Hotspots of mineral diversity

The locations on Earth characterised by a large number of mineral species, herein known as mineral diversity hotspots, are defined as a single location, or in some cases a small number of sub-localities within a geographically limited area, typically associated with a single or small number of processes of mineral formation. Commonly located within mining districts or in areas of volcanic activity, some of these hotspots were known in antiquity (Mount Vesuvius, Naples, Italy: Pelloux, Reference Pelloux1927; Russo et al., Reference Russo, Campostrini and Demartin2014) while others have only become known or have formed in recent decades (Tolbachik volcano, Kamchatka, Russia: Fedotov and Markhinin, Reference Fedotov and Markhinin1983). Many are associated with fairly well understood geological processes such as volatile-rich pegmatite crystallisation (Hagendorf Pegmatite, Bavaria, Germany: Mücke, Reference Mücke1981) or porphyry copper hydrothermal mineralisation (Chuquicamata Mine, Antofagasta, Chile: Bandy, Reference Bandy1938; Cook, Reference Cook1978) whereas others are associated with rare events of extraterrestrial origin (Allende meteorite, Chihuahua, Mexico: Fuchs, Reference Fuchs Louis1971; El Goresy, et al., Reference El Goresy, Nagel, Dominik and Ramdohr1977). Some are very well known to students of geology (Franklin and Sterling Hill mines New Jersey, USA: Dunn, Reference Dunn1995; Sapucaia mine, Minas Gerais Brazil: Cassedanne and Baptista, Reference Cassedanne and Baptista1999; Baijot et al., Reference Baijot, Hatert and Philippo2012) whereas others are as yet far less celebrated (Halamish wadi, Hatrurim Basin, Israel: Britvin et al., Reference Britvin, Murashko, Vereshchagin, Vapnik, Shilovskikh, Vlasenko and Permyakov2022). In all cases, however, these hotspots are characterised by the occurrence of a large number of minerals, and critical for this study, an abundance of previously unknown mineral species defined by type location designations.

A group of localities with a large number of known mineral species has been drawn from a compilation of such locations identified in the Mindat database. Distributed across all continents excepting Antarctica, these locations exhibit an observed total diversity of over 10,000 mineral-locality pairs (Hystad et al., Reference Hystad, Downs and Hazen2015a, Reference Hystad, Downs, Grew and Hazen2015b), with an average of 113 recognised mineral species per location. The Clara mine, Baden-Wurttemberg, Germany (Markl et al., Reference Markl, Keim and Bayerl2019) is currently recognised as the location with the greatest mineral species abundance, with over 460 mineral species identified. Additionally, all of the locations considered are the type locality of at least eight previously unknown mineral species, a cutoff that originates from the Mindat compilation. The location with the largest number of endemic mineral species in the database is the Tolbachik volcano, Kamchatka, Russia, the type locality of more than 140 mineral species. This location is composed of several cinder cone and fumarole sub-localities associated with multiple episodes of recent volcanic activity. Taken together, these hotspots are the type localities of over 1500 minerals, more than a quarter of all currently known mineral species. As such, they provide a robust representation of global patterns in the characteristics of clustering exhibited by mineral species. Importantly, it is recognised that when working in the field, mineralogists and well-trained amateurs do not record or report every occurrence of every mineral they might observe. The strengths, challenges and biases inherent in the use of online databases have been fully discussed elsewhere (Hazen et al., Reference Hazen, Grew, Downs, Golden and Hystad2015; Alroy et al., Reference Alroy, Marshall, Bambach, Bezuko, Foote, Fürsich, Hansen, Holland, Ivany, Jablonsky, Jacobs, Jones, Kosnik, Lidgard, Low, Miller, Novack-Grottshall, Olszewski, Patzkowsky, Raup, Roy, Sepkosik, Somers, Wagner and Webber2001; Alroy et al., Reference Alroy, Aberhan, Bottjer, Foote, Fürsich, Harries, Hendy, Holland, Ivany, Kiessling, Kosnik, Marshall, McGowan, Villier, Wagner, Bonuso, Borkow, Brenneis, Clapham, Fall, Ferguson, Hanson, Krug, Layou, Leckey, Nürnberg, Powers, Sessa, Simpson, Tomašovych and Visaggi2008).

In order to begin the exploration of the quantitative characteristics of the Earth's mineral hotspots, it is appropriate to consider the frequency distributions of the number of mineral species identified (observed diversity) as well as the number of type locality designations (proto-diversity) recorded for each such location. In geological systems, it is often useful to evaluate highly skewed frequency distributions by rank-ordering the magnitudes of all observations in order to obtain a function E(f) where E is the number of locations with more occurrences than the value f. The shape of graphs of this function provide insights into the statistical characteristics of the observed distribution, as well as suggesting potentially significant causal factors that might underly the formation of such distributions (Turcotte, Reference Turcotte1994; Rothman et al., Reference Rothman, Grotzinger and Flemings1994; Drummond, Reference Drummond1999). This rank-ordering technique, known as exceedance analysis, has been widely utilised in the natural sciences because it eliminates the necessity of creating data bin sizes of arbitrary magnitude. Exceedance plots of the observed and proto-diversity present within the group of hotspots considered herein are characterised by strongly concave-up curves (Fig. 1a and c). However, logarithmic transformations of the exceedance values illustrate significant differences between these two distributions. In the case of the observed diversity distribution, the base 10 logarithm of the exceedance values demonstrates that these mineral species-richness data define a log-linear or exponential function such that:

$${\rm lo}{\rm g}_{10}{\rm E}( f ) = ( {-4.44 \! \times \! {10}^{-3}} ) \, f + 2.06 \, ( {r^2 = 0.9916} ) $$

Figure 1. Mineral hotspots are defined as those locations, or groups of sublocations clustered in close geographic proximity, that are characterised by either an abundance of mineral species (observed diversity) or an abundance of minerals first discovered at that location (proto-diversity). Using the formulation E(f) where E is the number of locations with more minerals than the value f, known as the exceedance value, data are displayed from the most mineral-rich hotspots (Mindat.org). (a) The observed diversity exceedance distribution follows an exponential curve; (b) [log₁₀ E(f) = (–4.44 × 10³)f + 2.06]. The concavity of the proto-diversity curve (c) is much greater than the observed diversity data (a) such that the proto-diversity data define a power-law exceedance relationship (d) [log₁₀ E(f) = –1.47 × log₁₀(f) + 3.26] highlighting the extreme scarcity of locations rich in previously unknown minerals.

That is, mineral species richness at these hotspots is exponentially distributed such that a small number of locations possess very large amounts of mineral diversity (lower right Fig. 1a and b) while most other locations possess far fewer total minerals (upper left Fig. 1a and b); and there exists a mathematical relationship that describes the distribution of mineral richness present within these locations (Fig. 1b).

The curvature of the first occurrence proto-diversity data is much greater than that found for the observed diversity data (Fig. 1c vs. 1a). For this case, base 10 logarithms of both the exceedance values and the number of type locality designations result in the linearisation of the distribution to give:

$${\rm lo}{\rm g}_{10}{\rm E}( f ) = -1.47 \! \times \! {\rm lo}{\rm g}_{10}( f ) + 3.26 \ \, ( {r^2 = 0.9889} ) $$

From this, it is clear that even among the most locations with many known mineral species, those with high levels of proto-diversity are rare (Fig. 1d), such that those locations that have contributed the most to the ongoing expansion in the number of known minerals are orders of magnitude less common than localities that have produced a significant but more modest number of new minerals, thereby highlighting the importance of the mineral hotspot concept to the history and practice of mineral discovery, particularly in the latter half of the 20^th and first decades of the 21^st century. Such highly curved power-law distributions which are linearised by taking logarithms of both variables have been identified in a variety of complex and often self-organising natural systems (Corral and González, Reference Corral and González2019, for a comprehensive summary). The potential origins of these two different types of curves begin to become appreciable when one further considers the quantitative meaning of the distributions in the context of mineral forming processes. Interestingly, Hummer (Reference Hummer2021) has also identified a fractal like power law relationship in the number of mineral species populating the various point groups of the crystal systems.

As noted above, most mineral forming processes result in the crystallisation of a relatively small number of common minerals under conditions that frequently recur in time and space, such that at most locations within the Earth's outer lithosphere the observed mineral diversity is low. Previous studies have considered the spatio-temporal relationships in new mineral discovery globally (Ponomar et al., Reference Ponomar, Gavryliv and Putiš2023) as well as the clustering of chemical compositions using network analysis of rarity groups (Gavryliv et al., Reference Gavryliv, Ponomar, Bermanec and Putiš2022). As such, locations that are characterised by a very large number of mineral species must have been subjected to mineral forming processes that were characterised by chemical and physical conditions that were highly uncommon (Hazen and Ausubel, Reference Hazen and Ausubel2016). One possibility is that the greater the number of minerals observed at a location the more uncommon, perhaps the more extreme, the conditions must have been at the time of mineral formation. Additionally, one could consider the possibility that many of the locations with high levels of observed mineral diversity might have been subject to multiple phases of mineral formation under evolving conditions of temperature, pressure, or volatile content and chemical composition. Beyond efforts to identify new mineral species, mineralogists and petrologists work to tease out the specifics of the types and styles of paragenesis recorded at these geologically complex locations and it is information about the various modes of mineral formation that fully informs our understanding of mineral species abundance and scarcity relationships.

The statistical characteristics present within the frequency distribution of proto-diversity of hotspot locations suggests the identification of previously unknown minerals can be distinctly different from the identification of other rare but previously known species. As noted above, identification of a new mineral requires the convergence of a complex combination of geological processes and human activities, first for the formation of the mineral and then for its recognition. The complexity of the interrelationships of these processes is best highlighted by the histories of discovery of new minerals at hotspots. In some cases, new minerals have been discovered at a single locality at a fairly steady rate for up to 250 years, while at others new mineral discovery has accelerated rapidly due to a combination of geological and observational causes over a matter of only a few decades (Fig. 2). Further, the discovery history of unknown minerals is driven by complex interrelationships between several factors. First, how many previously unknown mineral species are present and available for discovery? Second, how rare are the as yet undiscovered minerals? Crystal-chemical structures that exist as only a few unit cells clustered together along the margins of previously known mineral grains are unlikely to ever be recognised, by even the most careful and technically advanced analytical techniques (Caraballo et al., Reference Caraballo, Michel and Hochella2015; Grew et al., Reference Grew, Hystad, Hazen, Krivovichev and Gorelova2017). Finally, how do advances in technology (Grey, Reference Grey2022) and focused human effort impact on the search for unknown minerals? It is likely that human factors play a significant role in determining the history of mineral discovery in that once a site becomes recognised as having a significant amount of endemic mineral diversity, efforts of individuals and research teams directed at searching for, analysing, characterising and reporting new mineral occurrences tend naturally to become concentrated at that location. An example of this phenomenon can be observed in the discovery history of new minerals identified at the Yadovitaya fumarole, second scoria cone, Northern Breakthrough sublocality of the Great Fissure eruption of the Tolbachik volcano, Kamchatka, Russia, where more than 20 new minerals have been discovered in an area of only 2 square metres (Pekov et al., Reference Pekov, Agakhanov, Zubkova, Belakovskiy, Vigasina, Britvin, Turchkova and Sidorov2020).

Figure 2. Mineral discovery curves from two hotspots illustrating different temporal trends in discovery. Proto diversity (P-D) is defined as the number of minerals for which each location is the type locality. (a) The curve for Mount Vesuvius displays a nearly linear increase in the number of new mineral discoveries over a period of over 200 years. (b) Conversely, the Tolbachik Volcano locality is characterised by a significant increase in the rate of mineral discovery after the great fissure eruption of 2012–2013. In both graphs the vertical axis is the fraction of currently known mineral species that had been identified at a given time.

Finally, it is worthy of noting that the proto-diversity present at a given location is a subset of the observed diversity for that location such that in most locations there will be many more previously known than newly discovered minerals. The majority of mineral hotspots are found to have proto-diversity values that range between 10% and 30% of the documented observed diversity at that location (Fig. 3). The difference in curve shape is a consequence and demonstration of the fact that more favourable factors need to converge for a new species to be discovered than for a previously known species to be found at a new locality.

Figure 3. The majority of the mineral diversity hotspots considered have proto-diversity values that range between 10% and 30% of the observed diversity for that location, illustrating the rarity of new mineral discoveries relative to the re-identification of previously known minerals, even in the most mineral-rich settings on Earth.

Scaling relationships in the abundance of known mineral species

In the following, consideration is shifted from the analysis of mineral diversity distributions at specific locations to the analysis of the global distribution of all known mineral species. As has been noted, it is well understood that there are a large number of rare minerals and there are a small number of common minerals (Hazen and Ausubel, Reference Hazen and Ausubel2016). How can these concepts of relative mineral scarcity and abundance be better quantified and understood? The database Mindat.org, hosted by the Hudson Institute of Mineralogy (Mindat, Reference Mindat2023) provides chemical, crystallographic and taxonomic data on the nearly 6000 minerals approved by the IMA. The database also tabulates the occurrence of these species globally in the form of over 1.4 million mineral-locality pairing reports (Hystad et al, Reference Hystad, Downs and Hazen2015a, Reference Hystad, Downs, Grew and Hazen2015b). Herein these mineral-locality pairs are used to explore quantitative relationships in the scarcity and abundance of minerals. Importantly, what follows is not an effort to estimate the total number of minerals that exist on Earth (Skinner and Skinner, Reference Skinner and Skinner1980, Hystad et al., Reference Hystad, Downs and Hazen2015a). Rather, herein a scaling relationship in mineral occurrence data is recognised and characterised in order to shed light on another facet of the continuum of abundances and scarcity exhibited by Earth's minerals.

As described in the preceding discussion of mineral hotspots, the identification of minerals, be they well-known or previously undiscovered, requires the somewhat fortuitous convergence of geological processes and human actions. As not all minerals that occur on Earth have been identified yet (Hystad et al., Reference Hystad, Downs and Hazen2015a; Hazen and Ausubel, Reference Hazen and Ausubel2016; Hazen et al., Reference Hazen, Morrison, Krivovichev and Downs2022), and because not all locations of mineral occurrences have been, or perhaps even could be, fully catalogued (Hystad et al., Reference Hystad, Downs, Grew and Hazen2015b), any compilation of the occurrences of minerals must be an underrepresentation of total global mineral diversity. However, the Mindat database is a constantly growing and evolving archive of known minerals, their geological context and geographic occurrence. Though certainly incomplete, Mindat has grown to a sufficient size and scope as to be taken as a reasonably representative summary of broad trends in global mineral distribution. The following evaluates the degree to which the mineral-location pair data proves helpful in understanding trends in the global distribution of mineral diversity.

If a mineral is known to occur only at its initial location of discovery, it is said to be endemic to that site. More than two-thirds of the nearly 6000 mineral species have been identified at 10 or fewer locations, and more than a quarter of the 6000 minerals are known only from a single location (Fig. 4a). The highly endemic nature of the majority of known minerals stands in contrast to the global abundance of a small number of common minerals such that less than 10% of all minerals are known to occur at more than 100 documented locations and less than 3% have been reported from more than 1000 locations; these general abundance relationships are well known both intuitively and qualitatively. When graphing the number of mineral species known to occur at a given number of locations a negative log–log linear relationship is observed:

$${\rm lo}{\rm g}_{10}{\rm F}( \lambda ) = -1.20 \, {\rm lo}{\rm g}_{10}\lambda + 3.19 \ \, ( {r^2 = 0.9975} ) $$

Figure 4. (a) Utilising the community-sourced database Mindat.org to harvest mineral-location pairs for all IMA accepted species in January, 2021, a power-law relationship between the number of species and the number of locations from which they are known is observed with minerals known from 10 or less locations [log₁₀ F(λ) = –1.20 log₁₀ λ + 3.19] which accounts for more than two thirds of all known species. (b) This power-law relationship is found to extend over several orders of magnitude with increasing dispersion around the regression as the logarithm of location frequency increases.

Where F(λ) is a function that describes the frequency of mineral species known to occur at the number of locations λ. This linear relationship is based on a regression of mineral-location data drawn from those minerals known to occur at ten or fewer locations (Fig. 4a), a subset that accounts for more than two-thirds of all known species. Importantly however, this linear relationship is found to also extend over several orders of magnitude of decreasing mineral frequency and increasing mineral-location pair abundance (Fig. 4b). It has been postulated that mineral species diversity could be fractal (Grew et al., Reference Grew, Hystad, Hazen, Krivovichev and Gorelova2017), such that closer study at microscopic scale would result in the identification of many more currently unrecognised species. The presence of these power-law, or fractal, relationships within mineral abundance strongly suggests that it is highly likely the potential for discovery of new minerals will not be exhausted in the near future. The Earth's total mineral inventory has been estimated previously by the ‘large number of rare events’ model (Hystad et al., Reference Hystad, Downs and Hazen2015a).

Dispersion around this power-law trend increases as the number of locations considered expands (Fig. 4b). While this might merely be an inevitable result given the arbitrariness of a non-systematic process of observing and reporting mineral-location pairs, it is sufficiently striking to be worthy of further consideration. The highly skewed nature of the dispersion of mineral-location pair data is most clearly illustrated by reviewing the distribution of location values linked to a single mineral. That is, the set of minerals exhibiting a unique abundance of observed locations (Fig. 5) – recognised as those datapoints falling along the abscissa axis of the graph in Fig. 4b (log₁₀ frequency = 0). The frequency distribution of this representational set of commonly occurring minerals is found to be highly skewed even after taking the logarithm of location frequency (Fig. 5). The power-law relationship calculated from the data in Fig. 4a intersects the abscissa axis within one bin of the modal value of the distribution of this population, thus suggesting that the underlying relationships that govern the large number of rare minerals maintains significant influence in controlling the distribution of common minerals.

Figure 5. Frequency distribution of those mineral-location pair data that plot along the abscissa axis of Fig. 4b in 0.1 log₁₀(λ) bins, illustrating the highly skewed nature of the dispersion of commonly occurring minerals. Importantly, the power-law trend calculated in in Fig. 4a intersects the abscissa axis within one bin of the modal value of this distribution.

Further, those minerals with location data most frequently reported in the Mindat database share some interesting characteristics (Table 1). When considering the ten most frequently reported minerals in the database, six were known to the ancients (effective discovery date of 0), seven are either precious metals or ore minerals, three are minerals commonly associated with the products of chemical weathering of rocks at the Earth's surface or as refractory minerals concentrated by weathering, and two are common minerals found in the continentally abundant rock type granite. Consideration of these most widely recognised species in the Mindat database provides more than just a summary of the extreme tail of the mineral occurrence frequency distribution (Fig. 4b). Rather, from these observations it is possible that several biases could impact the reporting of mineral-location data of common minerals that do not, by and large, impact the mineral-location relationship exhibited by those less common minerals (Fig. 4a). Such biases could act to cause the observed increasing dispersion in the number of reported mineral-location pairs and the volumetric abundance of common minerals. The postulated biases in reporting common mineral locations can take several forms. First the number of location reports can be greater than the proportional abundance (volumetric or geographic) of a mineral species. An overreporting bias of this type exists for precious metals, primary ore minerals, and minerals of unique interest to collectors. In such cases a mineral with a disproportionately high number of reported mineral-location pairs would be shifted to the right of what might be its expected abundance on plots of location frequency distributions given a globally random sampling of mineral occurrences (Fig. 4b). Alternatively, commonly occurring but economically and scientifically less-compelling minerals could be underrepresented in the mineral-location pair data due to a bias against re-reporting these widely distributed minerals, which results in their being shifted to the left on plots of location-frequency distributions. These two biases are probably responsible for a significant fraction of the observed dispersion for minerals with more than 100 reported locations (Fig. 4b).

Table 1. Ten mineral species with the most abundantly reported mineral-location data in the Mindat community-sourced database. Six species were known in antiquity (date of 0), seven are metals or ores, three are associated with chemical weathering at the Earth's surface, and two are common minerals found within the most abundant rock type within the continental crust, granite.

The Earth's most common minerals, however incompletely defined by mineral-location data, must be the product of the co-location of the Earth's most common elements with the most frequently occurring modes of mineral formation (Hazen et al., Reference Hazen, Grew, Downs, Golden and Hystad2015). However, there is an important distinction to be made between those minerals that have a large number of discreet and potentially highly valuable occurrences such as gold and those that make up a significant volume of geological material exposed at or near the Earth's surface, such as feldspar.

From these various considerations it is reasonable to conclude that the analysis of mineral location frequency data is most applicable, without being concerned by community sourced database biases, to those minerals that are rare in occurrence but that also comprise the majority of all known species. Likewise, such an approach is increasingly less applicable to the long tail of the location frequency distribution consisting of a smaller number of minerals with large and increasingly variable location frequencies.

Endemic and cosmopolitan distributions of recently discovered minerals

In addition to recording the geographic distribution of mineral occurrences, the Mindat database includes the date of acceptance of new mineral species by the IMA–CNMNC along with a wealth of information on literature citations of the species, which frequently detail a complex history of understanding, or in some cases misunderstanding and misidentification, of the accepted mineral prior to or after its acceptance. From these data, it is possible to quantify the number of newly recognised minerals approved by the CNMNC in a given year. Because the identification of a new mineral is based upon its recorded occurrence at a specific location – its type locality – in the year of its acceptance, it is expected that the vast majority of all minerals will initially only be known from a single type locality. Rare exceptions to this can occur when minerals are reclassified either due to analytical or technological advances or due to the reassessment of complex mineral series (Leake, Reference Leake1978; Burke and Leake, Reference Burke and Leake2005; Hawthorne et al., Reference Hawthorne, Oberti, Harlow, Maresch, Martin, Schumacher and Welch2012). The assignment of a date has become a formal and official process since the creation of the CNMNC (previously known as the Commission on the Minerals and Mineral Names, CNMMN) in 1959, whereas for all minerals ‘grandfathered’ into the IMA list of accepted minerals prior to that date the official ‘age’ of the mineral species is derived from literature sources.

In many cases, over time, additional locations for the occurrence of known minerals will be documented and added to online databases. Some minerals are ultimately recognised from a large and growing number of locations and can therefore be considered to have a cosmopolitan global distribution, while others remain known from only a small number of locations or are even exclusively endemic to their type locality. The process of ongoing documentation of additional mineral occurrences can best be understood by looking back to the number of new occurrences of minerals identified in previous years. That is, it is possible to use the Mindat database as ‘time machine’ to explore the history of discovery of additional mineral localities of recently discovered minerals. In order to do so, the frequency of occurrence of minerals accepted by the IMA in the years 1990 through 2020 have been evaluated. Due to the database's ongoing growth and evolution, occurrence data for minerals first discovered in those years was harvested from the database on January 19^th, 2021 thereby creating a temporal snapshot of knowledge about the distribution of newly discovered minerals. At that time, all of the 93 minerals accepted during the 2020 year were known from only a single location. Looking further back in time, the percentage of minerals added in previous years that remained endemic to a single location declines in a systematic way (Fig. 6a), such that only 9 of the 47 minerals added in 1990 continue to be known from only a single location in 2020. That is, over the 30 years since their acceptance in 1990, 38 minerals were found in one or more locations beyond their type locality. When considering all the minerals identified between 1990 and 2020, there is a systematic decline in the percentage that remain known only from their type locality that plots along an exponential curve:

$$\% {\rm M } = 10^{( -0.023{\rm Y} - 0.01) }\, ( {r^2 = 0.9282} ) $$

Figure 6. When first discovered, new mineral species are typically exclusively endemic to their type locality. Over time, most minerals are subsequently identified in other locations. (a) The percentage of minerals from a year in the past that are known only from their type locality decreases with increasing time describing an exponential curve [%M = 10^{(–0.23Y – 0.01)}]. (b) Similarly, the average number of known locations for minerals increases with time since their discovery following a linear function [N = 0.18Y + 0.95] such that an additional location is found, on average, every 5.5 years (1/0.18). The y-intercept value of 0.95 confirms the notion that most minerals are initially known from only one location.

where %M is the percentage of minerals from a year in the past Y that are known from only their type locality (Fig. 6a).

A second way to characterise the discovery of additional mineral locations is to calculate the average number of known localities for all minerals accepted by the IMA in a given year using the same snapshot of 1990 to 2020 data. In this case, a linear increase in the average number of known locations of minerals discovered in a given year with increasing age is observed (Fig. 6b). While dispersion around this trend increases with age, the relationship holds very strongly for minerals added to the database over the 15 years preceding the snapshot. The observed linear relationship is defined by the equation:

$${\rm N\ } = 0.18{\rm Y} + 0.95 \ \, ( {r^2 = 0.7871} ) $$

Where N is the average number of localities per mineral and Y is the years that have transpired since the acceptance of the mineral into the IMA database. Thus, on average, over the last thirty years, an additional locality of occurrence for recently discovered minerals is reported every 5.5 years (1/0.18 y), while the y-intercept value (0.95) supports the notion that newly discovered minerals are commonly known only from their type location. In both of these treatments, mineral abundance data has been normalised to the total number of minerals discovered in a given year in order to correct for temporal variation in the number of minerals identified annually.

When extending the analysis of minerals known from a single location back in time, both expected and unexpected results are observed. First, as expected, most endemic mineral species have only recently been discovered (Fig. 7a). For the majority of these minerals, future workers can be expected to recognise their occurrence in other locations (Fig. 6a and b). Second, and perhaps quite unexpectedly, there is a group of minerals that were first recognised long ago that have continued to remain known from only a single location, the date of discovery of some of these species extends back to the 19^th Century (Fig. 7a). Unlike the representation of endemic mineral species in Fig. 6a wherein the percentage of endemic minerals per year was used, this graph displays the absolute number of minerals that have remained endemic to their type locality since their discovery. Furthermore, since most widely distributed species have probably been discovered already, and as research focuses on known diversity hotspots with enhanced technology, the proportion of minerals with high endemicity is likely to increase.

Figure 7. Most minerals that are known from only their type locality have been discovered recently. However, there are some species that were first discovered in the past that remain endemic to their type locality for extended periods (a). Conversely, some recently discovered minerals are now known from a relatively large number of locations. The number of cosmopolitan species (here defined as 50 or more mineral-location pairs) increases with time. When aggregating the number of such species per decade, this increase follows an exponential curve [N_c = 10^{(0.26D + 0.28)}] (b).

These data suggest that it is unlikely that a previously unknown mineral will be discovered that comprises a significant volume of the Earth's lithosphere. However, workers will probably continue to find minerals that are subsequently identified at a relatively large number of locations globally. In order to evaluate this aspect of the distribution of mineral species those minerals with 50 or more known locations in the Mindat database are considered a cosmopolitan species. Though this is a somewhat arbitrary distinction based upon less than systematically obtained data, it is significant that the cutoff of 50 locations is a value which is significantly less than that point in the frequency of locations data where dispersion around the observed power-law linear relationship becomes pronounced (Fig. 4b). Because the discovery of both new minerals and new locations of previously known minerals is ongoing, for this analysis the January, 2021 snapshot of the Mindat database is used to tabulate the total number of cosmopolitan species that had first been identified in previous decades.

Of the 1,084 minerals recognised during the years 2011 to 2020, only two are found to have subsequently been recognised at 50 or more locations (clino-suenoite and ‘eleonorite’). Over the preceding six decades the number of cosmopolitan mineral species identified per decade increases such that during the 1960s 37 minerals were identified that in 2021 fit the definition of a cosmopolitan species (Fig. 7b). As such, the number of cosmopolitan species per decade is found to follow the exponential growth function:

$${\rm N}_{\rm c} = 10^{( 0.26{\rm D \, + \, 0.28}) } \, ( {r^2 = 0.9971} ) $$

Where N_c is the number of cosmopolitan species now recognised from previous decades D. An increase in the number of cosmopolitan species with age is perhaps not inherently surprising, however the highly systematic way in which the number grows suggests that a small but significant number of recently recognised species will ultimately be recognised as cosmopolitan through the efforts of future workers.