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The art of keys
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THE ART OF KEYS A.F. P arker-R h odes 1. Definition A diagnostic key is the way of summarizing descriptions of species or other taxa so as to facilitate the identification of specimens. It differs from a simple list of descriptions, such as we find for instance in Rea (British Basidiomycetes, C.D.P. 1922), not so much in content as in form. A key has a visual form, in contrast with for instance the use of edge-punched cards (mechanical form) or a computer program. There are various possibilities of logical structure within the concept of visual form; there are for instance the multi-entry table-like keys used by Rayner (Bulletin, 1970) for Russula spp. But here I confine my attention to the most widely used type, which has the logical form of a tree. Each taxon identified is in this type attached to the terminus of one (or more) branches descending through possibly several intermediate branch-points from a 'trunk' or initial branch-point; the description of the taxon is distributed among the characters attached to each branch at each branch-point, and can be read off by tracing the key backwards. It is thus unhandy if you want to look up the characters of a given species, but good if you want to find the name of a given specimen. 2. Layout In a visual object, as the key is, layout is all-important. Merely to present the logical structure of a key, without an appropriate visual form, is as inadequate a substitute as a table of figures is for a visual graph of the same data. Several forms of layout have been used for tree-type keys; the commonest are the offset type and the numbered type. The offset type of key has nothing to commend it except for very short or casual keys, where its simplicity is an asset. In this type, the branches at each branch-point are identified by being given the same depth of offset from the left margin, and each branch follows all the material subordinate to the preceding branch. This layout is wasteful of space, difficult to read, and ugly, unless the whole thing is short enough to be taken at a glance. The numbered type of layout identifies each branch-point by anum ber, and any branch that leads to another branch-point is made to end in the corresponding number, while those leading to species have instead the specific name. There is wide choice however as to how these elements are combined and presented. It is possible to mix the two types, having for instance offset keys for varieties under the species and interleaved among the parts of a numbered key, or conversely. This practice is to be deplored as confusing to the eye and brain. For numbered keys, there are several rather obvious points to make; but since there are many instances of their being disregarded in respectable publications (see 6), it is evidently not a waste of time to list them. 2.1. Each branch-point must be clearly set off from its neighbours and apprehensible to the eye as a unity; remember it has to be located if possible in no more time than it takes to scan a column of figures presented in order. 2.2. Its number must be its most striking feature. This can helpfully be in heavy type, and should ideally stand on a separate line above the branches; this line can also contain the back-reference. Less good, but allowable to save space, a cross-heading identifying a key section can be written in the same line as the number of its opening branch-point. Back-references should be to a branch,not merely to a branch-point. 2.3. The branches belonging to one branch-point should be so set out that they clearly belong together while yet being clearly distinguished from each other. This is best achieved by offsetting, and can be combined with attaching a label to each branch (which is essential for back-reference to be complete).
69 2.4. The number or name reached by a given branch must be well set off from the preceding lettering; it must be in a distinctive type-face (if only italics) and should have its own offsetting consistently down the page. Ideally, the names should not overlap with the material in the branch descriptions, but space saving may often prevent this; if so, bold type is all the more essential. Where a branchpoint num ber corresponds to a taxonomic entity (or to any ad hoc cross-heading) this may be written (in a different type from the species names, it should be needless to say) to the right of the number. 2.5. The use of cross-headings, whether formal taxon names or not , to break up the page, is as important to the visual clarity of a key (which is the main thing to aim for) as are cross-headings in a newspaper. They need not take up extra space, though they are better if they stand on a separate line from anything else. Even with the help of cross-headings, no key should be extended beyond about 50 branches or so; once this point is reached, major sections should be presented as separate keys, reached by a master-key at the beginning. The reason for this is that branch-point numbers get confusing if there are too many of them; relief comes from getting a name and starting again from I. 2.6. In a long series of keys, consistency of presentation is a very desirable thing, as it enables the user to have the help of reliable expectations at every point. Do not scruple to give the full layout treatment to a genus of two species (or even , in my opinion, to one of one species only!). If many taxonomic ranks are involved keep their names in appropriately differentiated typefaces, again with consistency throughout . 3. The Different Purposes of Keys Before going on to comment on the actual content of the material defining the branches, we must distinguish between different purposes for which a key may be composed. First, we distinguish between systematic key s, whose function is to present a system of classification (and only secondarily to help in identification, though if the classification is a good general-purpose one these aims should be not too much in conflict), and a non-systematic key whose sole aim is to identify specimens by the readiest characters that can be found. The latter are , of course, harder to construct , but also, paradoxically , are felt to be less weighty works and so we get too few good ones. Systematic keys are simply visual displays of existing material ; non-systematic ones embody real thought (they are , of course, no more 'artificial' than those which impose a classification on nature, and may be more 'natural' in their attention to what one actually observes! ). Either type of key may , as to it s content, be either descriptive or discriminative . That is, it may be so worded as to describe what objects actually exist, leaving unmentioned possible objects which are believed not to exist; this is the descriptive aim of all monographs and is generally taken as the ideal to be aimed at. But a key can also be so worded as simply to divide the similarity-space of its subj ect matter into regions, without regard to the fact, if it is a fact, that the boundary areas of these regions may be sparsely inhabited by real entities. The latter is logically what a classific ation is, and is what the key form is best adapted to do ; descriptive keys tend to be overweighted with information, and even if (as is strangely not always the case) they are provided with back-references, they present the description of each species in a badly fragmented state. In a discriminative key the thing to beware of is loss of redundancy. There are keys to fungi which will cheerfully offer the unwary user a Latin name for a bird-dropping (usually Tu/asnella sp. in my experience l). Espe cially mischievous are such keys which do not claim to describe all the speci es, but give no hint as to wh ere the missing ones may come out. If one is to divid e up one's material into regions of similarity , on e must make sure that enough regions are empty to
70 to accommodate the bird-droppings and suchlike noise that may be fed into the system. 4. What to write in the Branches The overall recommendation is, Keep it short. Even in a descriptive key, the finer details can helpfully be relegated to alphabetic "notes to the species" at the end. 1t is always desirable to emphasize the words which actually constitute the division being made at a given branch-point ; this can be by putting them first, in my view the best method, but the use of italics or other typographical aids is possible. For the sake of redundancy it is always desirable to mention any other characters which are convenient to use and happen to be applicable at the given branch , provided this does not over-load the text, for that hinders reading. But do not choose for this role anything that calls for the qualification 'sometimes'; characters which 'usually' hold may be helpful in making a doubtful cho ice, but 'sometimes' is always a waste of space. To make proper provision for defective specimens, insofar as this may be possible, it is better to key out a species in more than one place, than to avoid this by complicated rigmaroles of the kind which unskilful key-makers so easily fall into. A good key should sometimes enable a user to say "it must be so-and-so, even though it has no volva and grows in a salt-marsh", as well as, in other cases, the more usual but less plausible remark "it's not in the key". A common fault is to suppose that there is a virtue, or even a logical requirement, in making all branch-points binary. This is the pattern to be preferred, indeed, because the mind works best with binary choices, but there are some common situations which make multiple branching mu ch easier to follow. The worst cases of this are where a range of measurements is divided into three or more, which is common for spore sizes for example; if "spores less than 10 pm" is divided at the next branch point into "spores less than 6 pm" and "spores more than 6 pm", we are getting the information, that in the last case the spores are between 6 and I 0 pm, in silly driblets; and if this is written out at the last dichotomy, what's the use of having the earlier one anyway? Equally exasperating is when a list of colours is split up arbitrarily into binary pairs, especially as this is liable to be combined with the reprehensible use of "not so" : what else can one say, of a Russula for instance, in binary opposition to "Cap yellow"? In all such cases, multiple branch points should be used. It is helpful if the branches are labelled with the last letters of the alphabet, so that we know at the start that if the first branch is called "x" there are going to be three altogether, while if it is "y" there will be only one more . (Never, in this connexion, label branches by the branch-point number with diacritics: that number has got to catch the eye, which means being there on ce only.) There are also situations where a one-branch branch-point is in order. This is obvious where taxon names are used as cross-headings, since a subgenus, say, may only have one species; but any d.i.y. descriptions used as cross headings can have the same effect, and need not be avoided on that account. A lonely branch can have its label "z", and will cause no confusion. 5. The Selection of Characters In a systematic key , this has already been done by the taxonomist whose ideas are being presented ; but in a non-systematic key it is the selection of characters on which, apart from layout, the usefulness of the key depends. Obviously, this is a matter of judgment on which nothing very precise can be said, but there are guidelines which are evidently less obvious than they seem, since so often disregarded. The first point is that, in a non-systematic key, the first characters asked about should be easily observable, so far as is compati ble with making clear-cut divisions
71
of the material. The second point is to prefer characters which make clear divisions , insofar as they are easily ob servable. One can't always get both at once, of course; among the agarics, the favourite first choice is spore print colour, which is fairly easy to observe (though if you take it too literally , there may be no characters left when the answer comes through l), and fairly distinctive (though the frequency of colours not in the list, or intermediate, is widely underestimated). On the whole, it is best to give the next place after these considerations to characters highly weighted in traditional or widely used classifications, provided these are not too abstruse. Another point to bear in mind is that the time to run through the key is least if all the branches are, in the long run, equally used ; thus one should give some preference to a character which divides the material at a given point into more or less equal moieties, over one which peels off an oddity . The latter is of course far easier to do, for the key -maker; but it has the effect of exaggerating the import ance of peripheral species in the minds of those who repeatedly use the key. It is, of course, unobjectionable to 'peel off' a very common species. In fact, it is helpful if it can be done (which rarely happens) to get the species names coming out TOughly in the order of decreasing frequency of the species. Of characters to avoid, the worst is "Not so". At every branch-point, write out exactly what is meant by both branches; even if one of them has to be a string of alternatives. "Not so" tends to be used, out of sheer exhaustion, in opposition to a complicated logical formula, such as "Either A, or else not both Band C" ; in such a context, who knows what "Not so" means? Even when you've worked it out, you don't have much confidence that the key-maker got it right too. Another fault associated with logical formulae, when the 'not so' option is refused , is non-disjunction , that is, allowing the possibility of an object passing both branches, "either cap grey or gills white" vs, "gills yellow", for example. If you think there are no species with grey cap and yellow gills, you should say so, and if you don't , then you're just careless. Two opposite errors arise from quantitative characters. Exact measurements should only be cited where they are really exact, which happens most often when they are bounding values ; "spores more than (less than) l Oum" is acceptable , if really true (I OJ.lm inspires more confidence than IIJ.lm, thought), whereas " spores 9-1lJ.lm long " is not a good character to use except as support to something else. Ranges are a poor guide to what one will find, and have no statistical basis; what one needs, if the data are available , is a mean and standard deviation. Otherwise, the mean alone is less misleading than a "range". Very useful is to use common words like "large", "very small" and so on with approximate definit ions given in notes somewhere; such terms do not have the misleading associations of precision attaching to actual measurements. On the other hand, one should never rely on m erely statistical characters, unless there is no appreciable overlap. Where species are to be separated on such characters (and it would be rash to deny that such species may occur), they should be keyed out as one, and further described in the attached notes on the species. In relation to any given specimen, there is always a possibility of non-disjunction here, which should be banned from keys. Finally, care should be taken not to mention any character more than once on the way from trunk to terminus (unless one species gets more th an one mention, in which case redundancy of this kind may occur on one route). (Even worse is to incorporate contradictory cha ract ers into one routel) On the whole, entering any species more than once in a key is to be avoided (whereupon there is little dang er of these errors), hut to allow this often make s it possible to simplify what is said at certain points in the key , and if so the awkwardness of a double entry is well worth it.
72 6. Cautionary Tales I will now briefly examine a few well-known or recent keys covering groups of Basidiomycetes, and comment on them from the above point of view. I make no criticism of their actual contents apart from the form it is given in. A.A. Pearson produced a series of keys to some of the larger genera of agarics, such as Russula, all of them in the form of thin pamphlets, generally including both a tree-type key and a tabular arrangement. The tree-type keys are good except for their poor typography, no doubt due to exigencies of production at a low price, particularly they are to be com mended for omission of surplus information and avoidance of the kind of faults listed in 15. They lack back-references, but in the presence of a tabular presentation of the descriptions this may be excused . Kuhner & Rornagnesi's classic work "Flore analy tique des chamignons superieurs" is a monumental instance of a systematic and descriptive key . The whole book is cast in this form, and, it must be said, the strain shows. The individual branches are often inordinately long, and consequently hard to follow, not least for the authors, who more than once commit non-disjunction, and repeatedly oppose a complex logical formula with "pas ces characteres". Their layout is the offset type, with labelling by letters, which is not too hard to follow backwards or forwards, but leads to the keys being broken up into rather arbitrary sections ("restes") to avoid escalating offsets (the ludicrous effects of which can be seen in Singer's "Agaricales"). Another bad fault in this book is the way they not only don't offset the species names, but interpose between them and the definition leading to them, in running text , synonymies, cooking hints, notes on other authorities' varietal names, and suchlike matters. This makes the reading of the key as a key unnecessarily difficult. One feels that a large part of the matter forced into the key ought to have gone into extensive notes on each genus, leaving the key usable as such. In recent years P.D. Orton has produced many keys to a variety of genera and sections of genera in the agarics, mostly in the Transactions. His keys too are apt to be overloaded, and he has no aversion to relying on statistical discriminations; but my main criticism of him is his total disregard of the visual factor. His usual custom is to offset one branch of a branch-point relative to the other, making the branch point numbers exceptionally trying to find instead of impossible to miss as they should be. Astonishingly , in keys meant to be descriptive (as I suppose), and sadly even if not, he uses no back references, so that the keys in actual use are needlessly difficult if one has to retrace an error. This does not matter in a short key, but is catastrophic in say , Hygrophorus. D.N . Pegler's recent key to the Polyp ores, which appeared in a recent Bulletin, is one of the least satisfactory. Firstly , it extends without a break to over 100 branch-points. Even though he gives back references (though only to branchpoints), the absence of cross headings over this enormous mass of material makes back-reading very troublesome. The branches are spaced the same as the branchpoints, and labelled with branch-point numbers primed , all of which makes for poor readability, despite good typography and offsetting. In his key to the British Polypores he uses a mixed layout (numbered for the genera , offset for the species) which, even though few genera have many species in his system, makes difficulties in following the main key . The matter in the branches is wellchosen and simply put ; its very bareness however makes one wonder at the status of some of the genera named : can there really be enough supporting characters omitted, for the key's sake, to make these good genera? 7. Exemplary Behaviour To illustrate the principles I have been trying to inculcate in the foregoing
73 paragraphs, here is a key to the five British species of Dermoloma (Lange) Sing. The matter is (I hope) uncontroversial: the manner is all. Genus DERMOLOMA
o from y z :
52y in Key to Genera Spores amyloid Spores non-amyloid
I
3
with amyloid spores I from Oy y : Medium to large, cuticle blackish breaking up into granules; gills grey; stem pale with dark granules; spores 8 x 3.5 etc elytroides (Scop.ex Fr.) Sing. z Small, cuticle dark grey not becoming granular; stem and very ventricose gills dark grey; 2 spores 7.5 x 5 etc
2 from Iz y Cap noticeably darker than stem; gills strongly sinuate; cuneifolium (Fr. ex Fr.) Sing. z Colour uniform; gills uncinato-decurrent; slender stature josserandii Dennis & Orton with non-amyloid spores 3 from Oz y Large, blackish, granular; gills paler; stem white; spores 5.5 x 4 etc distinguendum Lund. z Smaller, dingy fuscous, not granular; gills & stem light grey; spores 6 x 4.5 etc atrocinereum (Pers.ex Pers.) Orton There is little point, in so short a key, in having the cross headings which are only put in to show the idea; though if they were named as subgenera, they would be included in any case (and also be inserted after the leads I, 3 at the zeroth branch point). Note that back-references need not stop short at the beginning of a key; and note too that, for consistency's sake, they are included throughout, even though in this case they are not really needed. This is presented as at least partially a systematic key (hence the emphasis on amyloid spores); in a non-systematic key one would rather first separate the larger granular species elytroides and distinguendum from the smaller ones. Such a key would be expected to have a set of notes to the species, to which author citations could be referred, and supplementary information on ecology, abundance, &c. given. Although the typographical conventions recommended above are illustrated in this example, their utility can only be fully appreciated in a much longer key.
THE ART OF KEYS A.F. P arker-R h odes 1. Definition A diagnostic key is the way of summarizing descriptions of species or other taxa so as to facilitate the identification of specimens. It differs from a simple list of descriptions, such as we find for instance in Rea (British Basidiomycetes, C.D.P. 1922), not so much in content as in form. A key has a visual form, in contrast with for instance the use of edge-punched cards (mechanical form) or a computer program. There are various possibilities of logical structure within the concept of visual form; there are for instance the multi-entry table-like keys used by Rayner (Bulletin, 1970) for Russula spp. But here I confine my attention to the most widely used type, which has the logical form of a tree. Each taxon identified is in this type attached to the terminus of one (or more) branches descending through possibly several intermediate branch-points from a 'trunk' or initial branch-point; the description of the taxon is distributed among the characters attached to each branch at each branch-point, and can be read off by tracing the key backwards. It is thus unhandy if you want to look up the characters of a given species, but good if you want to find the name of a given specimen. 2. Layout In a visual object, as the key is, layout is all-important. Merely to present the logical structure of a key, without an appropriate visual form, is as inadequate a substitute as a table of figures is for a visual graph of the same data. Several forms of layout have been used for tree-type keys; the commonest are the offset type and the numbered type. The offset type of key has nothing to commend it except for very short or casual keys, where its simplicity is an asset. In this type, the branches at each branch-point are identified by being given the same depth of offset from the left margin, and each branch follows all the material subordinate to the preceding branch. This layout is wasteful of space, difficult to read, and ugly, unless the whole thing is short enough to be taken at a glance. The numbered type of layout identifies each branch-point by anum ber, and any branch that leads to another branch-point is made to end in the corresponding number, while those leading to species have instead the specific name. There is wide choice however as to how these elements are combined and presented. It is possible to mix the two types, having for instance offset keys for varieties under the species and interleaved among the parts of a numbered key, or conversely. This practice is to be deplored as confusing to the eye and brain. For numbered keys, there are several rather obvious points to make; but since there are many instances of their being disregarded in respectable publications (see 6), it is evidently not a waste of time to list them. 2.1. Each branch-point must be clearly set off from its neighbours and apprehensible to the eye as a unity; remember it has to be located if possible in no more time than it takes to scan a column of figures presented in order. 2.2. Its number must be its most striking feature. This can helpfully be in heavy type, and should ideally stand on a separate line above the branches; this line can also contain the back-reference. Less good, but allowable to save space, a cross-heading identifying a key section can be written in the same line as the number of its opening branch-point. Back-references should be to a branch,not merely to a branch-point. 2.3. The branches belonging to one branch-point should be so set out that they clearly belong together while yet being clearly distinguished from each other. This is best achieved by offsetting, and can be combined with attaching a label to each branch (which is essential for back-reference to be complete).
69 2.4. The number or name reached by a given branch must be well set off from the preceding lettering; it must be in a distinctive type-face (if only italics) and should have its own offsetting consistently down the page. Ideally, the names should not overlap with the material in the branch descriptions, but space saving may often prevent this; if so, bold type is all the more essential. Where a branchpoint num ber corresponds to a taxonomic entity (or to any ad hoc cross-heading) this may be written (in a different type from the species names, it should be needless to say) to the right of the number. 2.5. The use of cross-headings, whether formal taxon names or not , to break up the page, is as important to the visual clarity of a key (which is the main thing to aim for) as are cross-headings in a newspaper. They need not take up extra space, though they are better if they stand on a separate line from anything else. Even with the help of cross-headings, no key should be extended beyond about 50 branches or so; once this point is reached, major sections should be presented as separate keys, reached by a master-key at the beginning. The reason for this is that branch-point numbers get confusing if there are too many of them; relief comes from getting a name and starting again from I. 2.6. In a long series of keys, consistency of presentation is a very desirable thing, as it enables the user to have the help of reliable expectations at every point. Do not scruple to give the full layout treatment to a genus of two species (or even , in my opinion, to one of one species only!). If many taxonomic ranks are involved keep their names in appropriately differentiated typefaces, again with consistency throughout . 3. The Different Purposes of Keys Before going on to comment on the actual content of the material defining the branches, we must distinguish between different purposes for which a key may be composed. First, we distinguish between systematic key s, whose function is to present a system of classification (and only secondarily to help in identification, though if the classification is a good general-purpose one these aims should be not too much in conflict), and a non-systematic key whose sole aim is to identify specimens by the readiest characters that can be found. The latter are , of course, harder to construct , but also, paradoxically , are felt to be less weighty works and so we get too few good ones. Systematic keys are simply visual displays of existing material ; non-systematic ones embody real thought (they are , of course, no more 'artificial' than those which impose a classification on nature, and may be more 'natural' in their attention to what one actually observes! ). Either type of key may , as to it s content, be either descriptive or discriminative . That is, it may be so worded as to describe what objects actually exist, leaving unmentioned possible objects which are believed not to exist; this is the descriptive aim of all monographs and is generally taken as the ideal to be aimed at. But a key can also be so worded as simply to divide the similarity-space of its subj ect matter into regions, without regard to the fact, if it is a fact, that the boundary areas of these regions may be sparsely inhabited by real entities. The latter is logically what a classific ation is, and is what the key form is best adapted to do ; descriptive keys tend to be overweighted with information, and even if (as is strangely not always the case) they are provided with back-references, they present the description of each species in a badly fragmented state. In a discriminative key the thing to beware of is loss of redundancy. There are keys to fungi which will cheerfully offer the unwary user a Latin name for a bird-dropping (usually Tu/asnella sp. in my experience l). Espe cially mischievous are such keys which do not claim to describe all the speci es, but give no hint as to wh ere the missing ones may come out. If one is to divid e up one's material into regions of similarity , on e must make sure that enough regions are empty to
70 to accommodate the bird-droppings and suchlike noise that may be fed into the system. 4. What to write in the Branches The overall recommendation is, Keep it short. Even in a descriptive key, the finer details can helpfully be relegated to alphabetic "notes to the species" at the end. 1t is always desirable to emphasize the words which actually constitute the division being made at a given branch-point ; this can be by putting them first, in my view the best method, but the use of italics or other typographical aids is possible. For the sake of redundancy it is always desirable to mention any other characters which are convenient to use and happen to be applicable at the given branch , provided this does not over-load the text, for that hinders reading. But do not choose for this role anything that calls for the qualification 'sometimes'; characters which 'usually' hold may be helpful in making a doubtful cho ice, but 'sometimes' is always a waste of space. To make proper provision for defective specimens, insofar as this may be possible, it is better to key out a species in more than one place, than to avoid this by complicated rigmaroles of the kind which unskilful key-makers so easily fall into. A good key should sometimes enable a user to say "it must be so-and-so, even though it has no volva and grows in a salt-marsh", as well as, in other cases, the more usual but less plausible remark "it's not in the key". A common fault is to suppose that there is a virtue, or even a logical requirement, in making all branch-points binary. This is the pattern to be preferred, indeed, because the mind works best with binary choices, but there are some common situations which make multiple branching mu ch easier to follow. The worst cases of this are where a range of measurements is divided into three or more, which is common for spore sizes for example; if "spores less than 10 pm" is divided at the next branch point into "spores less than 6 pm" and "spores more than 6 pm", we are getting the information, that in the last case the spores are between 6 and I 0 pm, in silly driblets; and if this is written out at the last dichotomy, what's the use of having the earlier one anyway? Equally exasperating is when a list of colours is split up arbitrarily into binary pairs, especially as this is liable to be combined with the reprehensible use of "not so" : what else can one say, of a Russula for instance, in binary opposition to "Cap yellow"? In all such cases, multiple branch points should be used. It is helpful if the branches are labelled with the last letters of the alphabet, so that we know at the start that if the first branch is called "x" there are going to be three altogether, while if it is "y" there will be only one more . (Never, in this connexion, label branches by the branch-point number with diacritics: that number has got to catch the eye, which means being there on ce only.) There are also situations where a one-branch branch-point is in order. This is obvious where taxon names are used as cross-headings, since a subgenus, say, may only have one species; but any d.i.y. descriptions used as cross headings can have the same effect, and need not be avoided on that account. A lonely branch can have its label "z", and will cause no confusion. 5. The Selection of Characters In a systematic key , this has already been done by the taxonomist whose ideas are being presented ; but in a non-systematic key it is the selection of characters on which, apart from layout, the usefulness of the key depends. Obviously, this is a matter of judgment on which nothing very precise can be said, but there are guidelines which are evidently less obvious than they seem, since so often disregarded. The first point is that, in a non-systematic key, the first characters asked about should be easily observable, so far as is compati ble with making clear-cut divisions
71
of the material. The second point is to prefer characters which make clear divisions , insofar as they are easily ob servable. One can't always get both at once, of course; among the agarics, the favourite first choice is spore print colour, which is fairly easy to observe (though if you take it too literally , there may be no characters left when the answer comes through l), and fairly distinctive (though the frequency of colours not in the list, or intermediate, is widely underestimated). On the whole, it is best to give the next place after these considerations to characters highly weighted in traditional or widely used classifications, provided these are not too abstruse. Another point to bear in mind is that the time to run through the key is least if all the branches are, in the long run, equally used ; thus one should give some preference to a character which divides the material at a given point into more or less equal moieties, over one which peels off an oddity . The latter is of course far easier to do, for the key -maker; but it has the effect of exaggerating the import ance of peripheral species in the minds of those who repeatedly use the key. It is, of course, unobjectionable to 'peel off' a very common species. In fact, it is helpful if it can be done (which rarely happens) to get the species names coming out TOughly in the order of decreasing frequency of the species. Of characters to avoid, the worst is "Not so". At every branch-point, write out exactly what is meant by both branches; even if one of them has to be a string of alternatives. "Not so" tends to be used, out of sheer exhaustion, in opposition to a complicated logical formula, such as "Either A, or else not both Band C" ; in such a context, who knows what "Not so" means? Even when you've worked it out, you don't have much confidence that the key-maker got it right too. Another fault associated with logical formulae, when the 'not so' option is refused , is non-disjunction , that is, allowing the possibility of an object passing both branches, "either cap grey or gills white" vs, "gills yellow", for example. If you think there are no species with grey cap and yellow gills, you should say so, and if you don't , then you're just careless. Two opposite errors arise from quantitative characters. Exact measurements should only be cited where they are really exact, which happens most often when they are bounding values ; "spores more than (less than) l Oum" is acceptable , if really true (I OJ.lm inspires more confidence than IIJ.lm, thought), whereas " spores 9-1lJ.lm long " is not a good character to use except as support to something else. Ranges are a poor guide to what one will find, and have no statistical basis; what one needs, if the data are available , is a mean and standard deviation. Otherwise, the mean alone is less misleading than a "range". Very useful is to use common words like "large", "very small" and so on with approximate definit ions given in notes somewhere; such terms do not have the misleading associations of precision attaching to actual measurements. On the other hand, one should never rely on m erely statistical characters, unless there is no appreciable overlap. Where species are to be separated on such characters (and it would be rash to deny that such species may occur), they should be keyed out as one, and further described in the attached notes on the species. In relation to any given specimen, there is always a possibility of non-disjunction here, which should be banned from keys. Finally, care should be taken not to mention any character more than once on the way from trunk to terminus (unless one species gets more th an one mention, in which case redundancy of this kind may occur on one route). (Even worse is to incorporate contradictory cha ract ers into one routel) On the whole, entering any species more than once in a key is to be avoided (whereupon there is little dang er of these errors), hut to allow this often make s it possible to simplify what is said at certain points in the key , and if so the awkwardness of a double entry is well worth it.
72 6. Cautionary Tales I will now briefly examine a few well-known or recent keys covering groups of Basidiomycetes, and comment on them from the above point of view. I make no criticism of their actual contents apart from the form it is given in. A.A. Pearson produced a series of keys to some of the larger genera of agarics, such as Russula, all of them in the form of thin pamphlets, generally including both a tree-type key and a tabular arrangement. The tree-type keys are good except for their poor typography, no doubt due to exigencies of production at a low price, particularly they are to be com mended for omission of surplus information and avoidance of the kind of faults listed in 15. They lack back-references, but in the presence of a tabular presentation of the descriptions this may be excused . Kuhner & Rornagnesi's classic work "Flore analy tique des chamignons superieurs" is a monumental instance of a systematic and descriptive key . The whole book is cast in this form, and, it must be said, the strain shows. The individual branches are often inordinately long, and consequently hard to follow, not least for the authors, who more than once commit non-disjunction, and repeatedly oppose a complex logical formula with "pas ces characteres". Their layout is the offset type, with labelling by letters, which is not too hard to follow backwards or forwards, but leads to the keys being broken up into rather arbitrary sections ("restes") to avoid escalating offsets (the ludicrous effects of which can be seen in Singer's "Agaricales"). Another bad fault in this book is the way they not only don't offset the species names, but interpose between them and the definition leading to them, in running text , synonymies, cooking hints, notes on other authorities' varietal names, and suchlike matters. This makes the reading of the key as a key unnecessarily difficult. One feels that a large part of the matter forced into the key ought to have gone into extensive notes on each genus, leaving the key usable as such. In recent years P.D. Orton has produced many keys to a variety of genera and sections of genera in the agarics, mostly in the Transactions. His keys too are apt to be overloaded, and he has no aversion to relying on statistical discriminations; but my main criticism of him is his total disregard of the visual factor. His usual custom is to offset one branch of a branch-point relative to the other, making the branch point numbers exceptionally trying to find instead of impossible to miss as they should be. Astonishingly , in keys meant to be descriptive (as I suppose), and sadly even if not, he uses no back references, so that the keys in actual use are needlessly difficult if one has to retrace an error. This does not matter in a short key, but is catastrophic in say , Hygrophorus. D.N . Pegler's recent key to the Polyp ores, which appeared in a recent Bulletin, is one of the least satisfactory. Firstly , it extends without a break to over 100 branch-points. Even though he gives back references (though only to branchpoints), the absence of cross headings over this enormous mass of material makes back-reading very troublesome. The branches are spaced the same as the branchpoints, and labelled with branch-point numbers primed , all of which makes for poor readability, despite good typography and offsetting. In his key to the British Polypores he uses a mixed layout (numbered for the genera , offset for the species) which, even though few genera have many species in his system, makes difficulties in following the main key . The matter in the branches is wellchosen and simply put ; its very bareness however makes one wonder at the status of some of the genera named : can there really be enough supporting characters omitted, for the key's sake, to make these good genera? 7. Exemplary Behaviour To illustrate the principles I have been trying to inculcate in the foregoing
73 paragraphs, here is a key to the five British species of Dermoloma (Lange) Sing. The matter is (I hope) uncontroversial: the manner is all. Genus DERMOLOMA
o from y z :
52y in Key to Genera Spores amyloid Spores non-amyloid
I
3
with amyloid spores I from Oy y : Medium to large, cuticle blackish breaking up into granules; gills grey; stem pale with dark granules; spores 8 x 3.5 etc elytroides (Scop.ex Fr.) Sing. z Small, cuticle dark grey not becoming granular; stem and very ventricose gills dark grey; 2 spores 7.5 x 5 etc
2 from Iz y Cap noticeably darker than stem; gills strongly sinuate; cuneifolium (Fr. ex Fr.) Sing. z Colour uniform; gills uncinato-decurrent; slender stature josserandii Dennis & Orton with non-amyloid spores 3 from Oz y Large, blackish, granular; gills paler; stem white; spores 5.5 x 4 etc distinguendum Lund. z Smaller, dingy fuscous, not granular; gills & stem light grey; spores 6 x 4.5 etc atrocinereum (Pers.ex Pers.) Orton There is little point, in so short a key, in having the cross headings which are only put in to show the idea; though if they were named as subgenera, they would be included in any case (and also be inserted after the leads I, 3 at the zeroth branch point). Note that back-references need not stop short at the beginning of a key; and note too that, for consistency's sake, they are included throughout, even though in this case they are not really needed. This is presented as at least partially a systematic key (hence the emphasis on amyloid spores); in a non-systematic key one would rather first separate the larger granular species elytroides and distinguendum from the smaller ones. Such a key would be expected to have a set of notes to the species, to which author citations could be referred, and supplementary information on ecology, abundance, &c. given. Although the typographical conventions recommended above are illustrated in this example, their utility can only be fully appreciated in a much longer key.