Extreme insular dwarfism evolved in a mammoth

Victoria L. Herridge, Adrian M. Lister


The insular dwarfism seen in Pleistocene elephants has come to epitomize the island rule; yet our understanding of this phenomenon is hampered by poor taxonomy. For Mediterranean dwarf elephants, where the most extreme cases of insular dwarfism are observed, a key systematic question remains unresolved: are all taxa phyletic dwarfs of a single mainland species Palaeoloxodon antiquus (straight-tusked elephant), or are some referable to Mammuthus (mammoths)? Ancient DNA and geochronological evidence have been used to support a Mammuthus origin for the Cretan ‘Palaeoloxodon’ creticus, but these studies have been shown to be flawed. On the basis of existing collections and recent field discoveries, we present new, morphological evidence for the taxonomic status of ‘P’. creticus, and show that it is indeed a mammoth, most probably derived from Early Pleistocene Mammuthus meridionalis or possibly Late Pliocene Mammuthus rumanus. We also show that Mammuthus creticus is smaller than other known insular dwarf mammoths, and is similar in size to the smallest dwarf Palaeoloxodon species from Sicily and Malta, making it the smallest mammoth species known to have existed. These findings indicate that extreme insular dwarfism has evolved to a similar degree independently in two elephant lineages.

1. Introduction

Dwarfism is a well-known evolutionary response of large mammals to insular environments, forming part of the ‘island rule’, whereby large mammals evolve smaller size, and small mammals larger size, on islands [1]. Mediterranean Pleistocene dwarf elephants, such as the Siculo-Maltese species Palaeoloxodon falconeri, represent some of the most extreme examples of insular dwarfism and have come to epitomize this phenomenon. However, poor taxonomy has hampered research into the causes and mechanisms of insular body size change in elephants and, by extension, broader topics such as the island rule.

The generic affinity of Mediterranean dwarf elephants is the subject of ongoing debate (see the electronic supplementary material). With the exception of the Sardinian Mammuthus lamarmorai, Mediterranean island elephants were thought to be phyletic dwarfs of a single mainland taxon, Palaeoloxodon antiquus, the straight-tusked elephant [2]. A study by Poulakakis et al. [3] challenged this consensus, presenting ancient DNA (aDNA) evidence for Mammuthus (mammoth) affinity of a rib bone fragment from Cape Malekas in Crete, the type locality for Palaeoloxodon creticus [4]. On the basis of this aDNA evidence and the purported geological age of this specimen (earlier than 800 ka), Poulakakis et al. recommended that Cretan P. creticus be revised to Mammuthus, and further suggested that Sicilian and Maltese taxa might also be referable to this genus. Their study was immediately challenged [5,6], and its credibility questioned owing to ‘serious theoretical and methodological flaws’ ([6], p. 56; see the electronic supplementary material). Poulakakis et al. defended their findings, but acknowledged the need for independent corroboration of their work ([7], p. 61); such corroboration is still outstanding.

Thus, the identification of ‘P’. creticus as a mammoth currently rests on the assertion that material from Cape Malekas pre-dates the arrival of Palaeoloxodon in Europe, precluding derivation from that taxon [8,9]. Temporal arguments are not sufficient to merit taxonomic revision, but the chronology is in any case open to question. The antiquity of Cape Malekas is far from certain, being based on a hypothesized biostratigraphical relationship with material from the Katharo Plateau (East Crete), which was in turn dated using a discredited amino acid racemization (AAR) methodology [10,11]. Even if the oldest Katharo Plateau AAR date is given credence (738 ka ± 20% [10]), the first appearance of P. antiquus in Europe dates to around the Bruhnes–Matuyama boundary (ca 780 ka) [12]; thus it cannot be ruled out as a potential ancestor, given that insular dwarfing can occur rapidly [13].

The generic attribution of the Cape Malekas elephants therefore remains uncertain. Despite well-preserved type material displaying a number of taxonomically informative characters, there has been no systematic attempt to assess their morphological affinity, although Bate [4] and Mol et al. [8] noted the low-crowned, Mammuthus meridionalis-like nature of the teeth. Here, we use an alpha-taxonomic approach to perform the first such analysis, comparing the Cape Malekas elephant material, including newly discovered in situ specimens, with Late Pliocene to Middle Pleistocene mainland European Palaeoloxodon and Mammuthus. We further compare the Malekas material with other insular dwarf elephants to take account of the allometric effects of insular dwarfism on taxonomically informative characters.

2. Material and methods

(a) Sample

We consider P. antiquus and M. meridionalis (the proposed ancestral taxa of ‘P’. creticus), and extend our analyses to two further species: Mammuthus rumanus and Mammuthus trogontherii. These species were present in Europe during the Late Pliocene (M. rumanus), Early Pleistocene (M. meridionalis) or Middle Pleistocene (M. trogontherii and P. antiquus). We limit our Cretan elephant sample to those specimens collected by Dorothea Bate, housed in the Natural History Museum (London), which are clearly labelled and registered with the locality ‘Cape Maleka’. This sample lacks cranial and post-cranial material [4], and thus taxonomic assessment must be based on the well-preserved molars (which include the lectotype of ‘P’. creticus fixed by Osborn [14], a lower third molar (M3), NHM M9381; figure 1b).

Figure 1.

(a) Location of Cape Malekas, Crete. (b) Lectotype of M. creticus [4] (NHM M9381) showing Mammuthus-like early wear (x) and enamel figure (y). (cf) In situ fossil from Cape Malekas: (c) natural mould of the occlusal surface of a probable upper molar; (d) posterior view of lower molar embedded in sediment; (e) probable lower M2 in cross section; (f) adult humerus in longitudinal section. Images (ce) are to same scale.

In elephants, the M3 is the final tooth in the dental series. It has a distinctive curved and posteriorly tapering morphology ensuring metric comparisons are made between homologous elements in different-sized taxa. Non-metric occlusal surface characters are applicable to the entire dental ontogenetic series (dP2-M3) [1416], and thus pre-M3 creticus teeth were scored in addition to M3s (total sample n = 6). Taxonomic or size-informative data (see below) were collected for M3s of the following taxa (locality information; source collection—abbreviations defined in the electronic supplementary material; total sample size):‘P’. creticus (Cape Malekas; NHM; n = 3); P. antiquus (various sites, UK and Germany, ca 500−120 ka; NHM, SMNS; n = 26); M. trogontherii (Süssenborn, Germany, ca 600 ka; SMNS, SRSQP; n = 28); M. meridionalis (Upper Valdarno, Italy, ca 2.0−1.8 Ma; NMB, MPM, MGPF; n = 26). Mammuthus rumanus data were collected from the literature [1719] (various sites, UK and eastern Europe, 3.5−3.0 Ma; n = 4). Data were also collected for M3s of the two smallest Mediterranean dwarf Palaeoloxodon species, Palaeoloxodon falconeri (Luparello and Spinagallo Caves, Sicily; UCat, GM; n = 17) and Palaeoloxodon cypriotes (Imbohary, Cyprus; NHM; n = 4). Data are available from the authors on request (Palaeoloxodon data from V.L.H.; Mammuthus data from A.M.L.). We restricted the P. falconeri sample to Sicilian localities, given ongoing debate over the conspecificity of Maltese and Sicilian elephants [20,21]. In addition, total bone length (TL: from most proximal end of lateral tuberosity to most distal end of lateral condyle) and diaphyseal length (DL: between proximal and distal epiphyseal lines, taken on anterior surface) were collected for adult humeri of P. falconeri from Spinagallo Cave, Sicily (UCat; n = 7), Palaeoloxodon tiliensis, a medium-sized (approx. 810 kg) dwarf Palaeoloxodon from Charkadio Cave, Tilos [22] (UoA; n = 6) and M. lamarmorai from Sardinia (MSNF). ‘Adult’ is here defined as those bones with fused distal epiphyses. Additional literature data and unpublished M. exilis data collected by Larry Agenbroad were used to supplement our insular mammoth dataset (table 1).

View this table:
Table 1.

Mammuthus creticus M3 and in situ Cape Malekas cf. M. creticus pre-M3 specimens (see text), compared with upper and lower M3s of insular dwarf and mainland elephants. Mammuthus creticus was compared separately with (i) P. falconeri and P. cypriotes (3-taxon HSD), (ii) M. rumanus, M. meridionalis and M. trogontherii (four-taxon HSD), and (iii) all included full-sized elephants (five-taxon HSD). Mammuthus primigenius data from Vartanyan et al. [23] and Veltre et al. [24]. M. exilis M3 data provided by L. Agenbroad (superseding the data of Agenbroad [25], which contain errors; L. Agenbroad 2011, personal communication). Asterisks indicates mean values that are significantly different from mean M. creticus M3 (Tukey–Kramer HSD, p < 0.05). Literature data for insular mammoths could not be compared statistically.

(b) Taxonomically informative characters

An alpha-taxonomic approach akin to that of Higham et al. [26] is justified here because (i) there are only two elephant genera (Mammuthus and Palaeoloxodon) on the European mainland during the Pleistocene, comprising a few very well-known species; (ii) it is biogeographically almost certain that one of these species was the ancestor of the Cretan dwarf species; (iii) the scoreable/measurable traits on the existing Cretan specimens are well-characterized and widely used to discriminate Mammuthus from Palaeoloxodon in mainland material. With these provisos, the absence of Palaeoloxodon apomorphies, and the presence of plesiomorphic character states observed in Mammuthus but not in Palaeoloxodon, can be used as evidence for Mammuthus affinity, and vice versa.

Three non-metric characters of the occlusal surface are accepted for discriminating Palaeoloxodon from Mammuthus [15]: the shape of the enamel loop visible on the occlusal surface; the early-wear pattern of that loop; and the existence and shape of any enamel ‘expansions’ in the mesial region of the enamel figure (‘mesial expansions’). Enamel-loop shape is scored in mid-wear as: 0, parallel-sided enamel figures that sometimes expand to form a sub-circular mesial region (diagnostic for Mammuthus); or 1, lozenge- or cigar-shaped (diagnostic for Palaeoloxodon). Early-wear pattern is scored as: 0, equal-sized enamel rings, or a sub-circular mesial ring between two elongated rings (diagnostic for Mammuthus); or 1, a long central loop between two much shorter loops, the ‘short–long–short’ pattern (diagnostic for Palaeoloxodon). Mesial expansions are coded as: 0, absent or vestigial (characteristic of derived Mammuthus species and seen in P. antiquus); 1, rounded loops (the plesiomorphic state for the Elephantidae—occurs in early Mammuthus, but not in Palaeoloxodon); or 2, pointed or ‘triangular’ (common in Palaeoloxodon). Mesial expansion character state 1 is therefore diagnostic for Mammuthus in this context, while state 0 is consistent with Mammuthus but cannot rule out Palaeoloxodon in the absence of other characters.

Metric characters followed standard protocols [15,27], except molar width (W), enamel thickness (ET) and lamellar frequency (LF; see the electronic supplementary material for details). M3 plate count (PC), hypsodonty index (HI: crown height/width × 100), relative length index (RLI: length/width × 100), ET and LF are useful for species-level identification in full-size elephants (see electronic supplementary material, S2) and are thus potentially informative on Cretan to mainland elephant taxon affinity within a genus. The potential impact of allometric change on these characters in dwarf taxa is poorly understood. For example, LF is expected to be of limited taxonomic value in dwarf taxa: full-sized elephants have been shown to exhibit intraspecific size-related trends in M3 teeth [28], and through the molar ontogenetic series (dP2-M3) [29]. Only W, length (L) and crown height (CH) are assumed a priori to be size characters and thus discounted as taxonomically useful (these can be used in size comparisons between the Cape Malekas elephants and other dwarf elephant taxa). The taxonomic value of PC, HI, RLI, ET and LF was assessed with reference to evolutionary patterns in Palaeoloxodon dwarfs (see §3).

Significant difference of creticus mean values from (i) mainland taxa and (ii) other dwarf elephant taxa was tested using ANOVA across species-groups, followed by a Tukey–Kramer honestly significant difference (HSD) test, a post hoc mean-comparison method that corrects for experiment-wide error resulting from multiple pair-wise comparisons [30]. Sample sizes are small (and thus the power of the statistical test to detect differences is relatively low, and prone to type II error), but this equates to a conservative test of morphological dissimilarity. Range data were used to identify morphological similarity, and minimize the type II error rate: if there is no significant difference in mean values, creticus data must also fall within that taxon's range to be considered morphologically similar.

3. Results and discussion

(a) New field data

In 2011, one of us (V.L.H.), with George Iliopoulos, University of Patras, located a fossiliferous deposit on Cape Malekas consistent with the description of the type locality of ‘P’. creticus by Bate [4,31]. Coastal cliff retreat on Cape Malekas has exposed fossil specimens in a well-cemented clastic deposit approximately 20–30 m above the present sea level, which appears to have no internal stratigraphy. Sediments are mostly fine-grained sands that fill fissures of a previously active karst system. Multiple disarticulated bone and tooth fragments are found within the matrix, which, in some localities, is capped by horizontal flowstone of up to 10 cm thickness. This deposit is the most fossil-rich of several 2–3 m wide ‘tongues’ of clastic sediment found in close proximity to one another, at roughly the same altitude, in the Cape Malekas region.

A lower molar fragment (field number, fn: MAL_11_01; figure 1d), a probable M2 (fn: MAL_11_02; visible in longitudinal section, figure 1e) and an adult humerus in longitudinal section (fn: MAL_11_04; figure 1f) were measured in situ (removal was not possible without risking damage to the specimens). The natural mould of the occlusal surface of a molar, probably an upper (fn: MAL_11_03; figure 1c), was also discovered, and can be unequivocally identified as the mould of the molar figured by Van der Geer et al. ([32], p.53), collected in the Malekas region by Paul Sondaar in 1973 (Jon de Vos 2011, personal communication).

MAL_11_02 has a PC of ∞10x; it is worn down almost to the root at the front, but a large root interpreted as the anterior root is visible (figure 1e), suggesting that only the anterior talon has been lost, and giving a reconstructed M2 PC of x10x. Molar widths and heights overlap considerably in M2 and M3 teeth in an elephant species; measurements on both in situ molars (including unworn crown heights) are consistent with Cape Malekas M3s (including type material) collected by D. M. A. Bate, and are thus probably conspecifics (table 1).

(b) Genus attribution

Cape Malekas teeth from the Bate collection, including the creticus type specimen NHM M9381 (figure 1b), were scored as follows (data in the electronic supplementary material): mid-wear enamel-loop shape ‘0’ = 4/4 (i.e. four out of four specimens that could be scored for this character show character state ‘0’), ‘1’ = 0/4 (note however that M9377 also shows character state ‘1’ in late wear; see the electronic supplementary material); early-wear pattern ‘0’ = 3/3, ‘1’ = 0/3; the shape of mesial expansions ‘0’ = 3/4, ‘1’ = 1/4, ‘2’ = 0/4. Palaeoloxodon falconeri and P. cypriotes M3s, conversely, show an enamel-loop shape typical of P. antiquus (16/16 and 4/4 scored as ‘1’, respectively), and mesial expansions that are either diagnostic for P. antiquus (P. falconeri: 16/16 scored as ‘2’), or consistent with it (P. cypriotes: 4/4 scored as ‘0’). All scoreable P. falconeri M3s also show an early-wear pattern diagnostic for P. antiquus (10/10 scored as ‘1’); no P. cypriotes teeth were at the appropriate wear stage to be scored for this characteristic. The creticus hypodigm thus displays occlusal surface traits that are diagnostic for mainland Mammuthus. Furthermore, the presence of rounded or ‘looped’ mesial expansion on M9378a suggests affinity with early Mammuthus taxa, M. rumanus or M. meridionalis, rather than the more derived M. trogontherii (see electronic supplementary material, S4). The Cape Malekas elephants are thus identified as mammoths, and are henceforth referred to the genus Mammuthus.

(c) Affinity with mainland species

Differences between Mammuthus creticus and full-sized mammoth species may result from allometric changes associated with dwarfism, as observed in P. falconeri skull shape [33,34], or reflect adaptation to small body size and/or insular feeding niche. Although we cannot tease apart these effects given the paucity of evidence, the Palaeoloxodon dwarfing model provides a useful analogue. We identified traits that (i) do not retain a taxonomic signal within Palaeoloxodon dwarfs and (ii) are shared between Palaeoloxodon dwarfs and M. creticus, and which thus may indicate size-related and/or adaptive convergence.

Palaeoloxodon cypriotes and P. falconeri are both significantly different from P. antiquus for mean M3 PC, LF and ET (HSD test of all three taxa, p < 0.05; see the electronic supplementary material for full statistical tables), but not for RLI or HI. Hence, PC, LF and ET are not robust indicators of taxonomic affinity for Palaeoloxodon dwarf taxa, and thus may not be for Mammuthus. Mammuthus creticus is also similar in PC, RLI and LF to the similarly sized P. falconeri and P. cypriotes (figure 2), further undermining the taxonomic usefulness of PC and LF. The strong size-dependency of LF in full-sized elephants [28,29] predicts this for any dwarf elephant, and significant differences in mean LF also exist between M. creticus and all full-sized mammoth taxa. Size effects on other characters are less well understood, but this approach suggests that PC should be interpreted with care and that HI is the most taxonomically useful character (table 2).

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Table 2.

Morphological similarity (not significantly different, and falls within the range) and dissimilarity (significantly different, and falls outside the range) of M. rumanus, M. meridionalis and M. trogontherii compared with M. creticus. Means are compared using a four-taxon Tukey's HSD, p < 0.05. Mammuthus creticus falls outside the range of, but is not significantly different from, M. trogontherii for ET, and M. rumanus for PC and RLI; given the small sample size and likelihood of type II error, this cannot be seen, on current data, as a robust indicator of either similarity or dissimilarity. Asterisks indicate character similarity between M. creticus and Palaeoloxodon dwarfs. Square brackets indicate characters that do not retain a taxonomic signal in Palaeoloxodon dwarfs.

Figure 2.

(af) Size and shape comparisons with M. creticus lower M3s. L (length) × W (width) × H (height) provides an estimate of tooth volume, capturing overall tooth size. Two 3-taxon Tukey HSD tests were carried out (i) between M. creticus, M. meridionalis and M. trogontherii, for taxonomic purposes, and (ii) between M. creticus, P. cypriotes and P. falconeri, for size and shape comparison within insular dwarfs. Asterisks indicate taxa that are significantly different to M. creticus at p < 0.05.

PC in M. creticus matches meridionalis ancestry without character change (mean M3 PC = 12 and 12.9, respectively), but following the Palaeoloxodon model, could have been achieved by reduction from the M. trogontherii state (mean M3 PC = 19). Mammuthus creticus falls above the M. rumanus range for both PC and RLI, but samples are small and the differences are not statistically significant (figure 2). The strongest evidence against M. trogontherii ancestry comes from the low HI, which would require a further character change from this high-crowned taxon not predicted by the Palaeoloxodon model. Mammuthus creticus is instead similar in HI to both M. rumanus and M. meridionalis, indicating an affinity with the low-crowned ‘early’ mammoths that is consistent with occlusal surface data. Although statistical support for M. meridionalis–M. creticus similarity is statistically more robust, with an implied colonization between 2.5 and 0.8 Ma, we cannot reject creticus affinity with M. rumanus. The latter could imply a Late Pliocene origin for M. creticus (known range of M. rumanus ca 3.5−2.5 Ma [17]), significantly earlier than previously thought.

(d) Comparison with other insular dwarf elephants

Insular mammoths are known from Sardinia (M. lamarmorai [35]) and the Californian Channel Islands (Mammuthus exilis [25,36]), as well as Wrangel Island (northeast Siberia) and St Paul (Pribilof Islands, Alaska; Mammuthus primigenius [23,24]). MAL_11_04 provides us with the first data for M. creticus skeletal dimensions and is particularly valuable, given that teeth can be problematic for body size estimation, especially in insular dwarfs [37,38]. Although measurement protocol cannot be exactly equivalent for in situ and disarticulated museum specimens, inclusion of this specimen extends our exploration of body size differences in dwarf elephants.

Mammuthus creticus falls below the observed ranges for M. exilis and Wrangel Island M. primigenius M3s, and for M. exilis adult humerus shaft lengths (tables 1 and 3). Only one M. larmarmorai M3 and one adult humerus are available for comparison with M. creticus. Body mass estimates based on humerus length indicate that at 310 kg, M. creticus was less than half the size of the approximately 750 kg M. lamarmorai (table 3). Although this degree of difference is observed in sexual size dimorphism of living elephants [42], elephant teeth are similar in absolute size in both sexes [43]. The M. lamarmorai M3 width is almost twice that of the M. creticus mean M3 value, and this is inconsistent with teeth being drawn from two populations of similar-sized, sexually dimorphic elephants (even allowing that, within an individual, M3s are somewhat wider than M3s). Mammuthus creticus is thus smaller than all other known insular mammoths, based on both dental and post-cranial evidence.

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Table 3.

Dwarf elephant humerus lengths, and body size estimation. In situ Cape Malekas humerus, MAL_11_04, shaft lengths were not significantly different from M. lamarmorai, P. falconeri or P. tiliensis (Tukey–Kramer HSD, p > 0.05; see text for further discussion). Mammuthus exilis humerus data from Roth [39] could not be compared statistically. Body mass estimation from Christiansen [40]: log body mass (kg) = −4.15 + 2.64 × log humerus TL (mm). Shoulder height estimation from Lister & Stuart [41]: shoulder height (mm) = 183.631 + 2.8744 × humerus TL (mm).

Mammuthus creticus molars are wider than, but similar in length and crown height to, those of P. falconeri and P. cypriotes (table 1), resulting in a tooth that is larger overall, though significantly different only from P. falconeri (figure 2a). The M. creticus adult humerus falls within, or just above, the upper range of P. falconeri for TL and DL, respectively, and well below the range of P. tiliensis (the next largest dwarf Palaeoloxodon species after P. falconeri and P. cypriotes [22]) for both DL and TL (table 3). This suggests a body size closer to P. falconeri (shoulder height: approximately 1 m; mass: approximately 240 kg) than P. tiliensis (1.5 m; approximately 810 kg), which is similar in size to M. exilis and M. lamarmorai (table 3). Thus, with an estimated shoulder height of 1.13 m, M. creticus is not only the smallest known mammoth species, but shows a degree of insular dwarfism approaching that of the smallest known elephant, P. falconeri.

Both the smallest (P. falconeri, P. cypriotes, M. creticus) and the largest (Sicilian Palaeoloxodon mnaidriensis, Palaeoloxodon creutzburgi) dwarf elephants occurred on the largest Mediterranan islands, belying a simple link between island area and degree of dwarfism. However, this reflects current, not palaeo-, island area, and while there are significant difficulties in such reconstructions (not least a lack of robust geochronology), palaeogeography is an essential element in determining the environmental drivers of island dwarfism. An early Pleistocene (M. meridionalis) ancestry for M. creticus would imply an island area similar to that of present-day Crete. However, a Late Pliocene origin (from M. rumanus) would suggest that the small-sized M. creticus evolved on a smaller island than previously thought, because the Cretan region is thought to have comprised a series of palaeoislands until 3 Ma [44]. Bonfiglio et al. [45] have similarly suggested that pre-Middle Pleistocene (the estimated age of P. falconeri [46]) Sicily was composed of two smaller palaeoislands within a Calabrian Arc archipelago.

4. Conclusion

This study provides morphological evidence of Mammuthus affinity for M. creticus, independent of the disputed aDNA and geochronological evidence. Early-wear pattern and enamel figure morphology in M. creticus are diagnostic for Mammuthus, while mesial expansion shape, relative crown height and PC suggest taxonomic affinity with either M. rumanus or M. meridionalis. Mammuthus meridionalis was extinct in Europe by 800 ka, or possibly 700 ka [41], placing an upper bound on the arrival of M. creticus’s ancestor on Crete. However, as we cannot rule out M. rumanus as a possible progenitor, the lower bound for isolation on Crete could potentially occur as far back as 3.5 Ma, significantly earlier than previously thought. Mammuthus creticus is similar in size to the smallest dwarf elephant species, P. falconeri, and smaller than all other known mammoth species. Our taxonomic reassessment and morphological comparisons show that extreme insular dwarfism occurred in Mammuthus, not just in Palaeoloxodon, and that M. creticus is the smallest mammoth ever to have evolved.


We thank George Iliopolous (University of Patras, Greece), David Richards (University of Bristol, UK) and Adrian Glover (NHM) for fieldwork assistance and manuscript comments/advice. We thank Larry Agenbroad for provision of his revised M. exilis summary data. Collections access: A. Currant (NHM), C. di Patti (GM), F. Sciuto (UCat), G. Theodorou (UAth), M. Patou-Mathis (IPH), R. Zeigler (SMNS), O. Sandrock (HLD), O. Hampe (HumU) and S. Dominici (MSNF). We also thank the two anonymous reviewers to help us improve this manuscript. This work was supported by NERC standard grant NE/F017839/1 and the Systematics Research Fund.

  • Received March 23, 2012.
  • Accepted April 18, 2012.


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