Materials and methods

We performed a literature review and the examination of public databases to gather information on the specific distribution sites of rare species. The databases consulted were the two most important Mexican internet-accessed databases, the SNIB of the Comisión Nacional para el Conocimiento y Uso de la Biodiversidad (CONABIO: www.conabio.gob.mx) and IBData from the Instituto de Biología, Universidad Nacional Autónoma de México (UNAM) (www.ibdata.ib.unam.mx).

First, we verified the distribution in 1° degree latitude and longitude grid cells for all rare endemic species. Then, as a case of study, we used the georeferenced data for the rarest species within the grid cell that was richest in rare species to estimate the EOO and AOO of each species with higher precision. This latter process was performed using the R package ConR (^{Dauby et al. 2017}). Although there are native non-endemics and introduced species that are only known from a single grid square (singletons), in this study we considered only species endemic to Mexico, since they constitute the main group of species considered in red lists, for example, the Norma Oficial Mexicana 059 (^{SEMARNAT 2010}) or the IUCN (^{IUCN 2022}, ²⁰²³).

The known distribution of endemic Mexican singletons was first determined by state distribution and mapped on the grid cell size used to determine patterns of alpha diversity. This made it possible to detect areas of high concentration of rare species throughout the Mexican territory. In addition, we determined the biome(s) in which species occurred by overlapping the species’ occurrences with the shapefile of the main biomes of Mexico (^{Villaseñor & Ortiz 2014}). We used this information to calculate the incidence of rare species by biome for each grid cell.

It has been discussed that site-level environmental conditions change at approximately 5 km (^{Graham et al. 2008}). Therefore, records of rare species from sites at least 5 km apart were considered to show sufficient environmental variation to be considered members of distinct populations. The number of records selected with this procedure was considered equivalent to the global species abundance distribution (gSAD) as defined by ^{Enquist et al. (2019)}, and was therefore used to assess the number of observations or samples for each species.

Results

The rarest vascular flora of Mexico (singletons) comprises 2,705 species, distributed among 51 orders, 140 families, and 722 genera (Table 1). There were rare species from all major taxonomic groups except for the basal angiosperms. The Asterids, Rosids, and Monocots had especially large numbers of rare species, while the Ferns and allies, Eudicots and Gymnosperms had the lowest numbers.

Table 2 includes the families and genera with the highest number of rare species. The three families with the highest numbers of rare species were Asteraceae, Fabaceae, and Crassulaceae; at the genus level, the highest number of rare species were from Salvia (Lamiaceae), Tillandsia (Bromeliaceae), and Echeveria (Crassulaceae). The 15 families listed in Table 2 (10.6 % of the total families with rare species) accounted for 62.3 % of all rare species, while the 15 genera in Table 2 account for 18.8 % of all rare species.

Distribution of rare species by grid cell. Figure 2 shows the grid cells with the rarest endemic species. Of the 253 grid cells into which the country is divided, 66 did not contain rare species; most of them cover only a small portion of the mainland territory (i.e., a large portion of the grid square area was water or shared with foreign countries). The other grid cells (N = 169) contained between one species (34 grid cells) to a maximum of 138 (grid cell 228), with a median of six species and a mode of one.

Figure 2 Frequency of the 2,705 rare Mexican endemic species in each of the grid cells used to subdivide the territory (1° latitude and longitude; see Figure 1). The first class shows values less than or equal to the median (six). 

A total of 85 grid cells (Table 3) had more than the median of six rare species. The five grid cells with the largest number of rare species were cells 228 (138 species), 227 (102), 225 (89), 211(85), and 240 (85). Three of these five richest grid cells were contained within the state of Oaxaca (227, 228, and 240), one was contained within the state of Guerrero (225), and one was mostly in Puebla with some extension into Oaxaca and Veracruz (211; Table 3, Figure 2).

Distribution of rare species by state. All the Mexican states include at least one rare species (Table 4); however, two states (Aguascalientes and Tlaxcala) had no rare species that were exclusively distributed in that state since all of the rare species present were in grid cells that included the area from a neighboring state. For example, of the 10 rare species recorded in the grid cells including territory in Aguascalientes, five are shared with Jalisco, four with Zacatecas and one is shared in the grid cell that contains areas of Aguascalientes, Jalisco, and Zacatecas (grid cell 160).

The states with the highest total numbers of rare species were Oaxaca (615), Jalisco (296), Guerrero (270), Chiapas (248), and Veracruz (240). When considering only the rare species that are state endemics (i.e., all known occurrences are within a single state), Chiapas moves to second place (228) and Jalisco to fourth (200), while the other states maintain the same order. In total, the known distribution of 75.5 % of all rare species is restricted to a single state.

Distribution of rare species by biome. Table 5 indicates the occurrence of rare endemic species among the five major biomes considered by ^{Villaseñor & Ortiz (2014)}. Not all the major plant groups are found in a single biome, although several include representative species (known only in that biome, Table 5). Ferns and Monilophytes as well as Eudicots and Magnoliids are better represented in humid environments, either in humid lowlands (HTF) or humid montane areas (HMF). Gymnosperms predominate in montane biomes (HMF and TEMF), although an equivalent number is present in the HTF, mostly characterized by Zamiaceae species. The most derived lineages (Monocots, Rosids, and Asterids) are in general more homogeneously distributed among the biomes. Temperate forests (TEMF) had the largest number of species of both Asterids and Rosids, Asterids are equally represented in HMF and XER, Monocots are second in Humid mountain forests (HMF) and Rosids in Seasonally dry tropical forests (STF).

Rare species and their status according to the IUCN criteria. Only 302 species recorded any risk status agreeing to IUCN standards ( Supplementary material); this number represents 11.1 % of the total rare species. From least to the greatest threat, 37 species are listed as Data Deficient (DD), 21 as Least Concern (LC), six as Near Threatened (NT), 24 as Vulnerable (VU), 115 as Endangered (EN), and 98 as Critically Endangered (CR). One species is considered extinct (EX, Faramea chiapensis Borh.).

The state of Oaxaca, in addition to concentrating the greatest richness of species, contained the three grid cells with the greatest numbers of rare species. Grid cell 228, which had the greatest number of rare species, was selected to develop a case study aimed at evaluating the species’ potential risk category according to IUCN criterion B. We selected a total of 91 species (out of 138) recorded in the grid cell that had occurrence records in the analyzed database. Table 6 provides the EOO and AOO surface area estimated, as well as the corresponding threat category; the number of localities per species and the unique localities after applying a filter of 5 km distance between all known localities are also indicated. Based on the calculation of the EOO, from lowest to highest risk, one species qualifies as Vulnerable (VU), 20 Endangered (EN), and 70 Critically Endangered (CR). Considering the AOO value, 30 species qualify as Endangered (EN) and 61 as Critically Endangered (CR). The number of localities per species ranged from one (35 species) to 30 (one species) when considering all known locations; after applying the 5 km distance filter, the number of unique localities ranged from one (41 species) to 17 (one species).

Discussion

^{Villaseñor & Meave (2022)} in the most recent listing of the vascular plants of Mexico, considered 25,077 species (native and exotic), which accounts for 7 % of all the vascular flora in the world (^{Murguía-Romero et al. 2023}). These authors reported 4,633 singletons in total; here we consider only the 2,705 that are also endemic to Mexico. Thus, there are 1,928 additional singletons representing native non-endemic (as well as several exotic) species. Thus, 10.7 % of the flora of Mexico constitute the rarest endemic elements.

The taxonomic dispersion of rare species is wide; they included 51 of the 77 orders (66.2 %) recognized for Mexico by ^{Villaseñor (2016)}, 140 of the 297 families (47.1 %), and 722 of the 2,854 genera (25.3 %). Therefore, rare species represent almost the entire evolutionary spectrum of vascular plants. Only the most basal group of the flowering plant phylogeny (Basal Angiosperms) had no rare endemic species, although some of its representatives with a greater distribution (non-singletons) will surely be included in some risk category when they are properly evaluated. Among the oldest rare species of the flora of Mexico, the genus Ceratozamia Brongn. merits special mention: this genus of gymnosperms originated a little more than 50 million years ago (^{Lu et al. 2014}). It contains about 36 species (^{Martínez-Domínguez et al. 2022}) distributed in Mesoamerica (Mexico to Honduras), 35 of them native to Mexico and 12 considered rare in this work. Rare species from this genus were found in ten grid cells (163, 178, 196, 228, 232, 238, 241, 242, 243, 248), making these locations potential centers of paleo-endemism, especially grid cell 196, which contained three of the rare species.

Among the rare species considered, some of hybrid origin also deserve special mention. The species list ( Supplementary material) includes 18 species (nothospecies) and two genera (nothogenera: × Pacherocactus, and × Patrocereus, Cactaceae). These taxa represent examples of evolutionary events by hybridization (and probably introgression) that shaped the great floristic diversity in the country. These phenomena will surely reveal the possible hybrid origin of many species of our flora (e.g., ^{Weiss-Schneeweiss et al. 2012}).

Asteraceae and Fabaceae stand out as the most important families in terms of their number of rare species. They likewise occupy the two first places when considering total Mexican floristic richness (^{Villaseñor 2016}). In third place is Crassulaceae, showing a relevant number of rare species, despite being in sixteenth place in terms of its total number of species in the country (^{Villaseñor 2016}). Orchidaceae and Poaceae, which are the third and fourth richest families in terms of total species, are positioned in fifth and twelfth place, respectively, when considering rare endemic species. Other families that are notable for their number of rare species, although not for their total number of species in Mexico, are Bromeliaceae (fourth place), Asparagaceae (eighth), or Acanthaceae (eleventh).

It is interesting to highlight that for ten families, more than a quarter of their total species in Mexico are rare species; these include Amaryllidaceae (25.6 %), Bromeliaceae (31.3 %), and Crassulaceae (34.9 %). Only Lecythidaceae, a monospecific family, is considered a rare family following the criteria applied in this work. For 40 genera, 100 % of their species are rare; these were monospecific genera, except Cotinus and Petronymphe (with two species), and Cremnophila (with three species). Based on figures proposed by ^{Villaseñor (2016)}, 22.7 % of vascular plant genera in Mexico contain rare species.

Although the number of rare species is greater in the tropical region of Mexico (2,139 species), a substantial number (566 species) is recorded from the extratropical region (above the Tropic of Cancer). The number of species recorded in the extratropical region of Mexico is strongly related to the prevailing biomes in this region; the largest number corresponds to the TEMF (240 species) and the XER (161), with low numbers in STF (62), HMF (34) and HTF (7).

Centers of endemism represent areas of special evolutionary history, and probably centers of diversification. To date, efforts have been made to identify areas of floristic endemism at the national level (e.g., ^{Rzedowski 1991}, ^{Villaseñor & Meave 2022}), at more local scales (e.g., ^{Ibarra-Manríquez et al. 1995}, ^{Vega-Aviña et al. 2000}, ^{Méndez-Larios et al. 2004}, ^{Salinas-Rodríguez et al. 2017}, ^{Villarreal-Quintanilla et al. 2017}, ^{Estrada-Márquez et al. 2020}, ^{Aragón-Parada et al. 2021}), and even for specific taxonomic groups (e.g., ^{Villaseñor 1990}, ¹⁹⁹¹, ^{Lira et al. 2002}, ^{Villarreal-Quintanilla et al. 2005}, ²⁰¹⁷, ^{Suárez-Mota & Villaseñor 2011}, ^{Salinas-Rodríguez et al. 2017}, ^{Delgadillo-Moya et al. 2003}, ²⁰¹⁹). However, mapping full sets of vascular plant species richness, especially endemic and/or rare species has been poorly done in Mexico. Few projects are focused on these topics or aimed at identifying species at risk. In addition, species’ EOO or AOO have been estimated only in single-species studies or considering groups of species (e.g., ^{Vázquez-García et al. 2013}, ^{Redonda-Martínez et al. 2021}, ^{Samain et al. 2022}), rarely considering the full set of endemic species. This is the first attempt to analyze the entire set of endemic species with restricted geographical distribution.

Rare species considered in this study mostly fall into one of the three types of rare species discussed by ^{Drury (1974)}. Although little is known about the size of their populations, they are species known from a few localities in a narrow geographic area. Likewise, they constitute part of the set of species defined as rare by ^{Rabinowitz (1986)} due to their restricted range of distribution. Taking this criterion of restricted geographic distribution as a first step toward a more precise definition of the rarity concept will lead to this concept becoming clearer, justifiable, and refutable. Thus, the restricted distribution to a single grid cell of 2,705 endemic species, meets the rarity criteria as defined based on restricted distribution.

Distribution of rare species by state. Species conservation strategies are carried out at different government levels. The numbers of rare species found in this study (Table 1) put into perspective the importance of national-level strategies in protecting this important component of their biodiversity. However, almost all states showed significant numbers of rare species (Table 4), and a high percentage of rare species were restricted to a single state's political territory. Consequently, state and municipal governments should commit to their conservation, considering information of this type in addition to previously published evaluations of species’ risk levels (e.g., ^{Vázquez-García et al. 2013}, ^{Redonda-Martínez et al. 2021}, ^{Samain et al. 2022}).

The importance of documenting lists like the one included in Supplementary material, even at the coarsest scale of state political divisions, allows for subsequent evaluations of species that would otherwise go unnoticed. Without a doubt, many species listed here will be documented in additional states or grid cells in the future, which will change their status from rarer to more widely distributed. An example is the orchid Anathallis oblanceolata (L.O. Williams) R. Solano & Soto Arenas. This species was initially considered micro-endemic to the state of Oaxaca and defined as a singleton, but recent studies have expanded its distribution to at least five additional states, now occupying a total of nine grid cells (^{Solano & Licona 2023}). However, despite the species showing a broader distribution than initially documented, this orchid is known from no more than 13 herbarium specimens or observations, highlighting its small number of populations.

Distribution of rare species by biome. It is important to underline the ecological fidelity of rare species to one or two contiguous biomes (Table 5); 1,734 species are reported from a single biome, while 510 have been documented from two biomes and only 50 species have been recorded in three biomes.

The biomes with the highest number of species showing ecological fidelity are the temperate forests (TEMF), with 745 species known only from that biome. Seasonally dry tropical forests (STF, 308 species), and the Xeric scrublands (295) follow, and the Humid mountain forests (HMF) and Humid tropical forests (HTF) have fewer rare endemic species, although their numbers are not negligible (200 and 183 respectively). A smaller number of species (971) was distributed in two or more biomes, showing adaptations to a slightly greater ecological variation, as an adaptive response to the biomes where they occur.

Distribution of rare species by grid cell. Strategies for the conservation of the documented rare species should lead to commitments at the federal level considering all rare species at the national level, at the state level considering the grid cells comprising their territory (for example five grid cells in Oaxaca, three in Guerrero, or two in Durango), or concerted actions among states that share territory with important concentrations of rare species (Table 3). The Island of Guadalupe (grid cell 31) or the Revillagigedo archipelago (summarized in grid cell 203) also deserve special mention; they represent the most important island component in addition to the conterminous country and display important numbers of rare species.

Future work will provide a better understanding of the biotic or abiotic factors that determine the sympatric occurrence of rare species. For example, what are the factors that promoted the evolution of the 138 species known only from grid cell 228? This grid cell includes the central valleys of the state of Oaxaca (including part of the Tehuacán-Cuicatlán valley), as well as an important mountain range, known as the Sierra Norte or Sierra de Juárez, characterized by an unusual richness of flora and endemism (^{Torres-Colín et al. 2009}, ^{Suárez-Mota et al. 2018}). Each of the 85 grid cells included in Table 3 merits its own study since they constitute centers of endemism that surely have historical and ecological components that, once known, will improve our understanding of the enormous floristic diversification that has taken place in the country.

Rare species and their status according to the IUCN criteria. In addition to geographic restrictions, population size, and ecological constraints are parameters used to assess risk status. The 302 species that already had an assigned IUCN risk category share a low population density, represented by the small number of observations in the field. As shown in Table 6, the other 2,403 rare species recorded in this study that have not yet been specifically evaluated also contain few records of occurrences, with many of them known only by the type specimen with which they were described. In addition, as shown in Table 5, they show ecological fidelity to one or two biomes.

Primary vegetation in Mexico faces significant risks from land use change. For example, in a cartographic evaluation of the land use and vegetation done by INEGI in 2005, 28 % of the national territory was surface without natural vegetation (^{Villaseñor 2015}). Specifically, the analysis revealed that practically all states have more than 30 % of their surface transformed, with especially high proportions in Chiapas (45 %), Guerrero (33 %), Jalisco (37 %), Michoacán (39 %), and Oaxaca (33 %), and in most extreme case, Veracruz, in which 80 % the state’s area was without primary vegetation. In the two decades since then, much more primary vegetation territory has surely been lost. Therefore, it is urgent to determine the risk level of most species, especially the rarest ones that show the strongest ecological fidelity, restricting their occurrences to one or two biomes (Table 5, Supplementary material).

The identification of only 302 species in some risk category based on the IUCN criteria prior to this study highlights the deficiencies in this aspect. For example, ^{Samain et al. (2022)} evaluated 1,474 tree species that are endemic or nearly endemic to Mexico and determined their IUCN risk status; among them, 119 are listed as rare in this paper, and 66 additional rare tree species here included were not considered in their evaluation. More than 88 % of rare species have not been formally categorized according to the IUCN classification, although our findings show that all of them should be classified at least as NT, based on their restricted geographical distribution.

Among the 91 species analyzed specifically for grid 228, only 10 of them are currently registered on the IUCN Red List (Table 6); the remaining 81 species, based on Criterion B for EOO (^{IUCN 2022}), all qualify for (at least) the Near Threatened (NT) category. Based on species records obtained from the online databases, we found here that some species fulfill the EOO and AOO criteria for inclusion in higher-risk categories, such as Vulnerable (VU), Endangered (EN), and Critically Endangered (CR) (see Table 6). If the study case with the 91 species in grid cell 228 is extrapolated to the 2,403 rare species in Mexico that have not yet been evaluated, it is likely most of them will also be classified in categories of greater risk of extinction. In addition, for the 10 species evaluated following the IUCN Red List criteria, the estimated AOO in this study raises the risk category in half of the cases (Table 6) -two species classified as Least Concern would become Endangered, one Vulnerable species would become Endangered, two Endangered species would be Critically Endangered.

Conservation biology relies on a good knowledge of species richness, endemism, and rarity. Data on Mexican richness and endemism have already been published using grid cells (e.g., ^{Cruz-Cárdenas et al. 2013}, ^{Rodríguez et al. 2018}, ^{Villaseñor 2016}, ^{Villaseñor & Meave 2022}). However, rarity as a concept has been poorly discussed in the Mexican botanical literature. In this study, we found that the rarest species endemic to Mexico, characterized by their restricted geographic distribution, accounted for 10.7 % of the total vascular flora. Identifying these species is a fundamental first step toward determining their risk status and selecting better sites for the conservation of the rarest elements of the flora of Mexico.

Rare species probably show low tolerance to several abiotic conditions and exploit a limited range of resources. In addition, it is not known how many of them are species of incipient evolution or which have reduced their distribution area due to changes in climate or stochastic fluctuations in the environment. It will be interesting to analyze the causes of their reduced distributions, both from a historical point of view (e.g., species’ position in the phylogeny) and from an ecological point of view (e.g., which environmental variables are most influential in explaining small geographical distributions).

As demonstrated in this work, despite the coarse scale of grid cells used, mapping species’ occurrences reveals patterns of geographical distribution (Figure 2). Here the concept of rarity used was based on the species' limited range. Although not fully demonstrated, the few examples used and the literature dealing with the assessment of the risk level of some species suggest that many of the species that are considered rare also have low abundances. Although population data are absent for most species, the number of records selected with the 5 km filtering of localities may help to consider the number of unique localities as equivalent to the global species abundance distribution (gSAD) as defined by ^{Enquist et al. (2019)}. Future studies on this topic will help to clarify the relationship between the number of localities (equivalent to populations) and the abundance of species using herbarium records. This information can be the starting point for future studies that more rigorously evaluate the level of risk of this important percentage of Mexico's flora. For the time being, all the species that have not undergone previous critical evaluations, should be considered at least under the Near Threatened (NT) category due to their restricted area of occupation.

The 2,705 rare species identified will be especially vulnerable to the climate changes that are occurring and the anthropogenic pressures that reduce the natural spaces where they thrive. Their recognition will now increase attention on them, allowing a more precise appraisal of their extinction risk and possible strategies for their conservation. Similarly, the identification of grid cells that are particularly rich in rare species (Figure 2, Table 3), as suggested by ^{Brown (1995)}, will allow explorations to identify the causes of such a concentration of rare species. For many of the species considered here as singletons, future fieldwork will likely document additional populations outside the current known grid cell; however, their status as rare and possibly under some threat criteria will not change substantially.