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A new species and new synonym in Heptagenia Walsh (Ephemeroptera: Heptageniidae: Heptageniinae) based on molecular and morphological evidence.

J. M. Webb , L. Sun , W. P. McCafferty , V. R. Ferris
DOI: http://dx.doi.org/10.1673/031.007.6301 First published online: 21 December 2007


A new mayfly species, Heptagenia whitingi Webb & McCafferty n.sp. is described from larvae, a male subimago, a female adult, and eggs collected from large rivers in the west-central portion of North America. Larvae are differentiated from other North American Heptagenia Walsh by a pair of large, rectangular pale markings on abdominal tergum 4, and the combination of having the posterior margin of the abdominal terga with bluntly pointed spines less than half the length of the fine setae, small blunt spines on the posterior margin of the caudal filaments, and numerous rows of setae laterally on the ventral surface of the labrum. A 630 bp partial sequence of the mitochondrial gene cytochrome oxidase 1 (COI) from three specimens of H. whitingi n.sp. was compared with those of 12 specimens representing eight other North American species of Heptagenia. Intraspecific sequence divergences based on Kimura-2-parameter (K2P) distance ranged from 0–1.1%. Interspecific sequence divergence based on K2P distance ranged from 8.9–20.0%. Heptagenia whitingi n.sp. differed from its sister taxon H. flavescens (Walsh) by 11.7%. Heptagenia diabasia Burks and H. elegantula (Eaton) differed from each other by only 1.1%; these two alleged species show a clinal pattern in larval abdominal coloration and there are no structural differences between the semaphorants. On this basis, H. diabasia is placed as a junior subjective synonym of H. elegantula, n.syn.

  • DNA barcode
  • Heptagenia whitingi
  • new species
  • new synonym
  • mayfly
  • COI


Mayflies of the genus Heptagenia Walsh (Heptageniidae: Heptageniinae) are distributed throughout the Holarctic biogeographic realm. Species reported as Heptagenia from Southeast Asia are actually members of other genera (Wang and McCafferty 2004, Webb et al. 2006). In North America, 12 species have been recently recognized, although some of these may prove to be synonymous. No analytical hypothesis of the relationships among the North American species of Heptagenia has been proposed. Nonetheless, based on characters of the genitalia the species have been divided into a flavescens group that includes H. flavescens (Walsh), H. townesi Traver, H. marginalis Banks, H. culacantha Evans, Botts & Flowers, H. dolosa Traver, and H. patoka Burks; an elegantula group that includes H. elegantula (Eaton), H. adaequata McDunnough, and H. diabasia Burks; and a pulla group that includes H. pulla (Clemens), H. julia Traver, and H. solitaria (McDunnough) (e.g., Traver 1935). Similar species groups have been proposed for the Palearctic species (Kluge 1987).

Male adults of the North American species can generally be identified using keys provided by Traver (1935) and Burks (1953), using a combination of color patterns and genitalic morphology. Females, however, cannot currently be identified to species with any reliability. Keys available for identifying larvae (e.g., Traver 1935; Burks 1953; Bednarik and Edmunds 1980; Webb et al. 2002) are inadequate as they rely almost entirely on color patterns and are mostly regional in scope. Complicating diagnostic issues are data that show that different environmental conditions cause variations in color patterns in heptageniid mayflies (i.e. McCafferty and Pereira 1984) and the fact that color patterns often are not apparent in preserved material. Moreover, the larvae of several species remain unknown.

We have examined specimens of a new species of Heptagenia from large rivers in the grasslands and parklands of north-central North America. Specimens of this species had previously been identified as H. flavescens (Lehmkuhl 1976; Whiting 1985; Whiting and Sheard 1990; Webb 2002; Webb et al. 2002; Ball et al. 2005). The new species differs from H. flavescens in abdominal color pattern and slight morphological differences in the relative size of abdominal spines and setation.

Because the morphological characterization of the new species may appear minimal, we sought to confirm its distinctiveness from other species by employing DNA barcoding. Barcoding has recently been proposed as a possible solution to some of the problems of traditional species identification (Hebert et al. 2003a). A short section, approximately 650 base pairs (bp), of the mitochondrial gene cytochrome oxidase I (COI) is used as a marker for species identification and/or discrimination in barcoding. Species identifications are obtained by comparing unknown sequences with those contained in a reference library of sequences obtained from identified specimens. The ability to successfully identify or discriminate species depends on the presence of a barcoding gap, a distinct difference between intra- and interspecific sequence divergences; in most taxa there is an order of magnitude difference between the two (Hebert et al. 2004; Ball et al. 2005). This method has been applied successfully in many invertebrate taxa, including mayflies (Hebert et al. 2003a, b; Hogg and Hebert 2004; Ball et al. 2005; Monaghan et al. 2005; Hajibabaei et al. 2006).

This study had three objectives: (1) describe a new species of Heptagenia; (2) provide barcode data for the new species using a partial sequence of COI; (3) provide preliminary data on the relationships of North American Heptagenia species based on COI.


Heptagenia whitingi Webb & McCafferty, new species

Mature larva (in alcohol)

Body length: 9.5–11 mm.


Brown with pale markings. Median pale spot near anterior margin usually quadrate in shape, sometimes connected by pale line to pale spot anterior to median ocellus. Lateral pale streaks wide at lateral margin, usually 0.25–0.5 X length of head capsule. Labrum 4X wider than long; ventral surface with single row of robust setae medially and many fine setae laterally (Figure 3). Maxilla with 7–8 comb setae on apical margin; galealacinia ventrally with row of fimbriate setae, dorsolaterally with dense row of fine setae; maxillary palp with many long setae on first segment and with row of setae on second and third segments.


Notum brown with pale markings. Fore femur pale with two brown transverse markings on anterior surface; hind margin with row of long fine setae and long robust setae; anterior surface with paddle shaped setae and fine setae. Fore tibia pale with median brown stripe, surface with scattered short fine setae, row of long fine setae near lateral ridge; lateral ridge with short paddle shaped setae; posterior ridge without row of long fine setae. Fore tarsus pale with brown stripe basally, with numerous scattered fine and paddle shaped setae. Middle and hind legs similar to fore leg except with more numerous setae and tibiae with row of long fine setae on posterior ridge. Claws without denticles.


Terga brown with distinct pale markings (Figure 1) and with numerous fine setae; terga 3–7 with paired pale markings medially, those on tergum 4 large and rectangular in shape; posterior margins with bluntly pointed spines and fine setae, spines less than 1/2 length of fine setae (Figure 4). Sterna mostly pale, sternum 9 brown laterally (Figure 2). Caudal filaments with fine setae; posterior margin of each segment with spines approximately 1/6 length of segment (Figure 5) and sparse robust setae.

Figure 1

Heptagenia whitingi Webb & McCafferty n.sp., dorsal habitus of holotype larva.

Figure 2

Heptagenia whitingi Webb & McCafferty n.sp., ventral habitus of holotype larva.

Figure 4

Heptagenia whitingi Webb & McCafferty n.sp., posteromedian margin of abdominal tergum 6, showing relative sizes of spines and fine setae.

Figure 5

Heptagenia whitingi Webb & McCafferty n.sp., spines on poster margin of one segment of the median caudal filament.

Male subimago (in alcohol, faded and damaged)

Wing length: 11 mm.

Body generally yellowish. Wings hyaline with veins yellowish-brown; interspace of C and Sc of fore wing basally with few, poorly developed cross veins. Legs yellowish. Abdomen brownish dorsally, with pair of pale median marks. Penes with well-developed dorsolateral projections, dorsal protrusion present on each side of midline and with sharp spine; titillators robust. Caudal filaments yellowish.

Figure 3

Heptagenia whitingi Webb & McCafferty n.sp., ventral surface of labrum showing single median row of robust setae and numerous rows of fine setae laterally.

Female adult (in alcohol)

Body length 8.5 mm.

Wing length: 10.3 mm.

Body yellowish, slightly darker dorsally. Wings hyaline with longitudinal and cross veins yellowish-brown; interspace of C and Sc of fore wing basally with few, poorly developed cross veins (Figure 6). Legs yellowish. Abdomen pale yellowish, terga 2–7 brown posteromedially. Subgenital plate truncate, posterior margin brown (Figure 7). Caudal filaments pale, slightly darker basally.

Figure 6

Heptagenia whitingi Webb & McCafferty n.sp., female adult, base of fore wing, showing poorly developed cross veins between C and Sc.

Figure 7

Heptagenia whitingi Webb & McCafferty n.sp., female adult, subgenital plate.


Length: 159 μm

Width: 98 μm

Chorion covered with numerous knob-terminated coiled threads (KCTs), those at one pole larger and more numerous (Figure 8).

Figure 8

Heptagenia whitingi Webb & McCafferty n.sp., egg.

Material examined

Holotype (in alcohol): Late instar larva, USA, Montana, Blaine Co.: Milk River, 16 miles west of Havre, at U.S. Hwy 2. 48.5958°–109.3633°, 14-VI-2000, W.P. McCafferty et al., deposited in the Purdue Entomological Research Collection, West Lafayette, IN (PERC). Paratypes: 1 larva, same data and deposition as holotype; Canada, Saskatchewan, North Saskatchewan River at Cecil Ferry, 53.2290°–105.5114°: 2 larvae (parts of one slide mounted in Canada Balsam), 15-VI-1986 E.R. Whiting, #JMW713 (PERC); 1 male subimago with associated exuviae, 15-VI-1986 E.R. Whiting, #JMW1914 (PERC); 8 larvae (parts of 1 slide mounted in Euparal), 6-VI-2000, J.M. Webb, #JMW1004 (PERC); 1 female adult with associated exuviae, 28-VIII-2000, J.M. Webb; 3 larvae, 28-VIII-2000, J.M. Webb (PERC); North Saskatchewan River at Borden Bridge, 52.3714°–107.1453°, 2 larvae, 3-V-2000, J.M. Webb, #JMW736 (PERC); South Saskatchewan River at Lemsford Ferry, 51.0300°–109.1200°: 3 young larvae, 23-V-1998, J.M. Webb (PERC); 6 young larvae, 30-VII-2000, J.M. Webb, #JMW1090 (PERC); 8 larvae, 16-IX-2000, J.M. Webb, #JMW1233 (PERC); 7 larvae, 3-VII-2001 J.M. Webb (PERC); 2 larvae, 17-V-2000 J.M. Webb, #JMW1190 (PERC); 7 larvae, 16-X-1999, J.M. Webb (PERC); 13 larvae, 30-IV-1998, J.M. Webb, #JMW1493 (PERC); 1 larva, 3-VII-2001, J.M. Webb, #JMW1616 (PERC). USA: Kansas, Wyandotte Co.: Kansas City, Missouri River at 7th St. Bridge, 39.1562 °–94.6232°, 5 larvae (parts of one on slide), 9-X-1979, KDHE and J. Fry (Snow Entomological Collection, Lawrence, KS); Missouri, Platte Co.: Kansas City, Missouri River at 7th St. Bridge, 39.1562 °–94.6232°,1 larva, 9-X-1979, KDHE and J. Fry (Snow Entomological Collection, Lawrence, KS); Montana, Dawson Co.: Yellowstone River at Intake, 47.2801°–104.5298°, 2 larvae, 17-XII-1974, R.L. Newell (PERC).


The specific epithet is in honor of the late Eric Whiting who collected and studied the Heptageniidae of central Canada.



Heptagenia whitingi is differentiated from all other North American congeners by the pair of large, rectangular pale marks on abdominal tergum 4 (Figure 1). Larvae of the new species are structurally most similar to those of H. flavescens, but in H. flavescens, the spines on the posterior margin of the abdominal terga are sharply pointed and greater than 1/2 the length of the fine setae (Figure 9). The color pattern of some individuals of H. whiting and H. adaequata can be similar, but the rounded pale median spot on the head capsule of H. adaequata should differentiate the two; additionally, the whorl of spines on the caudal filaments of H. whitingi are much shorter than those of H. adaequata and the tibiae of H. adaequata lack a median brown band.

Figure 9

Heptagenia flavescens, posterior margin of tergum 6.


It is not generally possible at this time to identify species of Heptagenia based on subimagos or females and as such diagnostic characters for the adult stages of H. whitingi cannot be provided. The posterior margin of the subgenital plate of female H. flavescens, however, is usually either pale or slightly shaded with brown along its entire length, whereas in the female of H. whitingi, the posterior margin has a distinct brown marking located medially (Figure 7). The lack of dark longitudinal marks on the abdominal terga of the adults distinguishes adults of H. whitingi from those of all other North American Heptagenia of the flavescens group except H. flavescens and H. patoka.


The eggs H. whitingi do not appear to differ significantly from North American congeners. Several species of North American Heptagenia have been previously described (Smith 1935; Koss 1968) but the described interspecific differences were minute and based on the size and distribution of KCTs. We examined eggs of several species using the light microscope and found that eggs from a single female can vary, particularly in the distribution of the KCTs. In order to determine if there are consistent interspecific differences in egg structure, further studies utilizing scanning electron microscopy must be performed.


Heptagenia dolosa, H. townesi, and H. patoka are not known in the larval stage. Based on the female adult and the male subimago, however, H. whitingi is easily differentiated from H. townesi and H. dolosa by the lack of distinct longitudinal dark markings on the abdominal terga. Heptagenia patoka is only definitively known from the holotype male imago. We examined the holotype (Illinois Natural History Museum, specimen #16200) and the abdominal coloration is similar to that of H. whitingi, but the slide upon which the penes are mounted is missing. Based on the descriptions and figures presented by Burks (1946, 1953), however, there do not appear to be any dorsolateral spines or medial protrusions; both are present on the penes of the subimago male of H. whitingi. It is possible that H. patoka is actually equivalent to Raptoheptagenia cruentata (Walsh) but this cannot be determined until the penes of the holotype are found. Specimens of H. patoka have also been reported from Indiana (Randolph and McCafferty 1998) but they were collected from locations where R. cruentata has also been collected and thus their identity is uncertain.

Heptagenia whitingi appears to be restricted to large, warm, turbid rivers. In the North and South Saskatchewan Rivers, the new species was only collected over a gravel substrate in fast water. This type of river supports a large number of specialized and rarely collected species such as Analetris eximia Edmunds, Anepeorus rusticus McDunnough, Macdunnoa nipawinia Lehmkuhl, Lachlania saskatchewanensis Ide, and Choroterpes albiannulata McDunnough.

View this table:
Table 2

Mean values and ranges of intraspecific sequence divergences (% difference, K2P distance) of COI MtDNA partial sequences of three North American species of Heptagenia for which more than one sequence was obtained.

View this table:
Table 3

Interspecific divergences (% difference, K2P distance) among COI MtDNA partial sequences of nine species of North American Heptagenia. If a comparative pair included at least one species for which multiple sequences were obtained, the mean value of distances between two sequences from the two species in a combination was used.

Barcode Analysis

Materials and Methods

DNA extraction, amplification and sequencing

13 specimens were sampled representing 8 of the 12 previously named North American species of Heptagenia, plus 3 specimens of H. whitingi (Table 4). The specimens had been stored in ethanol for periods ranging from less than one year to nine years. A piece of thoracic muscle or a leg from each individual specimen was dissected and rinsed in TE (pH 7.5). A Kontes Grinder was used to grind the tissue in 25 μl of Molecular Grinding Resin (Genotech, www.gbiosciences.com) in a 1.5 ml microfuge tube. The total genomic DNA was extracted using InstaGene Matrix (Bio-Rad, www.bio-rad.com) according to manufacturer’s recommendations. The mixture was incubated overnight at 56 °C, and then boiled and centrifuged as directed by the manufacturer. The supernatant was used as templates for PCR (polymerase chain reaction). The primer pair LC01490 (5′GGTCAACAAATCATAAAGATATTGG 3′ forward) and HC02198 (5′TAAACTTCAGGGTGACCAAAAAATCA 3′ reverse) (Folmer et al. 1994) was employed for the amplification of a 658bp fragment of COI. The temperature and time profile included an initial step of denaturing at 94°C for 1 min, 30 cycles of amplification with denaturation at 94°C for 30 sec, annealing at 43°C for 30 sec, and extension at 72°C for 1 min 30 sec, and a final single extension step, which was carried out at 72°C for 10 min. After being purified, some of the amplified DNA fragments were sequenced by automatic sequencing at the Purdue Genomics Facility, whereas others were cloned into the pGEM-T vector (Promega, www.promega.com) and transformed into Escherichia coli strain JM109 (Promega). Plasmid DNA was then extracted using the Qiaprep Spin Miniprep Kit (Qiagen, www.qiagen.com) from bacterial cultures containing inserts of the expected size as determined by PCR. Cycle sequencing of plasmid preparations was carried out using the Big-Dye Terminator v3.1 Cycle Sequencing Kit (PE Applied Biosystems www.appliedbiosystems.com) followed by automatic sequencing at the Purdue Genomics Facility. Both strands of DNA from several clones were sequenced. Sequences for H. adaequata and one specimen of H. whitingi (reported as H. flavescens) were obtained from GenBank (accessions AY3267816 and AY3267915, respectively).

Sequences were aligned using ClustalW in MEGA3 (available from www.megasoftware.net) and pruned to 630bp to remove ambiguous base calls. Table 4 shows collection locations and GenBank accession numbers for each specimen.

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Table 4

Species identifications, collection locations, GenBank accession numbers, and deposition of specimens analyzed. Sequences obtained from GenBank are indicated with (GB).

Data analysis

A matrix of Kimura-2-parameter (K2P) distances was calculated in MEGA3 (Table 1) and used to construct a neighbor-joining tree. Bootstrap analysis with 1000 replicates was performed on the neighbor-joining tree using MEGA3. The K2P model is appropriate when genetic distances are low (Nei and Kumar 2000) and has previously been used in studies of mtDNA barcoding (e.g., Hebert et al. 2003a, b, Ball et al. 2005, Hajibabaei et al. 2006).

View this table:
Table 1

K2P distance values among COI MtDNA partial sequences of 15 North American Heptagenia samples. Numbers with shaded background represent intraspecific divergence; others represent interspecific divergence.

Intraspecific sequence divergences based on K2P distance were calculated as the mean of all intraspecific pairwise divergences for a given taxon. Interspecific sequence divergence based on K2P distance was calculated as the mean of all pairwise divergences between two taxa.

To infer species relationships, a maximum parsimony analysis was conducted in PAUP* (v4.0b10, Sinauer Associates, Sunderland, MA). Sequences of two other Heptageniidae, obtained from GenBank were used as outgroups: Epeorus fragilis (Morgan) (GenBank accession AY326821), a member of the Rhithrogeninae, and Stenacron interpunctatum (Say) (GenBank accession AY326942), a member of the Heptageniinae. Bootstrap values were calculated with 1000 replicates.


Intraspecific sequence divergence

Sequences were obtained from more than one specimen for three of the nine species sampled. Intraspecific sequence divergence ranged from 0.0–1.1% (Tables 1, 2, Figure 10). Mean intraspecific sequence divergence was 0.68%. Intraspecific divergence was •1.1% for both H. whitingi and H. flavescens. All of the specimens of H. whitingi were from the same locale, whereas each of the H. flavescens specimens was from a different location, indicating that sequence divergence was approximately equal within and among populations. Geographic distance was not reflected by the distance data, i.e., H. flavescens (3) from South Dakota was more similar to H. flavescens (4) from Indiana than it was to either H. flavescens (1) or H. flavescens (2) from South Dakota and Nebraska, respectively. In every species for which more than one individual was available, the species was monophyletic in every tree.

Figure 10

Histogram showing the number of intra- and interspecific pairwise comparisons as a function of K2P distance.

Interspecific sequence divergence

Interspecific sequence divergence based on K2P distance ranged from 1.1–20.0% (mean 15.58%) (Tables 1, 3, Figure 10). With the exception of the H. elegantulaH. diabasia comparison (divergence = 1.1%), all species-pairs diverged by >8.9% and there was no overlap with intraspecific sequence divergences. The low divergence between H. elegantula and H. diabasia reflects their dubious specific status (see Discussion). When the H. elegantulaH. diabasia pair is excluded from the analysis, mean interspecific sequence divergences ranged from 9.0–19.4% (mean divergence = 15.99%).

Species relationships

The maximum parsimony analysis returned six most parsimonious trees. The topology of the strict consensus tree of the maximum parsimony results (Figure 12) was largely similar to that of the neighbor-joining tree (Figure 11), the only difference being the uncertain placement of H. culacantha in the maximum parsimony analysis. A maximum-likelihood analysis (not shown) was also similar to the neighbor-joining and maximum parsimony results.

Figure 11

Neighbor Joining tree based on Kimura-2-parameter distances of partial COI mtDNA sequences in MEGA3 for 15 specimens of North American Heptagenia. Bootstrap values greater than 50% are shown for respective branches. Species group membership is indicated by symbols located to the left of each specimen.

Figure 12

Strict consensus of six Maximum Parsimony trees inferred from partial COI mtDNA sequences in PAUP* for 15 North American Heptagenia samples and outgroup specimens of Epeorus and Stenacron. Bootstrap values greater than 50% are shown for respective branches. Species group membership is indicated by symbols located to the left of each specimen.

The elegantula group was found to be monophyletic in both the neighbor-joining and maximum parsimony analyses (Figures 11, 12). The maximum-likelihood results differed in that H. solitaria was the sister group of the H. elgantula + H. diabasia clade, resulting in a paraphyletic elegantula group (not shown). The flavescens group was paraphyletic in all analyses. Heptagenia flavescens and H. whitingi were found to be sister taxa in all analyses, as were H. marginalis and H. nr townesi.


As was suggested for mayflies in general (Ball et al. 2005), we found that sequences of COI successfully distinguished between species of Heptagenia because intra- and interspecific sequences differed by at least an order of magnitude in nearly every species comparison. Additionally, every species for which we had more than one specimen was strongly supported as monophyletic. The only species pair that showed lower than expected divergence was H. elegantula vs. H. diabasia. Morphologically, these species are almost identical with adults differing only by the shape of a marking on the frons, and larvae differing only in the extent of pale spotting. We have found no structural differences in any of the life stages. Differences in genitalia indicated by Burks (1946, 1953) are non-existent. Heptagenia elegantula is known as a western species, while H. diabasia is known as an eastern species. Their ranges, however, overlap considerably throughout central North America (e.g. McCafferty et al. 2001). Whiting (1985) and Webb (2002) suggested that these two species hybridize in Saskatchewan because larvae and adults with color patterns intermediate between the typical forms for each species were commonly encountered. We have observed similar intermediate forms co-occurring with typical forms of each species in North Dakota, South Dakota and Nebraska. Based on the clinal and inconsistent coloration differences and an absence of morphological differences among populations assigned to these species, together with COI divergence consistent with intraspecific variability, we place H. diabasia as a junior subjective synonym of H. elegantula, n.syn.

The large gap (more than an order of magnitude) between the intraspecific and interspecific barcode divergence is validation that H. whitingi is distinct from H. flavescens, with which it has been included in the past (i.e. Lehmkuhl 1976, Whiting and Sheard 1990, Webb 2002, Ball et al. 2005). Heptagenia flavescens and H. whitingi have slightly overlapping ranges in central North America, but we have not observed any specimens with a color pattern intermediate between the two species, and the difference in the relative size of the spines and setae on the posterior margin of the abdominal terga seems to be consistent as well.

This study provides a preliminary analysis of the relationships among species of North American Heptagenia. Although we were unable to obtain usable DNA from H. julia, H. patoka, H dolosa, H. pulla or any positively identified specimen of H. townesi, barcode data for at least one species of each species group was analyzed. Heptagenia julia and H. dolosa are doubtfully good species, however, so their absence would have had a minimal effect on the analysis. The monophyly of the elegantula group was supported. Larvae of H. solitaria are morphologically more similar to those of the elegantula group than they are to those of the pulla-group (unpublished), with which they have traditionally been included. Because we were not able to obtain sequences from either H. pulla or H. julia, we are unable to determine their relationship to H. solitaria. It is not surprising that the flavescens group was found to be paraphyletic in all analyses. The character defining the group, the widely divergent penis lobes, is likely plesiomorphic as this form is also found in the closely related genus Raptoheptagenia Whiting & Lehmkuhl (Wang and McCafferty 2004).

While a test of barcoding was not an objective of this study, the results conform to the generally observed gap between inter and intraspecific sequence divergence. Using barcodes, it should now be possible to identify previously unidentifiable lifestages of Heptagenia, such as subimagos and females. Furthermore, barcodes can be used for the association of larval and adult stages of a species without having to rear specimens.


We thank Shujuan Li (West Lafayette, IN) and Qi Zhang (West Lafayette, IN) for their assistance. Ed Dewalt (Champaign, IL), Colin Favret (Champaign, IL), David Funk (Avondale, PA), Luke Jacobus (West Lafayette, IN), Dennis Lehmkuhl (Saskatoon, SK, Canada), and John Morse (Clemson, SC) graciously provided specimens. Shelley Ball (Lincoln, New Zealand) provided technical advice and encouragement. This research was supported in part by a Purdue University Summer Research Grant to JMW.

  • Received January 22, 2007.
  • Accepted April 18, 2007.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, providedthe original work is properly cited.


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