Subsampling can be conducted in one of two ways. Subsampling can occur after data collection with the aim of standardizing sampling procedures or can occur before data collection, with the aims of standardizing sampling procedures and reducing collection effort . Subsampling is standard practice among neontologists; for example, transects and quadrats are very commonly used to subsample extant populations and communities .

When fossil floras are studied for insect herbivory, they are typically examined exhaustively: all leaves above a certain size threshold, or all leaves that are at least 50 % complete, are sampled. Subsampling strategies, analogous to the transects and quadrats used by neontologists, could be applied to insect herbivory in the fossil record. Such an approach would result in a reduction in the effort required to examine a single flora and would increase the rate at which such floras could be studied. However, at present, no guidelines are available to ensure consistent subsampling of fossil leaves or to ensure that subsampling routines adequately capture the trends that emerge from complete datasets. The aims of the present contribution are to test the effects of various subsampling routines on herbivorized fossil leaves and to establish guidelines for subsampling in future studies.

In previous contributions, four metrics have typically been used to compare insect herbivory across fossil host plants and assemblages. These metrics address three aspects of plant–insect interactions.

Damage type diversity (DT diversity) addresses the diversity of damage types for an individual plant host or assemblage. DT diversity is typically reported either unstandardized or standardized with sample-based rarefaction in which each plant specimen is treated as a sample . We recommend standardization with rarefaction curves that are scaled by the amount of leaf surface area examined .

Nonmetric multidimensional scaling (NMDS) is an unconstrained ordination method applied to address differences in herbivory across different plant hosts and assemblages. Plant hosts with identical levels of DT diversity (e.g., 5 DTs each) could have an identical suite of DTs (e.g., DTs 1, 2, 3, 4, and 5) or completely different suites of DTs (e.g., DTs 1, 2, 3, 4, and 5 at one site and DTs 6, 7, 8, 9, and 10 at the other site). NMDS addresses these potential differences in DT community composition. NMDS is typically performed with data at the level of functional feeding group rather than at the DT level ; functional feeding groups are the broad categories, such as galling and leaf mining, to which each DT is assigned. The use of coarser functional-feeding-group data is often intended to increase the signal-to-noise ratio .

The herbivory index (HI) is the percentage of leaf surface area removed by herbivores. The HI measures the intensity of insect herbivory, unlike DT diversity and NMDS, which reflect different aspects of the diversity of herbivory. Plant hosts with the same suite of DTs will be indistinguishable in terms of DT diversity and NMDS but will yield different herbivory indices if they vary in the amount of surface area removed by herbivores.

The last metric is the proportion of plant specimens showing evidence of insect damage. We consider use of this metric to be inadvisable for the following reasons. First, if all specimens are examined regardless of whether they are at least 50 % complete – a necessary approach for certain plant hosts such as Taeniopteris Brongniart from the early Permian of Texas – this metric may be biased if the degree of fragmentation varies by plant host or assemblage. Second, this metric may be biased if average leaf size varies by plant host or assemblage. Third, this metric and the HI are both intended to measure the same thing – the intensity of insect herbivory – and the HI is not biased by fragmentation or leaf size. Consequently, this renders moot the use of the proportion of plant specimens exhibiting insect damage.

The data used here are from three Permian fossil assemblages from north-central Texas that are dominated by broadleaf plant hosts (Fig. ). These assemblages predate the origin of angiosperms and the majority of plant hosts discussed here are gymnosperms. The oldest assemblage, from Mitchell Creek Flats (MCF), is dated as early Permian . The form genus Taeniopteris is the primarily dominant plant host at MCF but is represented by only 104 specimens, whereas the gigantopterid seed plant Zeilleropteris Mamay sp. is the secondarily dominant plant host . The assemblage from Colwell Creek Pond (CCP) is slightly younger than that from MCF and contains the primarily dominant plant hosts Auritifolia waggoneri Chaney, Mamay, DiMichele and Kerp, a peltasperm, and Taeniopteris, the form genus. Each are represented by over 400 specimens . The secondarily dominant plant host at CCP is Evolsonia texana Mamay, a gigantopterid, as at MCF. The third assemblage, from the middle Permian, derives from South Ash Pasture (SAP) . The primarily dominant plant host at SAP is the broadleaf conifer Johniphyllum multinerve Looy and Duijnstee, represented by over 400 specimens. The secondarily dominant plant host is, as at MCF and CCP, a gigantopterid: Euparyphoselis gibsonii DiMichele, Looy and Chaney. At all three sites, all specimens over 0.5 cm2 in surface area were analyzed for insect herbivory. Two other assemblages from the Permian of Texas, at the Coprolite Bone Bed and Taint localities, have also been analyzed for herbivory , as has one assemblage from the uppermost Carboniferous of Texas , but the original data are only available for MCF, CCP, and SAP.

Three plant hosts are represented by over 400 specimens: the codominant Auritifolia waggoneri and Taeniopteris spp. at CCP and Johniphyllum multinerve at SAP. However, the dominant plant at MCF is Taeniopteris spp., consisting of slightly more than 100 specimens. These contrasting abundance profiles illustrate the variability of sample sizes within fossil floras. A. waggoneri is a possible comioid seed plant that has compound leaves and is represented at CCP by specimens that range from large, complete fronds to minute fragments. All material identifiable as A. waggoneri was measured for insect herbivory. This material includes pinnae together with any attached petioles and axes, with pinnae accounting for the vast majority of surface area measured for this plant host. By contrast, Taeniopteris is a form taxon that is certainly polyphyletic at CCP: the majority of these specimens are interpreted to be of cycadophyte affinities and thus gymnospermous, but some specimens show evidence of probable spore-bearing fructifications and, therefore, cannot be assigned to any seed plant lineage. It is for this reason that the designation, Taeniopteris spp., is given, to denote that this leaf type contains two or more distantly related but indistinguishable plant taxa. Due to the elongate leaf shape and variable size of Taeniopteris, it is impossible to determine whether a given fragment represents more or less than 50 % of the original leaf. Unlike Auritifolia waggoneri, Taeniopteris spp. is not known to be represented by any affiliated axes preserved at CCP.

Johniphyllum multinerve at SAP is variable in morphology; when SAP was initially examined for insect herbivory, the broadleaf conifer specimens were divided into two distinct morphotypes based on leaf width and vein thickness. These two morphotypes were later assigned to the same species . Plasticity and structural variability of leaf morphology are common throughout the plant kingdom, and multiple leaf forms are frequently found on the same individual. Plasticity may be the result of environmental factors such as sunlight , biological interactions such as induced plant-host defenses from attacking insect herbivores , leaf age , or reproductive variability such as the fertile and sterile foliage of ferns . In turn, this plasticity may impact the extent of insect-mediated herbivory on different leaf forms. The amount of insect damage was considerably higher on one form than on the other, and the separation of these forms allows quantification of the potential differences in herbivory between forms belonging to the same nominal species. Because J. multinerve at SAP can be confidently divided into two discrete forms, this plant host can be considered to be even more morphologically variable than Taeniopteris spp. of CCP, despite being a monophyletic taxon.

Damage type diversity (DT diversity) and the herbivory index (HI), or percentage of leaf area removed, were analyzed under various subsampling routines. Ninety-five percent confidence intervals were calculated for all analyses of these two metrics. Confidence intervals were initially calculated for the complete dataset for each plant host; no subsampling routines were performed. All confidence intervals were calculated using 100 000 bootstrap replicates.

The subsampling routines fall into four categories. The first subsampling category is random: 100 and 200 specimens were randomly sampled for each plant host. The second subsampling category is size: the 100 and 200 specimens with the highest surface area were sampled. To represent a more realistic approach, another subsampling routine was conducted in which 200 of the largest 250 specimens were sampled. This process was carried out because it may be impossible to precisely identify the largest 200 specimens without first digitizing and measuring their surface area, a time-consuming process. The third category of subsampling routines uses a minimum size cutoff: the only specimens sampled were those above 1, 2, or 5 cm2 in total surface area. For Taeniopteris spp. at MCF and for all secondarily dominant, gigantopterid plant hosts, only the third category of subsampling routines was performed because an insufficient number of specimens was available for the first two categories of subsampling routines.

The last subsampling routine is by size but uses a sequential approach to provide a more detailed view of how mean values and confidence intervals respond to increases in sample size. First, the 100 largest specimens per plant host were sampled as above. Then the next 10 largest specimens – the 101st- through 110th-largest specimens – were added to the sample. This was then followed by the next 10 largest specimens, and the process continued until all specimens had been sampled. This subsampling routine can only be performed for plant hosts represented by at least 110 specimens.

To address the impact of subsampling on the differentiation of herbivore communities, we performed ordinations of functional-feeding-group (FFG) data at different levels of sampling. Fungal damage was excluded from all NMDS analyses. All NMDS analyses were conducted with the R package vegan, version 2.4–4 .

Among the primarily dominant plant hosts at CCP and SAP, represented by 400 or more specimens, the complete datasets yield nonoverlapping confidence intervals for each plant host (Figs. , ). Auritifolia waggoneri and Taeniopteris spp. at CCP have similar DT diversity, which is higher than the DT diversity of Johniphyllum multinerve at SAP. A. waggoneri has a higher herbivory index than either Taeniopteris spp. at CCP or J. multinerve at SAP.

Among the plant hosts represented by far fewer than 400 specimens, some resulting patterns are also clear from the complete datasets (Fig. ). Evolsonia texana at CCP has higher DT diversity than Zeilleropteris sp. at MCF and Euparyphoselis gibsonii at SAP. Taeniopteris spp. at MCF yields a confidence interval for DT diversity that overlaps with those of all three secondarily dominant, gigantopterid plant hosts. The herbivory indices of all four of these plant hosts overlap. Taeniopteris spp. at MCF yields the widest confidence interval, and Zeilleropteris sp. and Evolsonia texana yield the narrowest confidence intervals.

When only a subset of the specimens are sampled, random sampling causes the confidence intervals to widen the most. When only 100 specimens are sampled randomly, the width of the confidence intervals often doubles (Fig. ). When 200 specimens are sampled randomly, the confidence intervals narrow but are still noticeably wider than for the complete dataset. At both 100 and 200 randomly sampled specimens, the confidence interval for Johniphyllum multinerve at SAP overlaps with the confidence intervals for Auritifolia waggoneri and Taeniopteris spp. at CCP, although this overlap is not observed when the complete datasets are sampled (Fig. ).

When only the largest 100 specimens are sampled, confidence intervals can widen and mean values of DT diversity and the herbivory index can differ from the means calculated with the complete dataset. For Auritifolia waggoneri, the mean values of DT diversity and the herbivory index are minimally offset, but the width of the confidence intervals is noticeably larger than the width of the confidence intervals calculated with the complete dataset (Fig. ). For Taeniopteris spp. at CCP, the mean value for DT diversity decreases noticeably when only the 100 largest specimens are sampled, and the mean value for the herbivory index increases slightly; the width of confidence intervals under this subsampling routine is very similar to the width of the confidence intervals calculated with the complete dataset (Fig. ). For Johniphyllum multinerve at SAP, the mean value for DT diversity decreases noticeably when only the 100 largest specimens are sampled, as is also the case for Taeniopteris spp. at CCP (Fig. ). The mean value for the herbivory index becomes noticeably lower and the confidence interval widens. When the 100 largest specimens are sampled, the confidence interval for DT diversity of J. multinerve at SAP does not overlap with the confidence intervals for A. waggoneri and Taeniopteris spp. of CCP. The confidence intervals for the herbivory index of Taeniopteris spp. and A. waggoneri at CCP do not overlap under this subsampling routine, but the confidence interval for J. multinerve at SAP does overlap with the confidence interval for A. waggoneri at CCP.

When the largest 200 specimens are sampled rather than the largest 100, the mean values for DT diversity and the herbivory index differ less from the true means and the confidence intervals narrow. For Auritifolia waggoneri at CCP, sampling of the largest 200 specimens yields mean values and confidence intervals that are nearly indistinguishable from those calculated from the complete dataset (Fig. ). For Taeniopteris spp. at CCP, the mean value for DT diversity is noticeably lower than that calculated from the complete dataset, but the width of the confidence interval is nearly identical, and the mean value and confidence interval for the herbivory index are indistinguishable from those calculated from the complete dataset (Fig. ). For Johniphyllum multinerve at SAP, the mean values for DT diversity and the herbivory index remain offset from the means calculated from the complete dataset, but the offset is slight compared to that seen when only the 100 largest specimens are sampled; the confidence interval for the herbivory index remains relatively wide (Fig. ).

When 200 of the 250 largest specimens are sampled, the means and confidence intervals resemble those calculated from the 200 largest specimens. For Auritifolia waggoneri and Taeniopteris spp. at CCP, these two subsampling routines yield identical means and very similar confidence intervals (Fig. ). For Johniphyllum multinerve at SAP, the mean values are less offset when 200 of the 250 largest specimens are sampled; the confidence interval for DT diversity widens slightly and the confidence interval for the herbivory index is minimally offset (Fig. ). When the 200 largest specimens are sampled, or when 200 of the 250 largest specimens are sampled, patterns of overlap between different plant hosts' confidence intervals are identical to those recovered when the complete dataset is used for all calculations – though the distance between different plant hosts' confidence intervals is often reduced.

When the threshold for minimum specimen area is increased from 0.5 to 1 cm2, the impact on mean values and confidence intervals is either negligible or indiscernible for all seven plant hosts examined here (Figs. , ). When the threshold is increased to 2 cm2, the effect is again negligible for Auritifolia waggoneri and Taeniopteris spp. at CCP (Fig. ). For the herbivory index for Johniphyllum multinerve at SAP, the lower bound of the 95 % confidence interval is nearly unchanged, the mean value increases slightly, and the upper bound of the 95 % confidence interval increases noticeably – although this widened confidence interval still does not overlap with that of A. waggoneri at CCP (Fig. ). For Evolsonia texana at CCP and Euparyphoselis gibsonii at SAP, the increased sampling threshold of 2 cm2 does not have a meaningful impact on mean values or confidence intervals (Fig. ). However, for the two plant hosts at MCF – Taeniopteris spp. and Zeilleropteris sp. – the 2 cm2 threshold causes a decrease in the mean values and confidence intervals for DT diversity, though the herbivory index is unaffected (Fig. ).

When the threshold for minimum specimen area is then increased from 2 to 5 cm2, effects become more noticeable. The mean values and confidence intervals for Auritifolia waggoneri at CCP continue to resemble the values calculated from the complete dataset (Fig. ). The same is true for the herbivory index of Taeniopteris spp. at CCP, but the mean value and confidence interval for DT diversity are noticeably offset below the values calculated from the complete dataset (Fig. ). For Johniphyllum multinerve at SAP, DT diversity is offset below the true mean, far more so than is the case for Taeniopteris at CCP (Fig. ). The mean value for the herbivory index is offset above the value calculated from the complete dataset, and the confidence interval is nearly twice the width of the confidence interval calculated from the complete dataset. This causes overlap of the confidence intervals calculated for the herbivory indices of A. waggoneri at CCP and J. multinerve at SAP, a result that is not recovered from the complete datasets.

For the plant hosts represented by fewer than 400 specimens, the changes caused by a 5 cm2 sampling threshold can be even more extreme. Results for Evolsonia texana at CCP are unaffected by this change in sampling threshold (Fig. ); this is the only plant host for which only two specimens have a surface area below 5 cm2. For Euparyphoselis gibsonii at SAP, the 5 cm2 sampling threshold has a negligible impact on DT diversity. This threshold causes the mean value for the herbivory index to be slightly offset from the true mean and causes the confidence interval for the herbivory index to widen noticeably (Fig. ). For Zeilleropteris sp. at MCF, the 95 % confidence intervals for both DT diversity and the herbivory index barely overlap with the true mean values when the sampling threshold is increased to 5 cm2 (Fig. ). For Taeniopteris spp. at MCF, the 5 cm2 sampling threshold causes a slight change in values of the herbivory index and causes the entire 95 % confidence interval for DT diversity to fall well below the true mean (Fig. ).

When sampling increases sequentially, beginning with the 100 largest specimens and increasing with the next 10 largest until all specimens have been sampled, trends vary among plant hosts. For Auritifolia waggoneri at CCP, the mean value and confidence interval for DT diversity remain unchanged after the 220 largest specimens – measuring 11.36 cm2 and above – are sampled (Fig. ). After the 200 largest specimens have been sampled, the mean value for the herbivory index decreases slightly and the upper bound of the confidence interval decreases more noticeably while the lower bound of the confidence interval remains virtually unchanged.

For Taeniopteris spp. at CCP and Johniphyllum multinerve at SAP, DT diversity shows a stepwise increase that continues well after the largest specimens have been sampled. For Taeniopteris spp., the confidence interval for DT diversity narrows as sampling increases, whereas the width of this confidence interval remains almost unchanged for J. multinerve at SAP (Fig. ). As sampling increases, the herbivory index for Taeniopteris spp. at CCP decreases slightly and the confidence interval narrows noticeably. For J. multinerve at SAP these values change more dramatically, with the mean herbivory index decreasing, increasing, and decreasing again as sampling continues, while the confidence interval becomes far narrower (Fig. ).

Plant hosts' responses to subsampling routines correspond to their morphological variability. Auritifolia waggoneri at CCP, a monophyletic plant host with low morphological variability, yields the most accurate results under the different subsampling routines examined here. When at least 200 specimens of A. waggoneri are examined, with preference given to the larger specimens, subsampling yields results that are similar to, or indistinguishable from, the results calculated from the complete dataset (Figs. , ).

The dimorphic foliage of Johniphyllum multinerve at SAP can be split into two forms, here called Form 1 and Form 2. In addition to being more morphologically variable than A. waggoneri, J. multinerve is also more sensitive to subsampling routines. For example, sampling of the 100 largest specimens of A. waggoneri causes a very slight offset relative to the mean value calculated from the complete dataset; however, this same subsampling routine causes a far more dramatic offset of the mean value – and associated confidence intervals – for J. multinerve (Fig. ). By contrast, Taeniopteris is the only plant category examined here that is known to be polyphyletic. At CCP, Taeniopteris spp. shows similarly high sensitivity to various subsampling routines (Figs. , ). At MCF, where this plant host is represented by just slightly more than 100 specimens, subsampling can have an even more dramatic effect (Fig. ).

In addition to morphological variability, differences in the size of available leaf fragments may also play a role in sensitivity to subsampling routines. This almost certainly is the case for Johniphyllum multinerve at SAP, which is represented by relatively small fragments (Fig. ). Of the 475 specimens representing J. multinerve, only 89, or 18.73 %, have a surface area greater than 5 cm2. It is probably for this reason that a minimum surface-area threshold of 5 cm2 causes noticeable changes in the estimated DT diversity and herbivory index for this taxon (Fig. ). Furthermore, the two forms of J. multinerve differ in abundance, fragment size, and patterns of herbivory. Form 1 is represented by 112 specimens, which have an average surface area of 4.00 cm2; the three largest specimens belong to Form 1 (Fig. ). Form 2 is represented by 363 specimens, which have an average surface area of 2.92 cm2. Because Form 1 is less common, large fragments belonging to Form 2 are approximately three times as abundant as large fragments belonging to Form 1 (Fig. ). Form 1 also includes 14 out of 20, or 70 %, of the herbivorized J. multinerve specimens, despite its relative rarity (Fig. ).

The size differences between the two primarily dominant plant hosts at CCP may also contribute to their differing responses to subsampling. These two plant hosts are represented by nearly identical numbers of specimens – 421 for Auritifolia waggoneri and 430 for Taeniopteris spp. – but differ in surface area. Of the largest 35 specimens that represent these two plant hosts, 33 belong to A. waggoneri. The 150 largest specimens of A. waggoneri are noticeably larger than the corresponding specimens belonging to Taeniopteris spp. (Fig. ). At CCP, the 200 largest specimens of A. waggoneri have over twice as much total surface area as the 200 largest specimens of Taeniopteris spp. This may be one reason why the 200 largest specimens of A. waggoneri contain evidence for every DT found on this plant host at CCP, whereas the 200 largest specimens of Taeniopteris spp. lack the three DTs that are found on smaller specimens belonging to this same plant host . The polyphyletic nature and varying host-plant specificities of the insect herbivores on Taeniopteris spp. at CCP may also be a reason why the 200 largest specimens do not contain evidence of all DTs. Some herbivores, and the DTs they produce, may be restricted to larger Taeniopteris specimens with cycadophyte affinities, and other herbivores producing a distinct suite of DTs may be restricted to smaller Taeniopteris specimens that appear to contain sporangia and are, therefore, interpreted to be ferns.

When the threshold for minimum specimen area is raised from 0.5 to 1 cm2, the effect on DT diversity and the herbivory index is minimal (Figs. , ). This finding suggests that previous studies, which examined all fragments over 0.5 cm2 in surface area , took an unnecessarily conservative approach and that future studies can safely exclude all fragments less than 1 cm2. Furthermore, storage space for paleobotanical collections is often an issue. If storage space for a Paleozoic flora is limited, the leaves under 1 cm2 may be photographed as voucher specimens and then discarded in the field.

When the threshold for minimum specimen area is raised to 2 cm2, the effects are more noticeable but do not increase the amount of overlap between confidence intervals (Figs. , ). Therefore, for the plant hosts examined here, these effects are not strong enough to cause Type II errors. The most noticeable effects of the threshold increase from 1 to 2 cm2 can be seen in the DT diversity of Taeniopteris at MCF (Fig. ), a polyphyletic fossil genus that is barely represented by 100 specimens despite being the dominant plant host in its assemblage. In terms of morphology, evolutionary history, and sample size, Taeniopteris spp. at MCF can be considered a paleobotanical worst-case example. Nevertheless, no Type II error results from the offset of the mean value and confidence interval for DT diversity for this taxon. This finding suggests that exclusion of all leaf fragments under 2 cm2 would be a defensible subsampling strategy for future studies. None of the other a priori subsampling criteria implemented here – a minimum surface area of 5 cm2, subsampling of a uniform number of random specimens, or subsampling of a uniform number of the largest specimens – yield consistently accurate results.

The sequential approach taken here suggests another, albeit slightly more complicated, way in which sampling effort can be minimized. In the sequential approach presented here, the 100 largest specimens are sampled, followed by the next largest specimens in groups of 10. Under this sequential subsampling approach, sampling can cease when both the mean value and confidence interval for DT diversity remain unchanged while the most recent 100 specimens have been sampled, assuming that the herbivory index also changes minimally.

When the 150 largest specimens had been sampled for Auritifolia waggoneri at CCP, the mean value for DT diversity reached 35 and the 95 % confidence interval ranged from 28 to 42 (Fig. ). When sampling increased from the 150 largest specimens to the 250 largest specimens, these values remained unchanged and the relevant values for the herbivory index changed minimally. Under the sequential subsampling routine proposed here, sampling would cease at 250 specimens; at this level of sampling, results for DT diversity match those calculated from the complete dataset and results for the herbivory index are nearly indistinguishable from those calculated from the complete dataset. With this sequential approach, the smallest specimen sampled would be that which has a surface area of 8.41 cm2; the exclusion of all specimens measuring between 2 and 8.4 cm2 would represent a noticeable reduction in sampling effort without any meaningful effect on the results.

For Taeniopteris spp. at CCP, the mean value and confidence interval for DT diversity was not constant while 100 specimens are sampled sequentially by surface area (Fig. ). Under the sequential subsampling routine, all specimens of Taeniopteris spp. at CCP would be sampled until the minimum size threshold of 1 or 2 cm2 is reached. The necessity of exhaustive sampling, of specimens of all size classes, is likely caused by the polyphyletic nature of this group.

When the 240 largest Johniphyllum multinerve specimens at SAP were sampled, the mean value for DT diversity reached 16 and the 95 % confidence interval ranged from 7 to 25 (Fig. ). When sampling increased from the 240 to the 340 largest specimens, these values remained unchanged and the relevant values for the herbivory index changed minimally. At this level of sampling, values for DT diversity are only offset slightly (by one DT) from the values calculated from the complete dataset, and values for the herbivory index are essentially indistinguishable from those calculated from the complete dataset. With this sequential approach, the smallest specimen sampled would be that which has a surface area of 1.306 cm2 – sampling would have continued past the minimum size threshold of 2 cm2. However, if sampling had stopped when the minimum size threshold of 2 cm2 was reached, the results for DT diversity would be exactly the same and the confidence interval for the herbivory index would only be slightly wider. This finding suggests that a minimum size threshold and sequential sampling are compatible. Accordingly, specimens can be sampled sequentially from largest to smallest, continuing either until the addition of 100 specimens has not changed the results for DT diversity or until the minimum size threshold has been reached.

Unlike Auritifolia waggoneri and Taeniopteris spp., Johniphyllum multinerve at SAP can be divided into two separate forms, simply called Form 1 and Form 2 here. Form 1 is represented by only 112 specimens and, therefore, is not amenable to the sequential subsampling routine suggested here. However, for more abundant plant hosts that are represented by multiple, discrete forms, the sequential subsampling routine proposed here could be implemented separately for each form, with results presented individually for each form and in combination for the plant host as a whole. This approach would have two advantages. First, sequentially sampled data would not be confounded by differences in DT composition and specimen size between forms, such that results may stabilize earlier. Second, the collection of a separate dataset for each form of each plant host would facilitate more nuanced interpretations of insect herbivory: for example, if the two forms of a plant host correspond to sun leaves and shade leaves, these forms may host different component communities of insect herbivores.

Because prediction ellipses are generally smaller when calculated from the surface-area datasets than when calculated from the presence–absence datasets, we recommend using surface-area data for NMDS. Because prediction ellipses become noticeably smaller when sampling increases from 1000 to 750 cm2, we recommend sampling at least 1000 cm2 of leaf area for plant hosts and assemblages included in NMDS plots created with surface-area data. Because prediction ellipses continue to shrink noticeably at 1250 cm2 of surface area when presence–absence data are used, we recommend sampling at least 1500 cm2 of leaf area for plant hosts and assemblages included in NMDS plots created with presence–absence data. When prediction ellipses are generated in increasing intervals of 250 cm2 of surface area, sampling can be considered sufficient once the size of prediction intervals ceases to decrease. Because the plant hosts represented by the highest total surface area (Auritifolia waggoneri and Taeniopteris spp. from CCP) yield noticeably smaller prediction ellipses at all levels of sampling, we are not able to designate a surface-area threshold at which sampling can be considered exhaustive in the context of NMDS.

The exclusion of smaller specimens has a noticeable impact on the presence–absence dataset for Auritifolia waggoneri but not for Johniphyllum multinerve. When we excluded the 321st-largest through smallest specimen of A. waggoneri, because DT diversity did not change after we sampled the 220th-largest specimen from this species, NMDS confidence intervals for A. waggoneri became more likely to overlap with those of Taeniopteris spp. at MCF. The exclusion of the smallest specimens, therefore, made it more difficult to distinguish herbivore communities that appear to be distinct when visualized with complete datasets, even though the mean and confidence interval for DT diversity remained stable.

As evaluated with NMDS, CCP and MCF have herbivore communities that are so different that not only are all relevant p values equal to zero but their prediction intervals do not overlap. However, the herbivore communities for these two assemblages were originally described as being very similar, and at first glance appeared to be so . This finding raises the possibility that nearly all herbivore communities in the fossil record will appear significantly different when a minimum amount of leaf area is sampled, in which case p values of zero cannot be interpreted as reflecting any particular biological phenomenon, such as evolution or response to climate change. When NMDS is used to evaluate multiple assemblages belonging to different categories, such as studies in which various geologic intervals are each represented by multiple assemblages , pairwise distances between centroids can be compared within and between intervals.

The minimum fragment threshold and the sequential subsampling routine suggested here should be validated with studies of additional plant hosts, particularly angiosperms and needle-leaved conifers. One issue with the plant hosts examined here is that the vast majority of specimens are, in fact, fragments; the size of each specimen is partly a function of leaf area, in that a specimen cannot be larger than the leaf from which it came, but is largely a function of fragmentation. Sampling routines that proceed sequentially from the largest to the smallest specimens prioritize the most complete specimens to a greater extent than they prioritize the largest leaves. And for the plant hosts examined here, it is often impossible to estimate whether a given fragment represents 50 % or more of the original leaf area – for example, many Taeniopteris fragments are missing both the base and the apex of the leaf, and the width of a leaf is insufficient to estimate its length due to the variable morphology and size of this polyphyletic group.

Sampling of angiosperms often differs from sampling of the gymnospermous plant hosts examined here in that the only specimens sampled are typically those that include at least 50 % of the inferred original leaf area. For such plant hosts, sequential sampling of the largest to smallest specimens may not be necessary. A random subsampling approach would be more likely to work with angiosperms, and sampling could continue until the addition of 100 leaves does not change the results for DT diversity as outlined above. However, due to high similarity between the vein architecture of many angiosperms within a flora – as well as the significantly greater leaf diversity in a typical angiosperm flora compared to a gymnosperm flora – only strictly identifiable angiosperm fragments should be used: those assignable to a Linnaean species or to a defined morphotype. Consequently, the minimum size of the fragments would likely be greater than those of gymnosperms. Future studies could examine the extent to which random sampling, rather than sequential sampling by specimen area, works for plant hosts for which specimens are only sampled when at least 50 % complete.

Regardless of future results pertaining to the minimum fragment size threshold and the utility of a sequential sampling approach, data on insect herbivory in the fossil record will be of greater utility if measurements of herbivorized surface area are partitioned by damage type or at least by functional feeding group. Data collected in this manner would be conductive to nonmetric multidimensional scaling and would have the potential to reveal previously overlooked patterns in the evolution of insect herbivory.