Two simple ways to make taxonomic diagnoses more useful

Diagnoses are important aspects of description and identification processes, but they often do not make it clear whether they are useful for a particular specimen. I suggest that diagnoses always be accompanied by overt statements as to what taxonomic group the new taxon is being compared with, and whether it is a geographically, morphologically or ecologically restricted subset. I term the group to which the diagnosis overtly relates the reference group. Further, a paper that provides the features that the reference group must possess has the potential for being more broadly useful. For example, if the reference group is a subtribe but the authors explain how to separate that subtribe from all others in the subfamily, then a user must be able to identify only the subfamily before finding potentially useful information in the paper. I term this often more expansive taxon the recognition group. For 313 newly described insect genera for which diagnoses were provided, I assess the taxonomic level and number of genera in both the reference and recognition groups. The two groups were identical in almost half of the cases, were at the same taxonomic level but geographically or morphologically restricted in less than 9% and at a higher taxonomic level in the remainder. When authors explained how to identify the reference group from a larger recognition group, the number of genera from which the new one could be differentiated increased by a factor of more than four. I make a series of recommendations on how diagnoses can be improved based upon analyses of reference and recognition groups. Key words: Best practices, ease-of-use, identification, taxonomy, insects, higher-level classification Author-formatted, not peer-reviewed document posted on 15/11/2024. DOI:  https://doi.org/10.3897/arphapreprints.e141840

There is increasing demand for tools to aid in the identification of the world’s biota and while numerous modalities have been employed, at their description, new taxa are still mostly only identifiable using traditional morphological approaches. The most common of these methods are identification keys and diagnoses (Winston 1999; Borkent 2021; Packer 2024). Among the almost 600 newly described genera, less than 40% were associated with a key to aid in their identification (Packer 2024). Thus, diagnoses are critically important for biodiversity research, especially for newly described taxa for which they may be the easiest available tool permitting identification. Despite this, there is little advice associated with constructing diagnoses and even their inclusion is merely a recommendation of the Code of the International Commission on Zoological Nomenclature (ICZN 1999) which states: “Recommendation 13A: Intent to differentiate. When describing a new nominal taxon, an author should make clear his or her purpose to differentiate the taxon by including with it a diagnosis, that is to say, a summary of the characters that differentiate the new nominal taxon from related or similar taxa.” This leaves open the question of which taxa might be “related or similar” and how broadly those terms are to be interpreted. Both might best be understood in terms of the characteristics an organism possesses that indicate that the diagnosis might be relevant to a specimen at hand. This information is often not presented in a clear fashion. To improve how diagnoses may be formulated, I define two terms: reference group and recognition group. The reference group is the taxonomic group to which the diagnosis directly relates. For example, if the diagnosis states: “the new genus can be differentiated from others in the subtribe” then the reference group is the relevant subtribe. Similarly, if the diagnosis is a comparison to only one other genus (as is commonly the case when a new genus is separated from the one to which its species previously belonged) then the reference group is just the one genus in the comparison. The recognition group is the highest level in the taxonomic hierarchy for which identifying features were provided by the author(s)—the taxonomic group to which a user must determine that their specimen belongs for the information provided in the paper to be worth investigating further. The recognition group is frequently at a higher taxonomic level than the

group. For example, if the diagnosis is to genera within a subtribe but elsewhere in the paper the authors explain how to differentiate the subtribe within the subfamily but not how to separate that subfamily from others in the family, the recognition group is the relevant subfamily, but the reference group remains the subtribe. The reference and recognition groups are often at the same taxonomic level but may contain different numbers of genera. For example, the

group may be a geographically, morphologically or ecologically restricted subset of a named taxon at the same level in the hierarchy (western hemisphere Orientalidae, members of the Filiantenninae with swollen flagellomeres or members of the Asterophagini that form galls on rhododendron, to give some imaginary examples). Author-formatted, not peer-reviewed document posted on 15/11/2024. DOI:  https://doi.org/10.3897/arphapreprints.e141840 Inclusion of a recognition group that is more expansive than the reference group increases the number of genera from which the new genus is discriminated from. As this is a desirable component of new taxon descriptions, the larger the number of taxa included in the recognition group the better. Additionally, the higher up the taxonomic hierarchy the recognition group is, the easier it will be for users to know that the content of the paper might be relevant to

in their collection because higher level taxa are easier to identify. In this paper, I provide results of assessments of reference and recognition groups associated with the description of new insect genera published over an 18-month period starting in January 2021. I chose the genus level to ensure that the dataset was both tractable in size while also including a broad range of insects. The conclusions reached, however, should be applicable to any taxonomic rank for all groups of organisms.

In early 2022 I searched for newly described insect genera through Scopus searches using ordinal names combined with terms such as “new gen*” or “gen* n*” filtered for the year 2021. Searches were repeated in July and August 2022 but with 2022 as the filter. Papers dealing only with fossil taxa were removed from the sample. The resulting papers were downloaded where available online or through the library resources available to me and I attempted to obtain pdfs of papers published in Zootaxa (where the largest number of new genera were described) that were behind a paywall by contacting the senior authors and requesting a pdf (see Packer 2024 for more details). For each newly described genus, I looked for a section in the paper that had the word diagnosis (or a derivative such as “diagnostic”) as a heading or subheading. Papers lacking this were not assessed further. For each newly described genus associated with a diagnosis, I gathered the following information in addition to standard reference data: a) the reference group to which the diagnosis applied, b) the information that enabled a user to identify the reference group; c) where such information was placed; d) the recognition group; e) the reason for the difference between reference and recognition groups, when these were different, f) the number of genera in the reference group; g) the number of genera in the recognition group and h) what

or recognition groups were implied by the paper’s title. Some of these variables require additional explanation as follows.

and recognition groups were initially classified as given in each paper. The categories found were—a single genus, two or more genera (including genus complex, “phyletic series”, clade), subtribe, tribe, supertribe, subfamily, family, superfamily and order. In some cases, it was not possible to decide at which taxonomic level the diagnosis applied and in two cases the reference group was ecologically defined (Dorchin et al., 2021 and Gaimari et al., 2021). These levels were simplified to four categories for visualisation due to negligeable sample sizes for the more rarely used taxonomic levels: i) genus plus genus group, ii) subtribe to supertribe, iii) subfamily and iv) family level and above. When both reference and recognition groups could be detected and were different, I searched for rationales for their differences as stated in the papers. The following categories were found: i) geographic, ii) descriptions, iii) diagnoses, iv) keys, v) one or morphological Author-formatted, not peer-reviewed document posted on 15/11/2024. DOI:  https://doi.org/10.3897/arphapreprints.e141840 characteristics, vi) “size”, vii) “appearance”, viii) morphology-based phylogenies, ix) “taxonomic differences”. Categories ii) through viii) could also be lumped together under the broader category of morphological differences. For morphological differences, the number of features given differentiating reference from recognition groups was estimated for each genus. When data on number of genera in the reference or recognition groups were not provided in the paper, I searched elsewhere for the information. Taxon-specific databases such as the Orthoptera Species File (Cigliano et al. 2024) were particularly useful, but in some cases Wikipedia or Wikispecies pages had to be consulted. All such online searches were conducted in September 2024 and the sources of information used are indicated in Suppl. material 2 columns J and K. I attempted to correct the numbers of genera to those that would have applied at the time the paper was written: all new genera described after 2020 were subtracted from the totals whenever this information could be readily located. I used the numbers given by the authors without cross-correction as the information presented in the paper would relate to how the author understood the group at the time and it was not possible to decide which viewpoint might be most broadly accepted by the relevant taxonomic community. Also, it seemed likely that online sources might not reflect the authors’ understanding of the size of the reference and recognition groups. Online sources may be inaccurate for various reasons (for example, the wikispecies page for Gigantometopini (Hemiptera: Miridae) does not include the genus that is imaged on the page – Megalofaciatus, in the list of genera). Thus, I analysed group size data in two ways—first with only information provided by the authors and second with data from additional sources also included. When the number of genera in the reference and/or recognition group was geographically or morphologically restricted, it was often not possible to discover how many genera were relevant as such information is often not available unless stated by the authors. The distribution of number of genera in reference and recognition groups had very long right-hand tails. As averages are strongly influenced by relatively few large numerical outliers, I often provide the median which is a more accurate reflection of differences among subcategories. Where in the paper the information permitting separation of the reference group from the recognition group was provided was noted. Ideally this would be in the diagnosis itself, indicated by the term “diagnosis” in Suppl. material 2 (column I) or close by, either above it or following the description “close”. In more extensive treatments such as in revisions of higher-level taxa, this information might be given at the beginning of a taxonomy section and although perhaps at some remove from a new genus’ diagnosis, its placement in such cases was considered “sensible”. Another useful place for this information to be provided would be associated with a key to genera if one was provided “key”. Less useful were instances where the required information was far ahead of the diagnosis in an introduction “far” or near the end of the paper, usually in a discussion or concluding remarks “end”. Analyses are presented on a per-genus basis irrespective of the number of new genera treated in the paper as it is the genus that users need to identify. Additionally, sometimes authors used different levels in the taxonomic hierarchy for different genera described in the same paper. For example Lee et al. (2021) had one genus as the reference group for Palumbina but seemingly the entire subfamily for Tenupalpa (Lepidoptera: Gelechiidae: Thiotrichinae). Author-formatted, not peer-reviewed document posted on 15/11/2024. DOI:  https://doi.org/10.3897/arphapreprints.e141840

Three hundred and thirteen genera were described associated with one or more diagnosis in my sample. The papers are listed in Suppl. material 1 and the raw data associated with them in Suppl. material 2. Below, I note in which column(s) the relevant raw data for the various analyses can be located. I could not determine the reference and/or recognition groups unambiguously in two papers (Goncalves and Domahovski 2021; Motamedinia et al. 2021). Columns E and F in Suppl. material 2 show the taxonomic levels of the reference and recognition groups as noted by the authors. The two groups were identical as originally stated in 148 cases (47.6%), were at the same taxonomic level but the former was a morphological or geographical subset of the latter in 26 (8.4%). The reference group was one level below the recognition group in 111 instances (35.7%, four of these were further geographically restricted), two levels below it in 15 (4.8%), three levels in 10 (3.2%) and four levels in one (0.3%). Reasons for differentiating the two groups were found for 160 genera (51.1% of the total, data in Suppl. material 2 column H). More than one category of reason (as many as four) was given for 14 genera; thus, there were 177 rationales in total. Most of these (136) were morphological in nature (76.8% of the total number of reasons), 34 (19.2%) were geographic, 4 (2.3%) were phylogenetic and 3 (1.7%) were based upon taxonomic differences that were not detailed. Data for taxonomic levels based on the simplified four categories are presented in Fig. 1 for each order with at least 17 genera in the dataset as well as for the sum of all orders with fewer data (the largest of which was Dictyoptera with nine entries). Overall, reference groups around the tribal level were the most common (50.2% of instances) with the other three categories ranging from 14.5% (family level and above) to 18.1% (one or more genera) (Fig. 1). The number of cells in the table with entries less than 5 was too large for statistical analysis. Nonetheless, it is clear that Lepidoptera and the combined data for the smaller orders both stood out from the rest. For Lepidoptera, the percentage of reference groups at the generic level was 60%—more than twice that for the next largest value (29.4% for Orthoptera). This may reflect the image-based identifications commonly applied to members of this group and the greater discriminatory power expected of lepidopterists with decisions often based on wing patterns. For the smaller orders, the use of reference groups at the family level and above was substantially greater than in any of the larger orders (50.0% compared to an average of 11.8% among the others). This is perhaps unsurprising given that, by definition, the smaller orders have less diversity. For the recognition group, the taxonomic level data range from 10.9% for genus group to 38.8% for subfamily. Again, Lepidoptera and the combination of smaller orders are outliers requiring genus group-level identification and family or higher-level respectively for over half of the new genera respectively (Fig. 1). Author-formatted, not peer-reviewed document posted on 15/11/2024. DOI:  https://doi.org/10.3897/arphapreprints.e141840 Fig. 1. Distribution of reference (above) and recognition (below) groups among four taxonomic levels each expressed as a percentage ofthe total number of diagnoses provided separately for the six major orders as well as for the minor orders combined. 0 10 20 30 40 50 60 recognition group >=family subfamily tribe genus 0 10 20 30 40 50 60 70 80

group % Author-formatted, not peer-reviewed document posted on 15/11/2024. DOI:  https://doi.org/10.3897/arphapreprints.e141840 The number of genera in the reference group was stated in the paper in 257 cases (82.1%), are presented in Suppl. material 2 column J and ranged from one to 257, averaging 27.1 and with a median value of 13. When data from additional sources were included, the reference group was given or could be estimated for 299 genera (95.5%), ranged from 1 to over 2400, averaged 43.7 and had a median of 17. The authors provided the number of genera in the recognition group in 156 cases (49.8%) as shown in Suppl. material 2 column K. This number ranged from one to 265, with an average of 41.7 and median of 25. The number of genera in the recognition group could be estimated for an additional 138 genera (for a total of 294, 93.9%) when data from additional sources were included. The number of genera ranged from one to ~28000 (all beetles), averaged of 476.9 and had a median of 45.5. The increase in number of genera in the recognition group compared to the reference group could be estimated from the information presented by the authors for 150 genera (47.9%) and ranged from zero to 253 with an average of 18.3 and median of zero due to the large number of instances where the two groups were identical (91 instances - 60.7% of the genera where the datum could be calculated). With zeros removed, the average became 45.9 and the median value 32. Again, with zeros removed the number of genera from which the new one could be differentiated increased by an average of 8.4 times and a median of 4.1 times. When other sources of information were included, the increase in size of the recognition groups could be estimated in 289 cases (92.3%) and ranged from zero to almost 24000, averaged 440.7 and with a median of 9 which became 56 when zeroes were removed. Again, when identical recognition and reference groups were removed from the data where group size(s) estimated from extraneous information were included, discrimination of the recognition group resulted in an average increase of 127 times more genera, with a median of five times. When morphological features were given to separate reference and recognition groups, the number of features requiring observation varied from 1 to 49 with an average of 12.1 and median of 7 (Suppl. material 2 column L). One or more of the features required dissection (of genitalia or digestive system) in 47 cases ranging in relative proportion from one out of 26 features to both of two. The average proportion of features that required dissection among all features was 10.5%. Both sexes were required to identify the reference group in six cases and both sexes as well as the pupa in one more. Thus for 5.3% of the genera for which the relevant data were presented, it was seemingly not possible for a user to embark on checking the diagnosis for the new genus unless they either had both sexes, or a juvenile stage in addition to both sexes. Placement of the information that permitted identification of the reference group was in the diagnosis itself in 24 instances (14.8%), in a sensible position within the overall taxonomic treatment in 89 (54.9%) and close to the diagnosis in 21 (13.0%) (usually immediately above it or in a remarks section beneath the description). Less usefully, these data were given two or more pages above the diagnosis in 21 instances (13.0%), near the end of the paper in six (4.3%) and in a phylogenetic tree in one (0.6% - see recommendation #6 below). Keys were available to aid in the identification of 122 of the new genera (38.6%; Suppl.

2, column M). Papers lacking a key had significant differences in the taxonomic levels of their reference and recognition groups compared to those with keys, but the patterns were not Author-formatted, not peer-reviewed document posted on 15/11/2024. DOI:  https://doi.org/10.3897/arphapreprints.e141840 simple. Reference groups without a key were disproportionately less represented at intermediate taxonomic levels (subfamily and tribe) (χ2 = 16.7, p < 0.001) whereas recognition groups had fewer subfamilies for those genera not made identifiable with a key compared to all other taxonomic levels (χ2 = 27.1, p < 0.00001). The numbers of genera in reference or recognition groups did not differ significantly whether an identification key was, or was not, provided when based upon data provided by the authors (z = 0.75, p = 0.46 and z = 1.6, p = 0.11 respectively). When data from extraneous sources were included, there were significantly fewer genera in both

and recognition groups in papers without a key compared to those with one (in both cases z=2.31, p=0.021). Genera not made identifiable with a key were more likely to have the

and recognition groups identical (χ2 = 20.2, p < 0.00001), thus making the paper describing them less useful in two ways: lacking a key and having the smallest possible recognition group. The taxonomic information provided in the paper’s title (Suppl. material 2 column E) indicated the reference group precisely in 64 cases (20.8%), differed only in terms of geographic or ecological delimitation in 95 (30.9%), indicated a higher taxonomic level in 116 (37.8%) and a lower one in 24 (7.8%). The title reflected the recognition group in 25 cases (8.2%), differed only in ecological or geographic delimitation in 95 (30.9%), a higher taxonomic level in 79 (25.7%) and a lower taxonomic level in 107 (34.9%). Thus, the title of the paper may be considered misleading as to the taxonomic relevance of the information within (through over – or understating its generality) for ~80% of the genera.

Diagnoses are important components of the description of new taxa and their inclusion has been recommended by the ICZN since 1930 (Rheindt et al., 2023). But how might a user decide whether the diagnosis is relevant to a specimen they wish to identify? I have provided a framework whereby this information might be conveyed: the reference group being that to which the diagnosis applies directly, and the recognition group the taxon which the user needs to be able to identify before using the more finely discriminatory information in the publication. While these were often the same, there are two main advantages to proscribing a recognition group that is at as-high-a taxonomic level as possible, or at least as- high-a-level as might be reasonable depending on the audience. First, the more expansive the recognition group the easier it will be for a user to determine whether their specimen belongs to it or not and thereby decide that further investigation of the paper is warranted. Second, the larger the recognition group the more likely it is that users will already have the information to identify it. For example, if the diagnosis for the new genus compares it to only one other genus (especially if the shared features that differentiate them from higher taxonomic levels are not provided), the user needs to be able to identify the original genus. Precisely this situation was found in ten instances (where entries in Suppl. material 2, columns F and G both state “1 genus”. This does a disservice both to taxonomy and to those that use the results of taxonomic research: such papers will rarely be cited because so much additional information is required of a user for the paper to be readily comprehensible to them. Author-formatted, not peer-reviewed document posted on 15/11/2024. DOI:  https://doi.org/10.3897/arphapreprints.e141840 At the opposite extreme, if a new genus is diagnosed within a family but how to tell members of that family from all others in the order is outlined, the user needs only to be able to identify a specimen at the ordinal level for the information in the paper to be potentially useful. A good example of this was Lôpez-Pérez and Zaragoza-Caballero’s (2021) description of two new genera of beetles of the family Telegeusidae in which they also explain how to differentiate the family from all other beetles. In this instance, the user can get from more than 28000 genera to just one from a single research article (which included a global key to genera in the family). Recognition groups at the ordinal level were found in six instances (Suppl. material 2 column H). This approach is useful as even beginner entomologists would likely be able to recognise most insects at this level. Recognition groups at the family level were found in 58 instances. This might be considered the lowest level at which a useful recognition group can be defined for a wide range of users in that keys to families within orders (either globally or geographically) should be available to any committed entomological taxonomist. How expansive the information associated with a new taxonomic description is should depend on the target clientele of the paper. Braby et al. (2024) state that a diagnosis “should provide sufficient information to allow anyone to distinguish the new species from similar or closely related species” [italics mine]. By extension, diagnoses of genera should also allow anyone to identify the genus, indeed, their higher taxonomic rank should make their identification easier. Clearly these statements are too optimistic (not everyone has access to a microscope or literature for example), but it does seem that most new genus descriptions are aimed at an audience comprising no more than the few other taxonomic experts in the same group. This is a pity given the increasing global interest in, and acknowledged importance of, the world’s biota – especially given the repeated statements that the field of taxonomy is in crisis (e.g. Löbl et al. 2023). Of course, the title of a journal article should provide the reader with the information required to decide whether to proceed with the text of the paper as an identification tool relevant to specimens at hand. But in almost 40% of cases, the title suggested a broader (higher taxonomic level) relevance than was provided, potentially wasting user’s time. This doubtless

from the requirements of most journals to state the order and family that are the topic of the paper. Loosening of that regulation so that either reference or recognition groups or both can be provided, or overtly added, would seem useful and it would be preferable if stating what these are is mandatory. Some journals require a complete taxonomic breakdown for the new taxa at the beginning of the taxonomy section. For example, the instructions to authors for the European Journal of Taxonomy state with respect to the results “[T]this section should start with a contextual account of the current taxonomic hierarchy of the target taxon”. However, this can be misleading as it suggests that the subsequent information is relevant to the lowest level provided in that hierarchy. For example, in Biscaccianti et al (2022), the taxonomic hierarchy suggest the diagnosis might differentiate the new genus from those within its tribe, whereas it is separated from “all other known genera” of its family, which is much more useful. In the other direction, Chang et al. (2021) describe three new genera, each of which is diagnosed only with respect to one other genus, yet both the title and the taxonomic hierarchy suggest that tribal level Author-formatted, not peer-reviewed document posted on 15/11/2024. DOI:  https://doi.org/10.3897/arphapreprints.e141840 differentiation might be expected and no key is provided to assist. These issues could easily be avoided through overt statement of the reference and recognition groups. Recommendations Based upon the deliberations above, I provide the following eight recommendations. Although the data upon which these ideas were generated were from newly diagnosed insect genera, I believe they should apply to all taxa at all levels in the hierarchy, including the species level. 1. State reference and recognition groups overtly: “the diagnosis contrasts the new taxon with all others in the subtribe Diagnostina (reference group), this subtribe can be differentiated from all others in the family (recognition group) by….”. In some cases, there was some doubt as to whether the authors meant what they actually said – for example if a genus is separated from all others in its group but the paper’s title suggests that the taxa being considered are for a geographically restricted subset of that taxon. 2. State how both groups are understood. This would be analogous to the taxon concept (Meier 2017; Packer et al. 2018). This recommendation is necessitated by the seemingly disparate ways different authors sometimes understood the same taxon. In instances where there is taxonomic controversy as to group membership, authors should state which classification they are using. For example, Scheffrahn et al. (2021) and Arias et al. (2021) place the Termitidae into different orders and Ramos and Melo (2021) and Wood et al., (2022) put closely related bees into different families. The best way to do this would be to cite a reference that defined the group – “sensu Melo and Gonçalves (2005) or Michener (2007) respectively for the previous example. 3. State the number of taxa that are in the reference and recognition groups. This not only provides an additional potential check for the groups’ taxon concept but also gives the reader an idea of the complexity of the task of separating a specimen to be identified from others in the groups. 4. State the reference and recognitions groups in the (sub)heading to the diagnosis and start the diagnosis with information that permits differentiation of the reference group from the recognition group. Alternatively, provide the characteristics separating reference from recognition groups in an obvious position, immediately above the diagnosis perhaps. It was often necessary to search the entire paper to find out whether a recognition group could be detected and to find the features that separate the reference group from it: why hide the information that enables a potential citer to know whether the paper is worth further study? [Of course, authors may have mentioned the recognition group only “in passing” as their focus would have been on a more narrowly defined taxon.] 5. Provide information to differentiate reference from recognition groups briefly and use features that are decisive. As with keys (Packer 2024) as well as diagnoses (Packer unpublished data) features with exceptions or overlapping states are of limited utility as they are indecisive although if carefully worded, especially in the context of a combination of features, they may help exclude some taxa. Similarly, long descriptive text explaining how to identify the reference group will be more onerous for a user to get through: perhaps only a few features in combination will be sufficient. Author-formatted, not peer-reviewed document posted on 15/11/2024. DOI:  https://doi.org/10.3897/arphapreprints.e141840 6. Discriminatory information should be easy for a user to access. As a counterexample, to discover the defining features to differentiate the reference group from the recognition group in Chen et al (2021), the user must locate the characters that define the group from the phylogeny given in a supplementary figure (where the states are not provided though character numbers are), find the relevant matrix from among a set of supplementary tables wherein the 56 column and 55 row data matrix is provided to locate the relevant state numbers and then look at the character state descriptions elsewhere in the supplementary material. In this example, users must go through three unnecessarily time-consuming steps before obtaining an answer that could easily have been given in the body of the paper. 7. The information provided to differentiate reference from recognition groups should be as easy to assess as possible. If the features provided include information from both sexes, then those features will not be assessable from a single specimen or presumes users have associated the sexes correctly. If one or more of the features listed require dissection, unless they are the only suitable features, the information will be unnecessarily time-consuming to evaluate. 8. Be consistent with respect to the reference or recognition group being used. For example, Crispolon et al., (2021) listed their new genus under a subtribe but in the discussion stated that it could not be placed in a subtribe, causing some confusion for the reader.

Diagnoses will be made considerably more useful if authors, reviewers and editors ensure that two simple facts are overtly provided for each new taxon: a) what group is the diagnosis directly related to (the reference group) and b) how can that group be identified from among a broader range of organisms that might be relatively easy for a user to distinguish (the recognition group).

I thank Thomas Onuferko and Doug Yanega for comments on an earlier draft of this manuscript and Czarina Ortega for typing the list of references provided in Suppl, material 1. The impetus for this paper came partly from comments received on an earlier manuscript of mine from Wojciech Pulawski for which I remain thankful.

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