Plant Systematics and Evolution

, 283:211

Analyses of cpDNA matK sequence data place Tillaea (Crassulaceae) within Crassula


    • Department of Ecology and Evolutionary Biology, The Natural History Museum and Biodiversity Research CenterUniversity of Kansas
  • Christopher P. Randle
    • Department of Biological SciencesSam Houston State University
  • Priscilla Burgoyne
    • National HerbariumSouth African National Biodiversity Institute
    • Department of Environmental SciencesCollege of Agriculture and Environmental Sciences, UNISA
  • Gideon Smith
    • Biosystematics Research and Biodiversity Collections
    • H.G.W.J. Schweickerdt Herbarium, Department of BotanyUniversity of Pretoria
  • Ernst Jaarsveld
    • Kirstenbosch Botanical Garden
  • Stephen D. Hopper
    • Royal Botanic Gardens, Kew
Original Article

DOI: 10.1007/s00606-009-0227-z

Cite this article as:
Mort, M.E., Randle, C.P., Burgoyne, P. et al. Plant Syst Evol (2009) 283: 211. doi:10.1007/s00606-009-0227-z


Analysis of cpDNA matK sequences for a total of 43 members of the succulent plant family Crassulaceae, including 24 taxa of Crassula, recovered a well-supported clade comprising Crassula species that is sister to the remainder of the family. The resulting topologies do not support the monophyly of the currently recognized subgenera of Crassula, as one member of subgenus Disporocarpa (C. crenulata) is placed as sister to an otherwise monophyletic subgenus Crassula. The major synapomorphy that has been used to recognize the latter subgenus is a base chromosome number of x = 7 versus a base of x = 8 in the other subgenus. We cannot assess the utility of this feature for defining subgenus Crassula because a chromosome count of C. crenulata has yet to be published. The five accessions of the recently resurrected segregate genus Tillaea (of 24 total Crassula species) included here were placed in four separate, well-supported lineages, one of which is greatly removed from the other four accessions. This suggests that this genus is not valid and should not be recognized. An initial examination of the evolution of habit indicates that a perennial habit is ancestral and that the annual habit is a feature that has been derived at least twice in the genus.


CrassulaceaeCrassulaTillaeaSouth AfricamatKPRAP


The angiosperm family Crassulaceae (stonecrops, houseleeks, and plakkies) is a clade of approximately 1,500 species of leaf succulent, ranging from perennial herbs to shrubs. Members of the family are widely distributed and are absent only from Antarctica. Southern Africa represents a major center of diversity for Crassulaceae (Smith et al. 1997). Four largely South African genera, Crassula, Adromischus, Cotyledon, and Tylecodon comprise approximately 300 taxa (including subspecific taxa) or ~20% of the species diversity present in the family as a whole. Recent phylogenetic analyses of Crassulaceae have placed these genera in the first two branching lineages in the family (van Ham and ‘t Hart 1998; Mort et al. 2001). The first branching lineage in the topology, the Crassula clade of van Ham and ‘t Hart (1998), is well-supported (99% bootstrap) based on broad analyses of matK sequence data (Mort et al. 2001). Placed within this lineage is the haplostemonous, perennial genus Crassula as well annual taxa that have been variously placed within Crassula or recognized as the segregate genus Tillaea (see below). The remaining southern African genera of Crassulaceae, along with Kalanchoe, are placed within the next branching clade (i.e., the Kalanchoe clade) of Crassulaceae.

Crassula comprises approximately 150 species that are primarily southern African in distribution, with the vast majority of species occurring in South Africa. Members of the genus display a remarkable degree of floral, cytological, anatomical, and growth form diversity. For example, Crassula includes annual, biennial, and perennial members and ranges from small herbs to large, woody shrubs. This diversity has contributed to the difficulty of defining subgenera and sections within Crassula. Consequently, a combination of features has been used to define groups within the genus; however, there is little agreement on these groups or even on the generic boundaries of Crassula.

Adding to the taxonomic confusion within Crassula is the uncertain phylogenetic placement of the annual aquatic to semi-aquatic species that have been recognized as a separate genus, Tillaea, by some authors (Eggli et al. 1995; Gilbert et al. 2000). While not all annuals have been placed within this segregate genus, many have at various times been included in Tillaea. Species of Tillaea share a haplostemonous androecium with Crassula, but unlike the exclusively southern African Crassula species, taxa that have been included in Tillaea are distributed worldwide, with high species diversity in Australia (~28 species), New Zealand (~10 species), and a few species are also present in western South America. The only phylogenetic study to date to include both annual and perennial taxa was based on analyses of cpDNA RFLPs (van Ham and ‘t Hart 1998). This study placed the single annual species that was sampled within the Crassula clade and sister to a clade of the two perennial species of Crassula that were included (van Ham and ‘t Hart 1998). Given the limited taxonomic sampling from the genus, the phylogenetic placement of Tillaea relative to Crassula should be viewed as tentative. Yet, this study has been cited as justification for resurrecting the genus Tillaea to encompass the annual taxa within the Crassula clade (Eggli et al. 1995; Gilbert et al. 2000). However, not all treatments of the family have adopted this view (Berger 1930; van Jaarsveld 2003; Uhl 1948), but for clarity we will refer to the annual taxa as Tillaea to distinguish them from Crassula as strictly defined.

In his revision of Crassula from South Africa, Tölken (1977) did not recognize Tillaea as a separate genus, but instead placed the annuals from southern Africa in sections Helophytum, Glomeratae, and Dinacria. Taxa assigned to the latter section are distinguished by possessing flowers that are tubular, whereas the former two sections comprise species that possess stellate flowers. It is the annual species from sections Helophytum and Glomeratae that have been at times segregated into Tillaea. Regardless of taxonomy, assessing the monophyly and phylogenetic position of Tillaea relative to other Crassula species has important implications for patterns of character evolution (e.g., annual versus perennial habit) as well as for the biogeographic history of Crassula (Table 1).

As noted above, the phylogenetic position of Tillaea in Crassulaceae has yet to be assessed using DNA sequence data. Here we analyze cpDNA matK sequence data for a broad sampling of the diversity of Crassulaceae and 24 species sampled broadly from Crassula with the goal of determining if Tillaea is placed within the Crassula clade (van Ham and ‘t Hart, 1998). We also include nine annual Crassula taxa, five of which have previously been recognized as Tillaea, to determine the following: (1) if Tillaea is monophyletic, (2) if Tillaea is sister to a monophyletic Crassula, and (3) if the annual habit originated more than once. In addition, the resulting topology is used to test the monophyly of the subgenera of Crassula recognized by Tölken (1977) and van Jaarsveld (2003).

Materials and methods

Taxon sampling

Many partial matK sequences from Crassulaceae were available from previous studies (Mort et al. 2001, 2002; Table 1). Genera representing the seven major clades of Crassulaceae (as inferred by van Ham and ‘t Hart 1998) were sampled; sequences from Penthorum (Penthoraceae), Tetracarpaea (Tetracarpaeaceae), and Pterostemon (Pterostemonaceae), close relatives of Crassulaceae, were used to root the resulting topologies (Fishbein et al. 2001). Partial matK sequences were also available for several species of Crassula (Mort et al. 2001). Additional sequences were obtained from a wide diversity of species; attempts were made to sample those taxa that had either been placed in the genus Tillaea or had been reported as being annuals (van Jaarsveld 2003). Species that have been placed within Tillaea that are sampled in the present study include Crassula schimperi ssp. schimperi (=Tillaea pentandra Royle ex Edgeworth), C. thunbergiana ssp. thunbergiana (=T. decumbens Willdenow), C. decumbens var. decumbens (many species of Tillaea included; see van Jaarsveld 2003 for complete list of synonymy), and C. umbellata [=T. umbellata (Thunberg) Willdenow]. Annual species that have not previously been included in Tillaea were also sampled, including C. campestris, C. sabaeoides, and C. strigosa. Two specimens each of C. campestris and C. thunbergiana var. thunbergiana were included; these species are very difficult to distinguish from each other with the primary distinguishing character being a colorless seta on the leaf tips of the latter. Neither is easily distinguished from C. schimperi ssp. schimperi, although the former two species are annuals while the latter is reported to be perennial (Tölken 1977, 1985; Mort, personal observations). The perennial habit and decumbent (vs. erect) posture are primarily the distinguishing features between C. campestris and C. schimperi (Tölken 1977, 1985). Unfortunately, neither character is evident in herbarium preserved material. Both subgenera Crassula (8 species) and Disporocarpa (16 species) were sampled, including representatives of 10 of 20 sections.
Table 1

Species of Crassulaceae sequenced for matK



GeneBank no.

Adromischus maculatus (Salm-Dyck) Lemaire



Aeonium lindleyi var. viscatum (Bolle) H. Y. Liu

Mort 1492


Aeonium aizoon (Bolle) Mes

Mort 1425


Aichryson punctatum (C. Smith ex Link) Webb and Berthelot

Mort 1495


Cotyledon velutina Hook. f.

NBG 0035/70


[2] Crassula campestris (Ecklon and Zeyhor) Endlicher ex Walpers

Archibald and Mort 125


[2] Crassula campestris (Ecklon and Zeyhor) Endlicher ex Walpers

Archibald and Mort 225


[2] Crassula campestris (Ecklon and Zeyhor) Endlicher ex Walpers

Archibald and Mort 181


[14] Crassula compacta Schönland

Mort 0425


[6] Crassula crenulata Thunberg

BONN 05128


[18] Crassula deceptor Schönland

MO 840772


[2] Crassula decumbens var. decumbens (Adamson) Tölken

Archibald and Mort 180


[5] Crassula deltoidea Thunberg



[13] Crassula fasicularis Lamarck

WTU n.v.


[2] Crassula muscosa ssp. polpodacea (Harvey) G. D. Rowley

Archibald and Mort 239


[14] Crassula orbicularis L.

WTU 124


[6] Crassula ovata (Miller) Druce

Mort s.n.


[6] Crassula pellucida ssp. brachypetala (Drege ex Harvey) Tölken

Mort 0432


[19] Crassula perfoliata var. minor (Haworth) G. D. Rowley

MO 882392


[15] Crassula perforata Thunberg

Fishbein 377


[15] Crassula rupestris ssp. rupestris Thunberg

MO 800755


[15] Crassula rupestris ssp. marnieriana (H. Huber and H. Jacobsen) Tölken

Morgan 2152


[9] Crassula sarcocaulis ssp. rupicola Tölken

Mort 0416


[2] Crassula schimperi ssp. schimperi Fischer and C. A. Meyer

Archibald and Mort 250


[3] Crassula sebaeoides (Ecklon and Zeyher) Tölken)

Archibald and Mort 257


[2] Crassula strigosa L.

Archibald and Mort 197


[2] Crassula thubergiana ssp. thunbergiana Schultes

Archibald and Mort 157


[2] Crassula thunbergiana ssp. thunbergiana Schultes

Archibald and Mort 162


[2] Crassula umbellata Thunberg

Archibald and Mort 188


Cremnophylla nutans Rose

WTU 120


Dudleya greenei Rose

RSA 10158


Echeveria fulgens Lemaire

Mort 1596


Hylotelephium ewersii (Ledebour) H. Obha

K 197-80-01945


Kalanchoe lateritia Engler

MO 850883


Monanthes minima (Bolle) Christ

Santos s.n.


Penthorum sedoides L.

Haydn 2232 (WS)


Pterostemon rotundifolius Ramírez

Sanchez 256 (TEX)


Sedella pumila (Bentham) Britton and Rose

Ahart s.n.


Sedum burrito Moran

WTU 593


Sedum hispanicum L.

MO 1987-1140


Sempervivum ciliosum Craib

U 31473


Sempervivum globiferum ssp. arenarium (W. D. J. Koch) ‘t Hart Bleij

K 184-42-08087


Sinocrassula indica (Decaisne) A. Berger

Cody s.n.


Tetracarpaeatasmannica Hook. f.

Jordan s.n. (HO)


Thomsonella minutiflora (Rose) Britton and Rose

HNT 72129


Tylecodon ventricosus (Burman f.) Tölken

NBG 321/69


Unless otherwise noted, all specimens have been deposited in the Marion Ownby Herbarium at Washington State University (WS). Other herbarium abbreviations are as follows: Missouri Botanical Gardens (MO), Compton Herbarium (NBG), University of Bonn (BONN), University of Washington (WTU), Rancho Santa Anna Botanical Garden (RSA), Royal Botanic Gardens Kew (K), University of Utrecht (U), and Huntington Botanical Garden (HNT). Numbers preceding Crassula species indicate the numerical section designations of van Jaarsveld (2003) as follows: [2] = Glomeratae, [3] = Dinacria, [5] = Deltoidea, [6] = Anacampseroideae, [9] = Acutifolia, [13] = Kalosanthes, [14] = Rosulares, [15] = Perfilatae, [18] = Arta, [19] = Crassula

aJohnson and Soltis 1994

bMort et al. 2001

cFishbein et al. 2001

dMort et al. 2002

DNA extraction, amplification, and sequencing

DNA was extracted from fresh and silica-dried material using a modified CTAB protocol (Doyle and Doyle 1987). Approximately 0.7 g leaf material was ground in liquid nitrogen and mixed with 5 ml 4× CTAB (110 nmol/L). Extractions were incubated for 2 h at 60°C, followed by chloroform/isoamyl alcohol precipitation.

For most DNA accessions, matK was PCR-amplified using trnK-3914 F and trnK-psbA R primers (Johnson and Soltis 1994; Mort et al. 2001). However, in several species of Crassula, matK did not amplify using this primer combination, and therefore we used the primer combination trnK-710 F (Johnson and Soltis 1994) with either trnK-1800 R (Mort et al. 2001) or 1105 R (KGC TTT RGC TAA GGA ATT CG). PCR reactions of 50 μl included 20 μM dNTPs, 3.5 mM MgCl2, 0.64 μM of each primer, 1× PCR buffer, and 0.5 μl Taq polymerase (Promega, Madison). Reactions were carried out under the following temperature conditions: 2 min at 95°C; 30 cycles of 45 s at 95°C, 45 s at 44°C, and 4 min at 72°C; and a final extension of 10 min at 72°C. Amplicons were purified using the QIAquick PCR purification protocol (Qiagen, Valencia, CA). Cycle sequencing reactions of 10 μl were carried out using CEQ Quickstart chemistry (Beckman Coulter, Fullerton, CA), with 0.4 μM primer. Sequences were generated using matK-710 F, matK-1470 F, matK-1470 R (Johnson and Soltis 1994), and matK-1800 R (Mort et al. 2001); for several species the following primers designed for the current study were used: matK-472 F (GTT GTG CAA ACC CTM CGC) and matK-640 R (GAA ACC CCA GGA GGA ATT CG). Sequences were obtained using a CEQ 8000 Genetic Analysis System (Beckman Coulter, Fullerton, CA).

Phylogenetic analysis

Sequences were aligned in Clustal X (Thompson et al. 1997) and manually adjusted using Se-Al (Rambaut 1996). Parsimony tree search was conducted using PAUP* 4.0b10 (Swofford 2003), using 1,000 random addition sequences, TBR branch-swapping, and holding two trees per step. All characters were equally weighted, and indels were not included in the analyses. One thousand jackknife replicates were performed to estimate branch support, with 37% character deletion and the “emulate Jac” option selected. Each jackknife replicate tree search included ten random addition sequence replicates with TBR tree swapping and a single tree held per step. Bremer decay values were estimated using PRAP (Müller 2004), a program that creates a file executable in PAUP in which every node in the MP tree is assigned a reverse constraint tree. The difference in number of steps between the shortest tree when the constraint is enforced and the MP tree is equivalent to Bremer support (Bremer 1988). Additional tree searches were run to discover shortest trees when the monophyly of former members of Tillaea and the monophyly of all annual species were each enforced. Base chromosome numbers were scored using published chromosome counts (Uhl 1948, 1961, 1963). The evolution of an annual habit and base chromosome number was explored by tracing these features onto one randomly selected MP tree using the default settings in MacClade (Maddison and Maddison 1992).


Individual matK sequences ranged from 886 to 1,145 base pairs. The aligned matrix consisted of 1,302 aligned bases, of which 506 were parsimony informative. Tree search resulted in 18 most parsimonious trees of length 1,757 (CI = 0.620; RI = 0.840; Fig. 1). Previous studies utilizing cpDNA restriction site data (van Ham and ‘t Hart 1998) and matK with greater sampling of species outside of Crassula (Mort et al. 2001) were congruent on relationships among seven major clades in Crassulaceae. Topologies recovered in the current analysis are congruent with these previous analyses.
Fig. 1

Strict consensus of 18 MP trees (L = 1,757; CI = 0.620; RI = 0.840). Numbers on branches represent jackknife support/Bremer support; the arrow indicates the clade comprising members of subgenus Crassula, with the exception of C. crenulata of subgenus Disporocarpa. Numbers next to the tree indicate clades as enumerated by van Ham and t’Hart (1998): 2Kalanchoe, 3Telephium, 4Sempervivum, 5Leucosedum, 6Acre, 7Aeonium. Highlightedterminals represent annual taxa while the encircledT” represents species that have previously been included in the genus Tillaea

The results of the present study, similar to van Ham and ‘t Hart’s (1998) cpDNA RFLP study, place Tillaea and Crassula in a well-supported clade (100%, Bremer = 20) and sister to the remainder of Crassulaceae (Fig. 1). However, in contrast to van Ham and ‘t Hart (1998), our analyses place the accessions of Tillaea within, rather than sister to, Crassula with strong support (Fig. 1). Furthermore, these taxa do not form a monophyletic lineage, but instead are scattered among several lineages within Crassula. Crassula deltoidea and a clade comprising C. pellucida and C. sarcocaulis (92%, Bremer = 6) form a grade at the base of a weakly supported clade (<50%, Bremer = 2) comprising the remaining species sampled. Seven of the nine annuals sampled, including three species (four accessions) that have been included in Tillaea, are placed along with two perennials in a clade (51%, Bremer = 3). Although this clade is only weakly supported, it is found in each MP tree. It is also noteworthy that many of the internal relationships within this clade dividing the annuals into three groups receive strong support, which suggests that patterns of life-history evolution are likely complex within Crassula.

This largely annual clade is sister to a clade comprising four additional members of subgenus Disporocarpa as well as the eight members of subgenus Crassula sampled here. There is strong support for a subclade (100%, Bremer = 15) that includes the perennial tree-like shrub C. ovata and two annual species (C. decumbens and C. strigosa, the former of which has been placed within Tillaea species). All the members of subgenus Crassula sampled in the present study form a well-supported subclade (100%, Bremer = 39); however C. crenulata (subgenus Disporocarpa) is placed within the subgenus Crassula clade with strong support. Thus our results indicate that neither subgenus as currently recognized is monophyletic.


While other phylogenetic studies have included Crassula species, none of these were conducted for the explicit purpose of examining relationships within the genus (Fishbein et al. 2001; van Ham and ‘t Hart 1998; Mort et al. 2001). The present study, therefore has the greatest sampling of Crassula species thus far included in a single analysis; however, much of the diversity, especially within subgenus Crassula, is not included. Thus conclusions related to sister group relationships and broad patterns of evolution across the genus should be viewed as tentative. However, the sampling included here is sufficient to examine the putative monophyly of Tillaea as well as to place these taxa within the broad phylogeny of Crassulaceae. The only study to include Tillaea thus far was that of van Ham and ‘t Hart (1998), but only a single species was included and the sampling of Crassula species was very low (two species). The present study is the first to test the monophyly of Tillaea as well as to place these taxa within a broadly sampled Crassulaceae using DNA sequence data. In addition, sampling also permits an initial assessment of the monophyly of the two currently recognized subgenera of Crassula.

Phylogeny of Crassula

The most recent taxonomic revision of Crassula recognized two large subgenera, subgenus Crassula and subgenus Disporocarpa (Tölken 1977, see also van Jaarsveld 2003). These seem at least to differ in the base chromosome: x = 7 in subgenus Crassula and x = 8 in subgenus Disporocarpa. However, there are a few exceptions to this as several members of section Anacampseroideae (subgenus Disporocarpa) have a base chromosome number of seven. The two species of Anacampseroideae included here (i.e., C. crenulata and C. pellucida ssp. brachypetala) are not monophyletic based on the current analyses (Fig. 1), suggesting that this section may not be monophyletic. In the MP trees inferred in this study, neither subgenus is monophyletic; however, subgenus Crassula would be monophyletic except that it includes C. crenulata, also of section Anacampseroideae. While chromosome number has never been examined in this species, it is worth exploring in the future whether C. crenulata is among those species placed in subgenus Disporocarpa that have a base chromosome number of seven—an increase in taxon sampling may then show that Anacampseroideae is an unnatural grouping and that C. crenulata does indeed belong in subgenus Crassula.

The results of the present study support previous analyses that suggest the base number of Crassulaceae as a whole is x = 8 (Mort et al. 2001). A reduction to a base number of x = 7 appears to be synapomorphic for Crassula subgenus Crassula. However, C. crenulata (subgenus Disporocarpa) lacks a published chromosome count, which precludes a comprehensive assessment of the patterns of chromosomal change(s) within subgenus Crassula. Based on a recent study of Crassula species from New Zealand, it seems likely that the patterns of chromosomal evolution within subgenus Disporocarpa are quite complex. De Lange et al. (2008) examined morphological and chromosomal diversity among 16 populations of C. hunua and C. ruamahanga. Although it is impossible to distinguish these two species or segregates within either species based on analyses of 12 key morphological features, the authors found a high degree of chromosomal variation, with 11 different chromosome numbers ranging from 2n = 42 to 100 in populations of the two species. Future studies will examine the patterns of chromosome evolution in Crassula by expanding the taxonomic sampling across the genus to include multiple members of all recognized sections.

The evolution of an annual habit similarly appears to be complex and likely has arisen more than once in Crassula. Tracing the annual versus the perennial habit onto one MP topology indicates that a perennial habit is ancestral in the genus. Two independent origins of annuality are inferred, one on the branch uniting C. decumbens and C. strigosa, and the other at the base of the least inclusive clade containing both C. campestris and C. sebaeoides. In addition, two reversals to the perennial habit in C. schimperi ssp. schimperi and C. muscosa ssp. polpodacea are inferred. If species that have an annual habit are constrained to form a clade, tree search results in trees of 1,844 steps (CI = 0.591; RI = 0.779), 87 steps longer than the unconstrained MP tree. Although only preliminary, these results suggest that habit maybe a fairly labile feature among the earliest-branching lineages of Crassula.

Monophyly and phylogenetic position of Tillaea

Four species that have been variously included in Tillaea (i.e., Crassula decumbens var. decumbens, C. schimperi ssp. schimperi, two accessions of C. thunbergiana ssp. thunbergiana, and C. umbellata) were included in the analyses. Four of the five accessions included are placed within a single well-supported clade (100%; Bremer = 25). They do not, however, form a monophyletic group within this clade, but rather are placed with strong support in three distinct lineages (Fig. 1). The remaining sampled Tillaea accession, C. decumbens var. decumbens, forms a well-supported sister group relationship with the annual C. strigosa (100%, Bremer = 59) that is far removed from the other Tillaea taxa (Fig. 1). When the accessions of Tillaea were constrained to form a monophyletic group, the MP tree was 1,933 steps long (CI = 0.564; RI = 0.753), or 176 steps longer than the most parsimonious trees found in the unconstrained search. These results clearly demonstrate that there is no justification for recognizing Tillaea as distinct from Crassula based on cpDNA data. Furthermore, the two sequences of C. thunbergiana ssp. thunbergiana included were not resolved as sister taxa but were instead separated by several well-supported branches. Crassula thunbergiana, C. campestris, and C. schimperi are very difficult to distinguish morphologically, and the distinction may not be representative of any natural groupings.

The present study is the most robust estimate of phylogeny to date for Crassula. The results presented here are congruent with previous family-level studies of Crassulaceae in that a well-supported clade comprising members of Crassula is sister to the remainder of the family (van Ham and ‘t Hart 1998; Mort et al. 2001). However, it is clear from the present study that Tillaea is neither monophyletic nor sister to Crassula. Instead, the five accessions of Tillaea (of 24 total sampled Crassula species) were placed in four separate, well-supported lineages, one of which is greatly removed from the other four accessions. The previous results (van Ham and ‘t Hart 1998) used to justify segregating Tillaea suffered from very limited sampling of both Crassula (two species) and Tillaea (one species). Our results suggest that Tillaea should not be recognized as a genus distinct from Crassula, but inferring broad patterns of evolution in the genus is not possible with the current level of sampling. Future studies will sample more broadly across the genus and employ analyses of cpDNA and nrDNA ITS data to examine character evolution more robustly.


This research was supported by NSF DEB 0344883 to MEM. The authors wish to thank J.A. Archibald, D.J. Crawford, T. O’Leary, and P. Protti for helpful comments on previous versions of this manuscript. We dedicate this paper to Charles Uhl for his decades of contributions to the study of Crassulaceae.

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© Springer-Verlag 2009