All hook measurement data were extracted from the Dryad data repository (Wayland et al. 2013a, Wayland et al. 2013b, Wayland et al. 2013c) or the supplementary material of Wayland (2013). Importantly, the same protocol was used to measure hooks in these various studies. In brief, acanthocephalans were prepared for light microscopy by dehydration through an alcohol series followed by clearing in lactophenol. Measurements were made with aid of a digitizing tablet (KS 100, Version 3, Carl Zeiss Vision). Hook morphometric data (blade length and base width) were recorded from one longitudinal row in which all of the hooks were visible in profile using the method described by Huffman and Bullock (1975). Additionally, hook cross-sectional area was measured in samples of E. gadi Zoega in Müller, 1776 spp. Details of taxa sampled and their associated hook measurement data files can be found in Table 1. In the case of E. salmonis Müller, 1784, proboscis orientation was determined, and one dorsal row of hooks, and one ventral row was measured in each specimen.

Nuclear and mitochondrial DNA sequences have elucidated the phylogenetic relationships of six of these taxa: E. bothniensis Zdzitowiecki & Valtonen, 1987, E. 'bothniensis' (an allopatric, sibling species of E. bothniensis), E. brayi Wayland, Sommerville & Gibson, 1999, E. gadi sp. I (one of the sibling species of the E. gadi group identified by Väinölä et al. 1994 using allozymes), E. salmonis and the River Carron population of E. truttae Schrank, 1788 (Wayland et al. 2015). E. gadi sp. A and E. gadi sp. B are sympatric sibling species, discriminated using allozyme electrophoresis (Wayland et al. 2005). Their phylogenetic relationships to the other taxa are unknown, but some morphological evidence suggests that E. gadi sp. A and E. gadi sp. I might be conspecific (Wayland et al. 2005). N.B. in this paper the cryptic species of the E. gadi group are referred to using the notation of Väinölä et al. (1994) and Wayland et al. (2005); E. gadi spp. is used to designate the species group as a whole.

For the original description of the Meristogram algorithm, please refer to Huffman and Bullock 1975. In brief, the Meristogram algorithm comprises the following steps:

The moving average routine results in a non-uniform distribution of data-points along the percent-position axis. In the current implementation of the Meristogram algorithm an optional linear interpolation procedure is introduced between steps 4 and 5. The 'approx' function in R is used to calculate hook metrics (L, B, A & R) at each integer value in the range of percent-position values yielded by the moving average routine. This linear interpolation step often improves the appearance of the Meristogram, but more importantly, by providing common percent-position coordinates it facilitates comparison of Meristograms using multivariate statistics (please see next section).

This new implementation of the Meristogram algorithm also enforces a minimum moving average segment size. It seems reasonable to argue that each proboscis in a collection should be represented in every moving average segment. The minimum moving average interval is thus defined as 100/(x+1), rounded up to the nearest integer, where n is the length of the shortest row of hooks in the collection.

The Meristogram algorithm has been implemented in R (R Core Team 2015) with a graphical user interface developed using the shiny web application framework (Chang et al. 2015). Source code is available under version 3 of the GNU General Public License from the following repository: https://github.com/WaylandM/meristogram. All Meristograms reported in this study were generated using version 1.0 of the software (DOI: 10.5281/zenodo.34267). Experienced users of R can call the functions to generate and display Meristograms from the command line. The graphical user interface (Fig. 1) enables users to interactively control the moving average segment size, toggle linear interpolation on or off and save Meristogram data and plots to file. Full instructions on using the software can be found in the documentation: https://github.com/WaylandM/meristogram/blob/master/README.md. The Meristogram software will run on any platform compatible with R, which includes Windows, Mac OS X and Linux.

All data analyses were performed using the R language and environment (R Core Team 2015) and can be reproduced by running the script data_analysis.R provided as Suppl. material 1. The script is fully annotated and has been made available to enable readers to evaluate the methodology and verify the findings of this study.

Before considering inter-taxon differences in Meristogram, intra-taxon variation related to sex and choice of moving average interval was investigated. For each taxon, a set of Meristograms were plotted for each sex using the following moving average segment sizes: (1) minimum moving average interval (MMAI) for the taxon; (2) 1.5 × MMAI; (3) 2 × MMAI.

To assess inter-taxon variation, hook measurement data for females and males were pooled and a Meristogram was generated for each taxon using a moving average segment of 17% and linear interpolation. For comparative purposes it was important to use the same moving average segment for all Meristograms and 17% was the MMAI which could be applied to all taxa.

In addition to visual inspection of Meristograms, a more objective comparison of Meristograms was achieved with the aid of statistical pattern recognition methods. Meristogram data from all taxa were concatenated into a single matrix, where columns were hook variables at each integer percent-position and rows were taxa. Principal component analysis (PCA) was then used to reduce the number of dimensions in this data-set. Similarity of Meristograms was further assessed by hierarchical clustering of the scores for the first two principal components (accounting for most of the variation in the data-set) using the unweighted pair group method with arithmetic mean (UPGMA) algorithm and four different distance metrics (Euclidean, Manhattan, maximum and Minkowski).

Measurements of hook cross-sectional area, obtained using a digitizing tablet, were available for E. gadi spp. A, B & I. These measurements were strongly correlated with area calculated by the Meristogram (Fig. 2a, b, c). Coefficients of determination (R²) were 0.887, 0.882 and 0.816 for E. gadi spp. A, B & I, respectively. The estimated hook areas were remarkably close to the measured values for all three taxa. Linear regression demonstrated that in E. gadi spp. A & B, the Meristogram tended to slightly over-estimate hook area (Fig. 2a, b). In E. gadi sp. I, the Meristogram over-estimated the area of small hooks and under-estimated the area of large hooks, however the differences were minimal (Fig. 2c).

Strong evidence of sexual dimorphism was not found in the Meristograms for E. salmonis (Suppl. material 28) or E. truttae (Suppl. material 29), and sample size was too small to make a meaningful assessment of this phenomenon in the other taxa (Suppl. materials 22, 23, 24, 25, 26, 27). Thus for inter-taxon comparisons a single Meristogram was created for each taxon by pooling hook data from females and males. Variation in Meristogram pattern related to the size of the moving average segment was subtle (Suppl. materials 22, 23, 24, 25, 26, 27, 28, 29); nevertheless, for comparative purposes a 17% moving average segment (the smallest applicable to all acanthocephalans in the study) was used for all taxa.

The new software implementation of the Meristogram includes an optional linear interpolation step. Fig. 3a is the Meristogram for E. brayi generated using the original algorithm; data-points are not uniformly distributed along the percent-position axis. Fig. 3b is the same Meristogram smoothed using linear interpolation. The linear interpolation step doesn't alter the pattern displayed in the Meristogram, but can make it easier to visualize, especially in the case of acanthocephalans with small numbers of hooks per row, such as E. brayi.

Meristograms for each of the taxa in this study are presented below along with a brief description. For each taxon the meristogram characteristics which differentiate it from the other taxa in the study are identified. These differences have been termed 'Potential diagnostic features', because they have yet to be validated using independent data.

E. brayi

Description

Arched pattern with maximal values for L, B, A and R at positions 55%, 58%, 58% and 59%, respectively (Fig. 3b). Therefore, the largest and most robust hooks are expected to be found just proximal to the middle of a row. Although female and male worms exhibit the same pattern of serial variation in hook morphology (Suppl. material 24), they differ in the raw (pre-standardization) values for the four hook characters. For example, in female worms row maxima for L, B, A and R had the following ranges: 77-90µm, 24-30µm, 954-1,350µm² and 30.2-35.1, respectively. In male worms the largest values of L, B, A and R were: 60-75µm, 19.5-22.5µm, 585-798µm² and 29.8-35.3, respectively.

Potential diagnostic features

The following features of the Meristogram of E. brayi are unique among the taxa in this study:

E. salmonis

Description

Of the taxa in this study, only E. salmonis is known to display radial asymmetry in proboscis armature (Wayland et al. 2004). The Meristograms for dorsal (Fig. 4a) and ventral (Fig. 4b) hook rows are almost identical. Both display several loops, the most prominent being: a large distal loop bordered by L and B above, and R below; a proximal loop bordered above by B, and below by A and L. Maximal values of the four hook variables occurred at similar positions in both Meristograms. Dorsal hooks exhibit peak values of L, B, A and R at positions 26%, 51%, 37% and 59%, respectively; corresponding positions for ventral hooks are 27%, 59%, 37% and 64%, respectively. Therefore one would anticipate to find the longest hooks approximately a quarter of the way along a row from the distal end of the proboscis, the hooks with the greatest cross-sectional area around a third of the way along the row and the stoutest hooks just proximal to the middle of the proboscis.

In female worms the dorsal row maxima for raw L, B, A and R had the following ranges 95.7-126.7µm, 25.5-45.5µm, 1,265-2,494µm² and 29.1-43.8, respectively; corresponding values for ventral rows were 99.9-129.4µm, 25.7-47.2µm, 1,410-2,678µm² and 26.9-41.7, respectively. The hooks of male worms were typically smaller with dorsal row maxima for L, B, A and R of 70.1-91.3µm, 21.7-27.7µm, 720.4-1,095.0µm² and 31.3-39.8, respectively; and ventral row maxima of 76.9-97.5µm, 25.2-27.7µm, 896-1,278µm² and 31.4-35.5, respectively.

There is a region of very small hooks (low values of A and L) on the dorsal surface of the proximal end of the proboscis (positions > 79%), corresponding to a flattening of the tail of the Meristogram. Length and area of the last and smallest hook in dorsal rows of female worms ranged from 34.3-59.2µm and 137-477µm², respectively. In male worms the final hook in a dorsal row had a length of 26.4-42.1µm and an area of 94.8-242.1µm². On the ventral surface, hooks also become much smaller proximally, but not to the extent observed on the dorsal surface. The final hook in ventral rows of female worms measured 42.8-76.8µm in length and had an area of 218-782µm²; the corresponding hook in male worms had a length of 41-62µm and an area of 211-527µm². The smallest hooks are not the weakest; the latter are found at the distal end of the proboscis. In female worms the stoutness ratio of the first hook in a row was 15.5-25.1 on the dorsal surface of the proboscis and 12.7-23.9 on the ventral. The most distal hooks of male worms had stoutness ratios of 18.3-27.8 and 17.6-30.1 for dorsal and ventral rows, respectively.

Huffman and Bullock (1975) and Shostak et al. (1986) plotted Meristograms for E. salmonis, but did not distinguish between dorsal and ventral hook rows; their Meristograms resemble those presented here.

Potential diagnostic features

E. truttae

Description

The Meristograms of E. truttae from Drummore and the River Carron catchment display several loops; three prominent loops are shared by both collections (Fig. 5). In the 20-60% position region are two elongated loops, the upper defined by A and B, the lower by B and R. Between positions 60-80% is a loop bordered above by R and A, and below by L.

The Drummore collection has peak values of L, B, A and R at positions 40%, 72%, 70% and 77%, respectively (Fig. 5a). The longest hooks (71.1-81.4µm in females and 71.0-80.2µm in males) occur just distal to the middle of a row, and the shortest hooks (43.6-65.8µm in females and 47.7-65.3µm in males) at the proximal end of a row. The stoutest hooks (ratio values of 29.0-40.3 in females and 30.0-36.4 in males) are found in the proximal third of the row and the weakest (17.1-31.1 in females and 16.8-30.0 in males) at the distal end of the row. Hooks with maximal values of area (731-1,017µm² in females and 763-988µm² in males) and base (21.3-27.3µm in females and 21.6-26.6µm in males) are located around two-thirds of the way along a row from the distal end of the proboscis.

In the collection from the River Carron catchment maximal values of L, B, A and R are found at positions 33%, 64%, 43% and 75%, respectively (Fig. 5b). The longest hooks (67.6-91.0µm in females and 66.6-84.0µm in males) are found a third of the way along a row from the distal end of the proboscis, and the shortest hooks (42.6-66.2µm in females and 42.9-59.0µm in males) at the proximal end of a row. The most robust hooks (ratio values of 28.2-34.7 in females and 28.9-33.9 in males) are located in the proximal third of the row and weakest (18.0-26.0 in females and 17.1-26.7 in males) at the distal end of the row, mirroring the distribution in the Drummore collection. The hooks with greatest area (674-1,033µm² in females and 626-1,096µm² in males) are usually situated just distal to the middle of the row. The hooks with the broadest base (20.3-24.5µm in females and 19.2-26.1µm in males) are found two-thirds of the way along the row from the distal end of the proboscis.

Potential diagnostic features

E. truttae exhibits the least serial variation in hook size. The shortest hooks are 80% (River Carron catchment) - 82% (Drummore) of the length of the longest hooks in their respective rows. In the other taxa studied the shortest hooks are 42-71% of the length of the longest hooks. Similarly the smallest hooks of E. truttae have an area 62% (Drummore) - 66% (River Carron catchment) that of the largest hooks, whereas in the other taxa this value ranges from 17-51%.

E. bothniensis

Description

The curves for B, A and R follow a similar trajectory in the distal half of the Meristogram, with a particularly strong monotonic relationship between B and A (Fig. 6a). In this region a narrow loop is formed by B and R; a similar loop was observed in both E. salmonis and E. truttae. A smaller loop occurs in the 60-75% position region of the proboscis, bordered above by B and below by A and L; this latter loop is also present in the Meristogram for E. salmonis. Peak values for L, B, A and R are found at positions 34%, 53%, 52% and 61%, respectively. The Meristogram of E. bothniensis resembles the "arched pattern" Meristogram of E. gadi from Pseudopleuronectes americanus and Limanda ferruginea described by Huffman and Bullock (1975).

The longest hooks (57.2-66.0µm in females and 50.0-60.6µm in males) are located around a third of the way along a row from the distal end of the proboscis, and the shortest hooks (30.2-42.4µm in females and 24.7-43.3µm in males) at the proximal end of a row. The stoutest hooks (ratio values of 35.8-39.0 in females and 32.0-35.0 in males) are found just proximal to the middle of the row and the weakest (20.7-24.2 in females and 20.8-28.9 in males) at the distal end of the row. The hooks with the broadest base (18.7-22.5µm in females and 16.1-19.5µm in males) and greatest area (507-676µm² in females and 393-547µm² in males) are located in the middle of the row.

Potential diagnostic features

Apparently unique characteristics for this Meristogram are:

E. 'bothniensis'

Description

The Meristogram of E. 'bothniensis' (Fig. 6b) should be interpreted with particular caution, because it is based on hook data from just two female worms. Inclusion of additional samples would likely smooth the curves of this Meristogram. Maximal values of L, B, A and R occur at positions: 31%, 74%, 33% and 74%. It features four prominent loops, one in the distal half and three in the proximal half. The longest (63.5-67.6µm) and largest (596-747µm²) hooks are situated a third of the way along the row from the distal end of the proboscis, and the shortest (33.0-39.3µm) and smallest (135-187µm²) hooks at the proximal end of the row. The hooks with the broadest base (21.9-22.7µm) are also the stoutest (ratio values of 40.7-40.8), and are located in the proximal third of the row. The weakest hooks (ratio values of 19.0-22.3) are located at the distal end of the row.

Potential diagnostic features

The Meristogram for E. 'bothniensis' was created using data from just two specimens; additional data may well change the appearance of the Meristogram. For this reason diagnostic characters have not been proposed for this taxon.

E. gadi sp. A

Description

Maximal values of L, B, A and R occur at positions: 27%, 67%, 57% and 67% (Fig. 6c). In the region 45-75% position, three prominent loops are fomed by intersection of the four curves: the most distal defined by A, L and B; the middle loop bordered by B, L and R; the most distal loop composed of R, A and L. The longest hooks (66.1-72.6µm in females and 57.4-67.3µm in males) are located a quarter of the way along a row from the distal end of the proboscis, and the shortest hooks (40.9-49.1µm in females and 36.8-44.1µm in males) at the proximal end of the row. The hooks with the broadest base (26.0-32.1µm in females and 23.8-26.0µm in males) are also the stoutest (ratio values of 41.4-50.7 in females and 44.4-46.5 in males), and are situated two thirds of the way along a row from the distal end of the proboscis. The weakest hooks (ratio values of 19.1-29.3 in females and 26.1-27.2 in males) are found at the proximal end of the proboscis. Hooks with the greatest area (747-1,072µm² in females and 628-761µm² in males) are found just proximal to the middle of a row.

Potential diagnostic features

E. gadi sp. A is one of only three taxa in this study with a Meristogram in which none of the curves intersect at the distal end of the proboscis; the others are E. gadi sp. I and E. brayi. Differences in the shape of the curve for A might separate E. gadi sp. A from E. gadi sp. I, however given the small sample sizes for these two collections of worms, this diagnostic may not be robust. Moreover, there is tentative evidence that these two taxa are conspecific (Wayland et al. 2005). Meristogram characteristics distinguising E. brayi from all other taxa in this study are described above.

E. gadi sp. B

Description

The Meristogram of E. gadi sp. B possesses three prominent loops: a distal loop bordered above by B and L, and below by R; a loop mid-way along the proboscis bordered above by B, and below by A and R; a proximal loop bordered above by R and B, and below by A and L (Fig. 6d). Maximal values for L, B, A and R are at positions 25%, 42%, 35% and 74%, respectively. The longest hooks (47.2-56.9µm in females and 45.7-54.0µm in males) are located a quarter of the way along a row from the distal end of the proboscis, and the shortest hooks (31.0-48.8µm in females and 19.9-30.5µm in males) at the proximal end of the row, a similar profile to E. gadi sp. A. The hooks with the broadest base (17.7-20.4µm in females and 17.3-18.6µm in males) are situated just distal to the middle of the row and the largest hooks (421-528µm² in females and 400-502µm² in males) are found a third of the way along the row from the distal end of the proboscis. The stoutest hooks (ratio values of 41.0-52.1 in females and 38.9-43.3 in males) occur in the proximal third of the row.

The Meristograms of all of the E. gadi spp. in this study, broadly display what Huffman and Bullock (1975) describe as a "looped pattern". However, the Meristogram of E. gadi sp. B appears to be closest to the exemplar of the "looped pattern" depicted in Fig. 11 of Huffman and Bullock (1975).

Potential diagnostic features

E. gadi sp. B is the only taxon in this study in which the hook variable B peaks on the distal half of the proboscis.

E. gadi sp. I

Description

In the 45-80% position region of the Meristogram are three obvious loops (Fig. 6e). The loop situated mid-way along the Meristogram, and bordered by B, A and R, is also present in the Meristograms for E. gadi sp. B, E. 'bothniensis' and E. salmonis. Peak values of L, B, A and R occur at positions: 18%, 68%, 24% and 69%. The longest hooks (66.2-74.2µm in females and 61.6µm in the only male specimen) are situated in the distal quarter of a row and the shortest hooks (35.9-51.1µm in females and 43.8µm in the male) at the proximal end of the row. The largest hooks (592-827µm² in females and 545µm² in the male) are situated in the distal third of the row. As in E. 'bothniensis' and E. gadi sp. A, the hooks with the broadest base (20.9-24.2µm in females and 21.9µm in the male) are also the stoutest (ratio values of 36.9-47.3 in females and 45.9 in the male). In E. gadi sp. I, these most robust hooks are located two thirds of the way along a row from the distal end of the proboscis. The weakest hooks (ratio values of 20.5-26.2 in females and 21.8 in the male) are found at the distal end of a row.

Potential diagnostic features

Meristogram characteristics which may differentiate E. gadi sp. I and A from the other taxa in this study have been described in the section on E. gadi sp. A (above).

Visual inspection of Meristograms reveals some similarities and differences between taxa. For a more objective comparison, statistical pattern recognition was used to measure Meristogram divergence between taxa. In this analysis, a single Meristogram was generated for E. salmonis by pooling hook measurement data from dorsal and ventral rows of hooks; the hook measurement data from the other taxa were assumed to comprise a mixture of dorsal and ventral rows of hooks. The two collections of E. truttae were treated as separate entities, because of the divergence observed between their Meristograms (Fig. 5).

Principal component analysis (PCA) revealed the major sources of variation in the Meristograms. Fig. 7a is a scatterplot of the scores for the first two principal components (PCs), which between them account for 83% of the variation in the data. Similar scores for these two PCs, indicate relatively little divergence in hook patterns between E. bothniensis, E. 'bothniensis', and E. gadi spp. A and B. Conversely a large negative score for PC1 demonstrates that E. salmonis has diverged markedly from the other taxa in hook pattern. A more modest positive score for PC1, separates E. truttae from its congeners. The loadings plot for the first two PCs (Fig. 7b) shows that hook area in the 69-85% position region of the proboscis is driving the separation of taxa in PC1; the proximal hooks of E. salmonis being proportionally much smaller than those of the other taxa, whereas those of E. truttae are a little larger. E. brayi shows strong divergence from the other taxa in PC2; E. salmonis and E. gadi sp. I display some separation from their congeners in this axis. Hook area in the 15-32% position region of the proboscis is driving the separation of taxa in PC2.

Hierarchical clustering of the scores for the first two PCs depicts relationships between Meristograms as a dendrogram (Fig. 8). Three distance metrics (Euclidean, Manhattan and Minkowski) yielded identical dendrograms (Fig. 8a, b, d). The dendrogram created using the maximum distance metric was almost identical to the other three dendrograms, differing only in the depiction of the relationship between E. salmonis and E. brayi. Concordance between dendrograms created using different distance metrics suggests that the clusters found are robust.

The differences in Meristogram between the central and southwest Scotland collections of E. truttae suggest intraspecific, geographical variation in hook patterns. However, given the existence of cryptic species in Echinorhynchus (Väinölä et al. 1994), the alternative explanation of interspecific variation should also be considered. Despite this subtle difference in Meristogram, the two populations of E. truttae displayed a much stronger affinity to each other, than to any of the other taxa in all cluster analyses (Fig. 8). Interestingly, Proboscis Profiler, a tool inspired by the Meristogram and designed to detect heterogeneity in collections of acanthocephalans, did not classify these two collections of E. truttae as distinct morphotypes (Wayland 2010).

None of the eight Echinorhynchus taxa in this study appear to share identical Meristograms, based on the available hook measurement data. However, sample sizes were small (six or fewer specimens for E. 'bothniensis' and E. gadi spp. A and I) and so very unlikely to encompass the range of morphological variation potentially displayed by these taxa. Such variation might render some of the proposed diagnostics ineffectual, particularly for the discrimination of the closely related E. truttae, E. gadi spp, E. bothniensis and E. 'bothniensis'.

Not surprisingly, Meristogram analysis appeared to be most effective at discriminating taxa for which conventional characters are diagnostic, such as E. brayi, E. salmonis and E. truttae; these are also the taxa showing the greatest genetic divergence (Wayland et al. 2015). Differentiation of the cryptic sibling species was more of a challenge, in part because of the small sample sizes. Nevertheless, some observations suggest diagnostic characters which could be evaluated with additional data. For example, the Meristogram of E. bothniensis was arched, whereas that of E. 'bothniensis', was looped. If this difference is real and not an artifact of small sample size (n=10 and n=2, respectively), then this represents the first morphological character to separate these allopatric sibling species. A previous attempt to discriminate these taxa using conventional morphometrics or the Proboscis Profiler tool was unsuccessful (Wayland 2013). E. gadi spp. A and B have been discriminated morphologically on the basis of absolute differences in hook size in the 10-20% position region of the proboscis (Wayland et al. 2005). Meristogram analysis suggests that an additional diagnostic character could be the location of the hooks with the broadest base, which is proximal in E. gadi sp. A and distal in E. gadi sp. B.

Morphology and ecology suggest that the NE Atlantic E. brayi is closely related to E. canyonensis from the Monterey Submarine Canyon in the Pacific (Wayland et al. 1999). The two species have similar hook formulae and are anatomically almost identical, differing in only two conventional characters: the length of the lemnisci relative to the proboscis receptacle and shelled acanthor length. Both species are parasites of deep-sea zoarcid fishes. When Huffman and Kliever (1977) described E. canyonensis, they were aware that “many helminth populations cannot be adequately characterized with line drawings and a list of morphometrics, especially in this genus [Echinorhynchus]” and so included a Meristogram as an additional diagnostic character in the hope that it would “be useful in the future”. The Meristograms of E. brayi and E. canyonensis are similar in that they both show an arched pattern and the four curves intersect at around the 60% position (compare Fig. 3 with Fig. 5 of Huffman and Kliever 1977). However, there are key differences in the order of the four curves. Distally the order of the curves from top to bottom is L, A, B, R in E. canyonensis, whereas in E. brayi it is L, R, B, A. Diagnostic differences are also apparent in the proximal region, for example at the 80% position the order of the curves from top to bottom is L, R, B, A in E. canyonensis and R, L, B, A in E. brayi. It is important to note that the published Meristogram for E. canyonensis was created with a moving average interval of 19%; the diagnostic differences can be observed in E. brayi Meristograms generated using moving average intervals in the range 17-26% (Fig. 3, Suppl. material 24).

Hierarchical clustering shows relationships between taxa based on overall similarity (Fig. 8). This phenetic method makes no distinction between plesiomorphies and apomorphies, and therefore a dendrogram it produces may have a different topology to the actual phylogenetic tree. Fig. 9 shows the phylogenetic relationships of six of the taxa in this study, as inferred from nuclear and mitochondrial DNA sequences (Wayland et al. 2015). Sequence data are not available for E. gadi spp. A and B. Remarkably, hierarchical clustering of Meristogram data using the maximum distance metric (Fig. 8c) yielded a dendrogram depicting relationships between the taxa which are in perfect agreement with the molecular phylogeny. Dendrograms created using three other distance metrics (Fig. 8a, b, d) clustered E. brayi and E. salmonis together, but were otherwise congruent with the molecular phylogeny.

Concordance between the dendrograms and the molecular phylogeny is evidence of a strong phylogenetic signal in the Meristogram. This raises the prospect of using Meristogram characteristics to define monophyletic groups within Echinorhynchus and thus facilitate a revision of this large and expanding genus. However, distillation of discrete character states suitable for taxonomy, from the continuous variables that comprise the Meristogram, is likely to be a significant challenge.

The formula used by the Meristogram for estimating hook cross-sectional area has been shown to be accurate. However, since hook metrics are standardized, estimates of hook area are only required to be proportional to the actual area. Although no evidence of sexual dimorphism was found in this study, users of the Meristogram should be alert to this possible source of intra-specific variation. In E. truttae females tend to have slightly larger hooks than males (Wayland 2013), but this difference is eliminated by the standardization procedures in the Meristogram algorithm. The size of conventional taxonomic characters in the Acanthocephala has been shown to vary with age, sex, species of definitive host and geography (Amin and Redlin 1980, Shostak et al. 1986). Further work is required to determine if these factors influence the appearance of the Meristogram.

Meristograms have been shown to be sensitive to the choice of moving average interval and so in comparative studies it is important to use the same value of this parameter for all hook collections. The systematic homogeneity of a sample of acanthocephalans should be assessed before applying the Meristogram. Molecular markers are the first choice of tool for detecting cryptic species, but when they cannot be applied, the Proboscis Profiler (Wayland 2010) may detect distinct morphotypes in the sample, using the same hook data collected for the Meristogram. Proboscis Profiler was inspired by the Meristogram algorithm and complements it by providing statistical pattern recognition techniques to detect morphological heterogeneity in collections of acanthocephalans.

Users of the Meristogram are encouraged to share their hook measurement data, either by including them as supplementary files to publications or submitting them to public repositories (e.g. Dryad, Zenodo, etc.). In addition to facilitating further comparative analyses, these datasets are potentially useful in the testing and refinement of the Meristogram algorithm.

Having demonstrated the utility of the Meristogram in acanthocephalan systematics, the author is keen to facilitate its use. Free software is provided for systematists who would like to apply the technique themselves. Additionally, the author would welcome the opportunity to analyse hook morphometric data for other acanthocephalan workers as part of a collaborative project.

The Meristogram is not limited to the analysis of the hooks of the acanthocephalan proboscis. It can potentially be applied to any organism in which there are patterns in the longitudinal variation of serially homologous structures, e.g. "the taxonomic diagnosis of the vegetative characters of plants when fruiting structures are not available; species-level diagnosis of feather structures in fragments encountered in gut contents (or poacher's clothing), etc." (Professor David Huffman, personal communication, July 7, 2010). The freely available source code for the current implementation of the Meristogram should provide a helpful starting point for anyone who would like to adapt the method for novel applications.