Introduction

In Mexico there are more than 23,000 native species of vascular plants (^{Villaseñor, 2016}), but knowledge about their geographical distribution is still deficient. The number of species in many areas of the country is underestimated and the current records of distribution do not cover their entire range (^{Gómez-Pompa et al., 2010}; ^{Koleff et al., 2008}; ^{Sosa & Dávila, 1994}; ^{Villaseñor et al., 2005}). Floristic knowledge can improve with new explorations and collections in poorly explored regions of the country. Another avenue for improvement is filling in gaps in information, especially the taxonomic identification of material that has already been collected and stored in herbaria but has not been curated at species level (^{Villaseñor, 2015}).

The biodiversity crisis, where many species are becoming extinct mainly due to the loss of their natural habitat, is aggravated by the lack of knowledge of many species. The correct taxonomic identification of organisms is essential to accelerate knowledge of biodiversity and reduce the negative effects of this crisis (^{Villaseñor, 2015}). Biological information derived from taxonomic studies is used as source of information in evolutionary work and the quality of taxonomic information used in phylogenetic studies is determinant of the quality of the results found. Misidentification of organisms whose sequences are published in molecular databases -such as GenBank- can lead to erroneous results and inferences (^{Nilsson et al., 2006}). The study of diversity patterns at different space-time scales requires inventories based on taxonomic units delimited and correctly identified under a system in which comparisons can be made between them, allowing the study of variations in diversity (^{Gotelli, 2004}). Proper species identification is also key to the study of biodiversity distribution. Inaccurate identification can not only provide erroneous estimates of species ranges of distribution, but also on the diversity and composition of communities, committing both biogeography studies and the identification of priority conservation areas (^{Bortolus, 2008}).

^{Van Regenmortel (2016)} considers that a classification of viruses based only on nucleotide sequences is a classification of genome sequences and not of viruses. Molecular techniques can support the construction of genome-based classifications, and will be useful for the identification of microorganisms, cryptic species or when only organic fragments are available; it should also be noted that these techniques are not without problems or criticism (^{Nilsson et al., 2006}; ^{Will & Rubinoff, 2004}). On the other hand, most consider still necessary to maintain a taxonomy focused on morphology and its information is still valid in many areas of biological research (^{Dunn, 2003}; ^{Gotelli, 2004}). Integrative taxonomy, on the other hand, incorporates multiple sources of evidence, morphological, molecular, ecological, biogeographical, etc., into the analysis of taxonomic-nomenclatural decisions (^{Rajpoot et al., 2016}; ^{Sheth & Thaker, 2017}). Still in this modern approach, identification keys based on morphological characters are the tools that make taxonomic classifications operational and are fundamental for the knowledge of biodiversity, however this 21st century is the "era of molecular biology and genomics" (^{Dunn, 2003}; ^{Scotland et al., 2003}; ^{Walter & Winterton, 2007}).

Strategies for automatic taxonomic identification systems can be classified into 2 large groups: identification supervised by a human and unsupervised identification. In the former group, there are computer programs such as IntKey (^{Dallwitz et al., 1995}, ¹⁹⁹⁸) or Lucid (www. lucidcentral.com), in which the interface allows the user to indicate the observable characteristics of the specimen, usually through the character-character state scheme. Supervised identification keys can be classified into 2 main types: a) monothetic keys, which follow a predefined sequence of questions about the character states of the specimen, such as traditional dichotomous keys, and b) polythetic keys, in which the user can select the answer to a question from more than 1 of the character states as they are observed in the specimen being identified ( ^{Murguía-Romero & Villaseñor, 1992}).

Among unsupervised identification systems are image recognition systems by automatic vision (^{Bonnet et al., 2015}; ^{Watson et al., 2004}; ^{Weeks et al., 1997}), in which a photograph of the specimen being identified is analyzed by the system and as a result it proposes an identification. These types of systems are designed for use by nonexperts, but they are still far from the effectiveness of expert taxonomists (^{Bonnet et al., 2015}; ^{Gaston & O'Neill, 2004}). On the contrary, users of supervised identification systems can be non-experts or experts.

The polythetic condition can be defined as a particularity of a class or group, for example a taxon, which is defined by a variable set, and is unique to the class of properties, none of which is necessarily present in each member of the class (^{Dubois, 2017}) (Fig. 1). Specifically, in taxonomic identification, the polythetic condition is when a specimen can be associated with a taxon, not by a group of unique diagnostic characteristics, but by a set whose combination is unique. This polythetic condition, which refers mainly to the classification process, can also be applied to the identification process, in which this condition is more likely, since in many cases some of the diagnostic characters used in the classification are not present or not observable in the identification process. Many dichotomous keys are monothetic; however, when more than 1 route is provided for some taxa, they can be considered polythetic. In the unsupervised identification, the specimen can be identified as member of a taxon even without having information on its key or diagnostic characteristics (^{Morse, 1975}).

Figure 1 Schematization of the difference between 'polythetic' and 'monothetic' concepts. The presence of a property is indicated by the number 1. Individuals 1-4 constitute a polythetic group, where each individual records 3 of 4 properties and no property is common to all individuals. Individuals 5-6, 7-8 and 5-6-7-8 form 3 monothetic classes with 3, 3 and 2 properties, respectively, present in all members. Modified from ^{Van Rijsbergen (1979)} and ^{Van Regenmortel (2016)}. 

Materials and methods

Our strategy was to design a polythetic taxonomic identification system based on a model we call "Dynamic Identification" ( ^{Murguía-Romero, 1992}; ^{Murguía-Romero & Villaseñor, 1998}). This system allows the user to operate in 2 directions: by introducing information on the character states present in the specimen being identified and waiting for the system to report the taxa as possible identities, or the user can explore the character states that occur in a taxon considered as a possible hypothesis to refute or accept. This model has been the result of past experiences in the creation of interactive online keys ( ^{Murguía-Romero, 1987}; ^{Murguía-Romero & Villaseñor, 1993}).

The system was designed following a three-layer architecture (^{Fowler, 2002}): 1) the user interface, 2) the business layer or algorithms of the application, and 3) the data layer. The system design is based on: a) the usability of the software, b) polythetic identification, c) the theoretical model of dynamic identification, and d) the use of relational databases. The points b and c constitute the algorithms and methods that the system automates in layer 2.

Other important features considered during the design were the use of colors to indicate system states to the user, the construction of a responsive interface, that is, an interface that adapts to different devices' screen sizes, the use of cell phones and the possibility that the user may or may not be connected to the internet, the use of open source software for its construction as much as possible, and when open source software was unavailable, the use of free software, thus avoiding the payment of rights.

Dynamic identification model

The theoretical framework of computer development was the Dynamic Identification Model ( ^{Murguía-Romero & Villaseñor, 1998}), whose main characteristics are its simplicity and the possibility of indicating a hypothesis or name of the taxon suspected of being the identity of the specimen (Fig. 2). Regarding its first characteristic (simplicity), it is implemented considering 4 aspects: a) the type of data of the taxonomic data matrix is Boolean, that is to say 'true' or 'false'; b) the concept of 'statement' is created, which is a sentence that specifies a character state along with the character to which it belongs; for example, the statement 'Woody plants (trees or shrubs)' represents the pair 'character - character state' (character: life form; character state: trees or shrubs); c) system with few windows, minimizing the need for navigation, and d) scanning in 2 directions through the same interface; in one direction you can find out which taxa present a certain set of character states and in the other the character states that are present in a given taxon or set of taxa.

Figure 2 The 9 areas of the logical navigation space of dynamic identification (adapted from ^{Murguía-Romero & Villaseñor, 1998}). Both axes represent character states indicated by the user; on the horizontal axis character states are explicitly indicated (circles with solid lines); on the vertical axis, the character states are indicated by an identification hypothesis (the character states present in the hypothetical taxon, represented as circles with dashed lines). The shaded area logically represents the set of character states that may be present in the specimen being identified. 

The possibility of indicating a hypothesis, that is, the name of the taxon suspected of being the identity of the specimen, makes explicit use of the supervised identification process. Since it is a human being who is interacting with the system (rather than automatic image recognition), the user refutes their own suspicions about the possible identities of the specimen, making an interactive user-system feedback process.

Currently the system does not implement denial, that is the possibility that the user indicates that a certain character state is not present, or the denial of a hypothesis (indicating that he suspects that a taxon is not the identity of the specimen). Thus, only the quadrants in the corners of figure 2 are implemented in the interface. This decision was made not because denial could not be programmed or implemented, but because of the complexity that it would add to the user interface, making it less understandable and intuitive.

Results

The design was implemented on a web platform called AbaTax (www.abatax.abaco2.org). The website can be used on any device (cell phone, tablet or computer) and adapts to display optimally on that device. Users can create their own polykeys by preparing Excel files in specific formats with lists of taxa, characters and character states, as well as the presence-absence data matrix. This is explained in more detail in the section 'Creating polykeys in AbaTax'. If the files comply with the structure required by the system, the construction of the polykey only requires importing the files and recording some administrative data, such as names of the authors, name of the taxonomic group and date of creation.

Several polykeys are currently available on the AbaTax platform, mainly for plants, such as the FAMEX polykey for families of flowering plants (Magnoliophyta) of Mexico and the GENCOMEX polykey for the genera of Compositae of Mexico; additionally, there are 20 additional available publicly and 80 privately, accessible only to the user who created them or whoever decides to share the corresponding link and password. The results of the system with the proposed design are shown below, exemplifying it with the FAMEX polykey and with the polykey for species of Ageratina (Asteraceae) of the State of Mexico, both available for use and consultation at www.abatax.abaco2.org.

The dynamic identification interface was implemented using 2 lists (Fig. 3), one for character states (left) and one for taxa (right). The list of character states is displayed in a statement format composed of a single sentence that associates the character and character states to make the list more readable.

Figure 3 Basic view of the dynamic identification interface when displaying the FAMEX polykey (www.abatax.abaco2.org). a) Interface with the button "Show statements" off; b) interface with the button "Show statements" on. The list on the left shows the a) character - character states, or b) character state statements; the list on the right shows the list of possible taxa considered as identities of the specimen being determined. The symbol indicates the selected characters, and the taxa that comply with the selection are blue shaded. 

Figure 3 shows the interface when the user has selected 2 statements: herbaceous plants (annual or perennial, including subshrubs) and plants with thorns (on stems or leaves). At the top of the interface a message displays: selected character states: 2 of 150 and possible identities of the specimen: 49 of 264. Throughout the session the user can select more statements, following their observations on the specimen, in order to reduce the list of possible identities of the specimen to a single taxon.

The 'advanced view' button allows the user to access an alternative mode of identification by entering a hypothesis (figure 4, Acanthaceae as selected taxon). In this mode, statements corresponding to character states occurring in the family are highlighted with a green background, and the user will know that the identification hypothesis is contradicted if he selects statements that are not highlighted. In 'advanced view' mode, the number of buttons on the top bar is increased, since it is possible to filter the various areas of the logical navigation space (Fig. 2). For simplicity, the negation that is included in the dynamic identification model has not been implemented, so only positive assignments, both in the statements (selection of character states) and in the taxa (hypotheses), are considered. Thus, 4 possible elements are generated. The button with the trash icon is used to start a new session, deleting the selections previously made.

Figure 4 Advanced view of the dynamic identification interface. The Acanthaceae family has been selected as an identification hypothesis (first line in the list on the right); statements congruent with this hypothesis are highlighted in green and with a S the selected ones. Any selection by the user of a character state statement that is not highlighted would indicate that the state refutes the hypothesis, that is, that the specimen does not belong to the Acanthaceae family. 

For each statement and taxon, it is possible to associate 1 or more images available to the user to support the taxonomic identification process (Fig. 5a). On the other hand, the polykey's information is stored in a relational database, from where the character and character state of each statement is displayed in the interface. That is useful for the automatic generation of taxonomic descriptions. An example for a species included in the polykey 'Species of the genus Ageratina (Asteraceae) in the State of Mexico' is shown in figure 5b.

Figure 5 Views of attributes in the key "Species of the genus Ageratina (Asteraceae) in the State of Mexico". a) Displayed image of the species A. adenophora; b) taxonomic description generated automatically for the same species. 

Creation by importing Excel files

This method is recommended when a polykey is created for the first time. It is necessary to specify 5 Excel files, each with a single sheet: cat_taxa: list of taxa; cat_caracter: list of characters; cat_estado: list of character states associated with each character. For each one a statement is defined which is then displayed in the polykey interface; cat_grupo: groups to which each character belongs, used to organize the automatic generation of taxonomic descriptions; dat_matriz: presence-absence matrix of each character state for each taxon.

These Excel files can be created directly by the user or generated by exporting a taxonomic database created in AbaTaxEdit, a system based on Microsoft Access ® specifically for this purpose, also available on the AbaTax website.

The use of the web interface is recommended to make modifications to existing polykeys created by importing Excel files. Through this interface the user can modify the presence-absence data matrix, the list of characters, character states and taxa (Fig. 6).

Figure 6 AbaTax interface used to modify or add taxa in the polykey. 

AbaTax incorporates 2 options for access and visualization. The user can publish the taxonomic key within the system as follows. Private, only the user is able to view and access using their own password. This option is recommended when the specialist is still working and making modifications. Public, the key is made available to everyone, allowing any user to access it and use it freely.

Review and editing of the keys through collective work of multiple users

The importance of multiple specialists working collectively is an important point that AbaTax has considered within its functionalities. AbaTax offers the possibility of inviting more users to collaborate on the same polykey, under different types of access, such as only for review (read only) or also for editing.

Abatax has been migrated to a mobile application with iOS and Android operating systems (Fig. 7), which can be downloaded for free. Actually, the FAMEX key is installed by default, being able to install any other available public key, which can then be used without an internet connection. Cell phone applications have the advantage that they can be used in places where there is no Internet connection, so they are useful tools in the field.

Figure 7 Representative screens of the AbaTax mobile application. a) Start's menu screen showing that 2 keys has been installed: FAMEX (key to families of flowerings plants of Mexico) and GENCOMEX (key to genera of Asteraceae of Mexico); b) list of elegible character states of the FAMEX key; c) list of possible identities of the specimen given the list of selected character states. 

Discussion

Building new informatics programs for taxonomic identification depends on development methodologies, as well as the use of new technologies. Today, interactive keys have been built without following or without documenting the process of their development, omitting many relevant technical aspects, such as the method of computer development, system architecture, how information is stored internally, and which algorithms are used to process it. The construction of increasingly efficient taxonomic identification tools depends on previous experiences; their documentation in an explicit and orderly manner will result in new tools being able to take advantage of those previous experiences, using them as true building blocks for more solid and useful technology for biodiversity research. Unlike previous keys, ours documents the development process, reports technical details including the method of computer development, system architecture, and how information is displayed to be used.

Useful future identification tools must be constructed considering 3 aspects: 1) the model and algorithm underlying the tool, 2) the data model for storing information, and 3) the criteria applied in the design of the user interface. The dynamic identification model is both, a way of specifying the identification algorithm and a model that is familiar to users that carry out taxonomic identification. By allowing the user to propose an identification hypothesis, the tool approaches the way in which the taxonomist already goes about the identification process, making a fluid experience.

^{Penev et al. (2009)} indicate that polykeys "are generally based on taxa matrices vs characters, and these matrices can also be the basis of other taxonomic products, as long as the matrix format is general enough and adequate software is available". The relational database model is currently the information storage tool with the most general format (^{Codd, 1970}, ¹⁹⁹⁰), which is why we propose storing the data matrix in a relational database rather than other formats that require translators to exchange information between different systems. Even for almost 2 decades, it had been anticipated that the DELTA format, over time, would be transformed into a relational database model (^{Pankhurst, 1991}), but until now there is still no alternative proposal to translate it in a relational database. Regarding the condition that "adequate software be available" so that data matrices are useful for generating other taxonomic products (as defined by ^{Penev et al., 2009}), we believe that 'relational database management systems' (RDBMS) should be exploited to the full extent of their possibilities before looking for alternatives. Currently, RDBMS are the most general tools for information management, and their use will result in better communication of information between different systems and less effort in programming algorithms to generate additional taxonomic products with the same information, for example, taxonomic descriptions.

The use of a relational database as a model to store information in computer programs to generate interactive keys facilitates the evolution of the architecture of these systems. The relational model is a universal, precise, and agile way of indicating the type of information contained in the software and its degree of normalization. In addition, it shows in a synoptic way the structure of the information through the different tools of the model, such as relationship diagrams or the catalog and dictionary of the database. All of this facilitates the understanding of the limits and possibilities of the software that makes use of a particular database model.

When designing computer identification tools, the available technological possibilities must be taken into account, as well as the usability criteria that allow an intuitive and direct user approach to the identification process. Taking advantage of the characteristics offered by computer technology (such as the use of colors or mobile applications) and incorporating them in a structured way (through formal models) into automated taxonomic identification keys will allow tools to be built in a more efficient way and increase their usefulness in improving knowledge of biodiversity.

The statement structure used in AbaTax is closer to the mental model of the taxonomist than the character-character state paradigm. An interface based on statements has several advantages over one based on character-character state. On the one hand, a logical sentence is presented to the user that unites concepts in a natural way, as is done, for example, in taxonomic descriptions, which taxonomists are already accustomed to, facilitating their reading and understanding. Secondly, a list of sentences usually requires fewer clicks in the machine-taxonomic interaction, since in the character-character state structure, character states are usually only displayed once the character is clicked, a step that is not necessary in the list of sentences. Thus, character-character state may be the information structure that underlies the tools, but is not necessarily the optimal format for the user who wishes to identify a specimen. The "statement" groups together in a single unit 2 concepts that must ultimately be related, while the duplex character-character state must be presented in the interface as such, occupying not only graphical space, but also mental space, since it leaves to the user the task of joining the 2 and associating their meaning. The "statement" already presents this association in a way that is logical from a taxonomic point of view, providing a direct and clear meaning, with the possibility of including additional details.

AbaTax was launched in June 2015; since then, consultations of its identification keys exceed 14,000, with an average of 250 queries per month. The FAMEX key for families of flowering plants in Mexico has more than 8,000 queries to date, while the GENCOMEX key, for genera of Compositae of Mexico more than 2,000 (Fig. 8). The total views of the AbaTax page number around 18,000. More than 3 quarters of these total visits (14,000 or 77.8%), include consultations of polykeys. The FAMEX mobile application has been downloaded 1,220 times and has recently been made available for download from the Google Play and Apple's App Store stores, making it easy to install and distribute. Workshops, presentations at conferences and talks have been organized to publicize the AbaTax tool. All these experiences have been useful to evaluate the usability of the system, as well as to obtain user feedback and improve the interface.

Figure 8 Accumulated visits to the keys on the AbaTax platform. Total visits are indicated as blue circles, visits to the FAMEX key as orange squares, and visits to the GENCOMEX key as gray triangles. 

The comments on the AbaTax tool that we have received from workshop attendees and teachers and students who have used it in bachelor's and graduate level courses have been useful to guide the improvement of the tool by correcting errors, adapting the interface and improving computational efficiency.

In the context of a particular classification, taxonomic identification keys are currently the most efficient tool for the assignment of a specimen's taxonomic name to a specimen. An essential step in curating any biological collection is the assignment of a taxonomic name, without which specimens lose value, and thus the resources invested in collecting the specimens are largely wasted. Identification keys that take advantage of computer automation can facilitate this often arduous task.

The creation of polykeys on the web also facilitates their universal use, not only because they can reach more users, but because their distribution extends to more types of devices, such as tablets or cell phones. The tools for the creation of identification polykeys must explicitly document the data model in which the information is stored internally, the model of the interaction between the user and the tool, and the criteria used to design the user interface. Nowadays, the web represents a mechanism that can be used to face the biodiversity crisis, in which the task of generating reliable floristic listings is essential and where the correct taxonomic identification of collected specimens is a necessary prerequisite.