fully factorial randomised block design. The yields of the two serpentine plants increased significantly as Mg concentrations in the nutrient solution were increased from 0.5 to 4 mM but decreased in the 10 mM Mg treatment. For C. foliolosa yields decreased significantly from 0.5 to 10 mM Mg, indicating the sensitivity of this non-serpentine plant, and the relative tolerance of the serpentine plants to extremely high levels of Mg. Shoot and root Mg and Ca concentrations in C. heratensis and A. murale were higher than those in C. foliolosa in the low and moderate Mg treatments, supporting the view that many serpentine plants have a relatively high requirement for Mg. Maximum Mg concentrations were found in the roots of C. heratensis. Yields of C. heratensis and A. murale did not change significantly as Ca levels in nutrient solution increased from 0.2 to 2.5 mM Ca, However the yield of C. foliolosa increased significantly from 0.2 to 1.5 mM Ca, indicating sensitivity in this non-serpentine plant and tolerance of the two serpentine plants to low levels of Ca correlated with tissue Ca concentrations, probably because of a greater ability for Ca uptake at low-Ca availability. Calcium deficiency in the low-Ca treatments could be a reason for reduced yield in the non-serpentine plants.  相似文献   

20.
Summary Contrasts in physiognomy and floristic composition of the vegetation of serpentine and non-serpentine substrates are very strong in the northern part of the Rhodesian Great Dyke, and the boundaries between these types are very sharp.Principal components analysis and reciprocal averaging are used to carry out a gradient analysis of the vegetation. The variation in the vegetation of the study area is interpreted in terms of one complex gradient representing a, series from relatively favourable to unfavourable for plant growth. Toxic effects of the substrates and water conditions are the main variables in this interpretation; the latter factor has a reversed effect on serpentine as compared to the non-serpentine substrates, and is less important than the toxicity factor.Comments are made on the table arrangement suggested by reciprocal averaging.The relatively favourable substrates were generally richer in species, but highest and lowest species numbers did not occur at the extremes of the interpreted gradient. The trend in the number of families per stand is similar to that in species numbers for the non-serpentine substrates, but is lowest in the badly-drained serpentine habitat interpreted as most unfavourable to plant growth. The species/family ratio per stand does not show much variation between any of the communities.The percentage of monocotyledonous species is strikingly higher in the communities on serpentine as compared to those in non-serpentine habitats. The total number of dominant species is not markedly different in the communities, but this means that dominant species are relatively more common in the floristically poorer communities of the serpentine, especially those with relatively high total cover values. Values for eveness and Simpson's index of heterogeneity calculated per stand largely confirm this. Again the number of monocotyledonous species amongst the dominants is surprisingly high in the communities on serpentine. Several suggestions explaining the relative success of monocotyledons in serpentine habitats are discussed.Nomenclature is according to the present (1.1.1977) usage at the National Herbarium, Salisbury, Rhodesia.One of us (M.J.A. Werger) wishes to gratefully acknowledge the financial support for this study by the Netherlands Foundation for the Advancement of Tropical Research (WOTRO) and by the Faculty of Science, University of Nijmegen. We are very much indebed to Jo Louppen and Mike Dale for their help with the computations and their comments on the results.  相似文献   

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