The Taxonomy of Mineral Occurrence Rarity and Endemicity

28 Pages·2022·1.353 MB·English

by  Liubomyr Gavryliv, Vitalii Ponomar, Marko Bermanec, Marián Putiš

731
TheCanadianMineralogist
Vol.60,pp.731-758(2022)
DOI:10.3749/canmin.2200010
THE TAXONOMY OF MINERAL OCCURRENCE RARITY AND ENDEMICITY
LIUBOMYR GAVRYLIV§
ComeniusUniversity,FacultyofNaturalSciences,DepartmentofMineralogy,PetrologyandEconomicGeology,
Ilkovicˇova6,84104,Bratislava,Slovakia
VITALIIPONOMAR
UniversityofOulu,FacultyofTechnology,FiberandParticleEngineeringResearchUnit,
PenttiKaiterankatu1,90014Oulu,Finland
MARKOBERMANEC
UniversityofBern,InstituteofGeologicalSciences,Baltzerstrasse1þ3,CH-3012Bern,Switzerland
MARIA´N PUTISˇ
ComeniusUniversity,FacultyofNaturalSciences,DepartmentofMineralogy,PetrologyandEconomicGeology,
Ilkovicˇova6,84104,Bratislava,Slovakia
ABSTRACT
NearlyahalfofknownIMA-approvedminerals(asofNovember2021)arereportedfromfourlocalitiesorfewerandso
may be considered rare mineral species. These minerals form a continuum with more common species (e.g., rock-forming
minerals),allofwhichconstituteimportantconstituentsofEarthandcontributorstoitsdynamics.Tobetterunderstandthe
taxonomyofmineralrarity,evaluationshavebeenmadeonthebasisofk-meansclusteringandkerneldensityestimationof
one-dimensionaldataonmineraloccurrencemetrics.Resultsfromsecond-andthird-degreepolynomialregressionanalyses
indicatethepresenceofadivergencebetweentheobservednumberofendemicmineralsdiscoveredsince2000andthosethat
arelikelytorepresent‘‘true’’endemicspecies.Thesymmetryindex,calculatedusingtheapproachofUrusovforeachrarity
cluster,revealsagradualdecreasefromubiquitoustoendemicfrom0.64to0.47.Anetworkanalysisofelementco-occurrences
withineachrarityclustersuggeststheexistenceofatleastthreedifferentcommunitieshavingsimilargeochemicalaffinities;
thelattermayreflecttherelativeabundanceofmineralstheirelementstendtoform.Theanalysisofelementco-occurrence
matriceswithineachgroupindicatesthatcrustalabundanceisnottheonlyfactorcontrollingthetotalnumberofmineralseach
elementtendstoform.Othersignificantfactorsinclude:(1)thegeochemicalaffinitytotheprincipalelementinthegroup(i.e.,
sulfurfor chalcophileandoxygenfor lithophileelements)and(2) dispersionoftheprincipalelementthroughgeochemical
processes.Thereisapositivecorrelationbetweenthelithophileelementgroup’sabundanceintheEarth’scrustandthenumber
ofcommonmineralstheytendtoform,butanegativecorrelationwiththenumberofrarespecies.
Keywords:rarity,endemic minerals, data analysis,symmetry index.
INTRODUCTION characteristicassociatedwithahighriskofextinction,
implying that once a biological species becomes
From the biological point of view, rarity may be extinct, they will not re-emerge (Vermeij &
considered evidence that a species has characteristics Grosberg 2018). In mineral ecology, most of what
that differ from a more common taxon (Kunin & are considered endemic minerals are not likely to
Gaston 1993). In bioecology, rarity is a population disappear, except those falling into category 3 of
§Correspondingauthore-mailaddress:[email protected]
Downloaded from http://pubs.geoscienceworld.org/canmin/article-pdf/60/5/731/5721758/i1499-1276-60-5-731.pdf
by Mineralogical Association of Canada user
on 17 November 2022
732 THECANADIANMINERALOGIST
Hazen & Ausubel (2016). Further, metamict minerals metric based on the number of localities where
and those formed in the mantle may be considered minerals have been recorded close to, or at, the
exceptions. However, the question of our current surfaceof theEarth.
abilitytorecognize‘‘mineralfossils’’shouldberaised Hazen&Ausubel(2016)suggestedaprototypeof
apartfrom these minerals. Possibly,thegeneral rarity ataxonomyofmineralogicalraritybasedprimarilyon
of the bulk of endemic minerals will be diminished thetaxonomyofbiologicalrarity.Accordingtothis,a
through the application of new analytical methods to mineralmaybeconsideredrareifitisknownfromfive
identify such minerals and the study of hard-to-reach or fewer localities. Furthermore, it was proposed that
locations,includingthatwhichhaveanextraterrestrial rare species generally conform to one of four distinct
origin.Forinstance,ferroskutterudite,(Fe,Co)As,was categories (with slight overlaps) based on the reason
first reported from dolomite-calcite veins of the for their rarity: (1) a restricted P-T-X range, (2) rare
Noril’sk ore field (Russian Federation; Spiridonov et combinations of essential elements, (3) instability
al. 2007) and was considered endemic until it was under prolonged exposure to ambient conditions, and
described from a second locality, the Puy-les-Vignes (4) difficulties in the recognition of the mineral or
breccia pipe, Massif Central, France (Staude et al. challenges associated withits discovery.
2012). It has been subsequently discovered at As large-number-of-rare-event (LNRE) models
Wittichen, Schwarzwald, SW Germany (Harlaux et depend primarily on the distribution of rarer species
al. 2015), and from Pira Inferida Yard, Fenugu Sibiri (Hazenetal.2016,2015a,Hystadetal.2019b,Grew
Mine (Sardinia, Italy). By contrast, harstigite, Ca Mn et al. 2016, 2017, Liu et al. 2018, Hazen et al. 2017,
6
Be (SiO ) (Si O ) (OH) , known only from its type Morrisonetal.2017),itisnotedthatraremineralsare
4 4 2 2 7 2 2
locality at Harstigen Mine, Persberg ore district vitaltodeveloping amore completeunderstandingof
(Sweden),hasbeenanendemicmineralfor136years overall mineral diversity and in predicting the total
(Flink1886). numberofmineralspeciesyet-to-bediscovered.Based
Nearly 21% (1232) of all IMA-approved minerals on predictive population models, the total number of
(5762 as of November 23, 2021) are known from a ‘missing’ minerals in several different subsets has
single locality, thus making them endemic mineral been evaluated for a range of elements, including: C
species.Another28%(1616)occuratbetween2and5 (Morrison etal.2020, Hazen etal. 2016),Co (Hazen
localities, meaning that almost half of all known etal.2017),Cr(Liuetal.2017),B(Grewetal.2016),
minerals are rare according to the systematics of Li(Grewetal.2019),andV(Liuetal.2018)minerals.
Hazen & Ausubel (2016), the other half being Since the predicted number of undiscovered minerals
considered common or widespread. Those that are isbelievedtohavebeenunderestimated,owingtothe
considered as being widespread are typically rock- acceleration in the rate of the mineral discovery over
forming minerals, which play critical roles in reflect- the last decade (Hazen et al. 2015b), Hystad et al.
ing the Earth’s composition and dynamics. The crust (2019a) employed Bayesian methods in an effort to
comprises almost 2.5% of the Earth’s volume, with estimatethetotalnumberofmineralspeciesthatmay
fewerthan100mineralsmakingup99%ofit(Hazen exist within the Earth’s crust, obtaining a number of
&Ausubel2016).Ofthese,90%aresilicatesand75% ~3700 mineral species which have not yet been
are tectosilicates (Deer et al. 2004). Despite being discovered.Hazen&Ausubel(2016)emphasizedthat
widespread in the crust, 22% of the known tectosili- the precision of mineral ecology studies, which
cates(i.e.,40species)arerecordedatonlyonelocality employ statistical methods, is primarily dominated
on the Earth’s surface, indicating the importance of bythosemineralspeciesfoundatoneortwolocalities.
discriminating between the rarity taxonomy of those Similar to biological ecosystems, where only a few
minerals directly accessible to us and those that are species are widespread, but most species are rare, it
not. waspositedthattheEarth’smineralsmightalsofollow
Another example is bridgmanite, which has been asimilardistributionmodel.
estimatedtoconstituteupto93%ofthelowermantle Furthermore, Hazen et al. (2015a) note that up to
(Tschauneretal.2014).However,ithasbeenrecorded 15,000 mineral species could plausibly be discovered
at only one locality at the surface of the Earth, on Earth-like planetary objects. Of course, this
probably owing to its instability under ambient depends on the possibility that these bodies possess
conditions (category 2 according to Hazen & environmentswithP-T-Xconditionsthatareeithernot
Ausubel 2016). As such, bridgmanite may be consid- present,orremaintobediscoveredonEarth.However,
ered an endemic mineral sensu stricto, but a even if these bodies began as did Earth, it might be
widespread mineral sensu lato. Here, mineral rarity expected that there would be a difference in the
isdefinedbasedonthedistributionofamineralwithin numberofraremineralsbetweenthosefoundonthem
the available geospatial data, the latter representing a and those found on Earth. The latter implies that
Downloaded from http://pubs.geoscienceworld.org/canmin/article-pdf/60/5/731/5721758/i1499-1276-60-5-731.pdf
by Mineralogical Association of Canada user
on 17 November 2022
THETAXONOMYOFMINERALOCCURRENCERARITYANDENDEMICITY 733
mineralrarity andabundancecannotyetbeexplained The present paper: (1) provides a thorough and
by a completely deterministic model, at least not reliable taxonomy of mineral rarity and classification
without the introduction of additional parameters ofIMA-approvedmineralsintoraritygroupsbasedon
which are notyetknown orsufficiently understood. dataanalysis;(2)comparesthesecategoriesinthelight
The issue of mineral rarity was also highlighted oftheirdiscoveryhistoryandcompositioninorderto
fromthecrystalsymmetrypointofviewintheworks reduce the dimensionality, increase interpretability of
of Urusov (2002, 2007), where the concept of thetaxonomy,andminimizetheinformationloss;and
‘‘evolutionary desymmetrization of mineral matter’’ (3)assesses theevolution ofmineral rarity.
was proposed. This underpins the gradual increase in
thepercentageoflow-symmetry(particularlytriclinic) MATERIALS AND METHODS
mineral species as compared to those of higher-
symmetry classes. In this context, Urusov (2007) The basic data used in this study comes from the
mentions several mechanisms by which secondary, list of IMA-approved mineral species, including their
lower-symmetry minerals form at the expense of mineral formulae, crystal systems, locality counts,
higher-symmetry species. The general process here is discovery years, and classification within the Nickel-
one that follows a passive mineral and symmetry Strunzclassificationscheme.Thesewereappendedto
evolutionary model, similar to that as proposed by through subsequent data searches and extractionfrom
Krivovichev et al. (2018): it implies that while new otherresources.Someofthisdataisprovidedbyweb
mineral species of lower symmetry are formed, the resources and some is accessible through hard-copy
precursor, older mineral species continue to be form publications. The bulk of information on the crystal
and be produced, i.e., they do not disappear entirely. chemistry of minerals, their occurrence, associated
Thisphenomenonhas ledto arelativeincrease inthe minerals, and discovery localities was accessed
percentage of rare minerals (mostly lower symmetry) through digital versions of The American Mineralo-
discovered (often within a single deposit and in very gist, The Canadian Mineralogist, and Mineralogical
low abundance) over the last five decades primarily Magazine journals and reviewed afterward. The IMA
through the application of high-resolution analytical
list served as a primary skeleton of information and
techniques. This suggests that a hypothesis of a
wassupplementedwithdatacomingfromtheoriginal
‘‘natural selection’’ algorithm may be applied to the
literature.
mineralkingdom,underwhicheverymineraltendsto
minimize desymmetrization to ensure stability. The Materials
latteristheprincipleofminimumdesymmetrizationas
proposed by Urusov (2002). Accordingly, large-scale
TheIMAListofMineralSpecies.Theofficiallistof
globalprocessesintheEarth’scrustfavordesymmet-
IMA-approved mineral species (http://cnmnc.main.jp/
rization in the minerals that develop. However, this
imalist.htm) is alsoaccessible via theRRUFF Project
tendency could be reduced in specific environments
(https://RRUFF.info/IMA)(Lafuenteetal.2016).The
with extreme geochemical conditions, precisely those
RRUFF Project IMA list allows users to search over
where most rarespecies haveformed.
5740 (as of November 12, 2021) species by mineral
Rarity,inthecontextofthediscussionpresented,is
name,composition,crystalsystem,spacegroup,point
consideredmoreasarelativeconceptthananabsolute
group, unit-cell parameters, origin, paragenetic mode,
one. Mineral species are considered relatively rare
IMA status, and even water solubility. Additionally,
compared with the abundance of other species, or
theRRUFFresourceprovidesdataoncrystalstructure
based on their sharing unique crystal-chemical prop-
groups, oldest known age, Raman spectra, and other
ertiesandrestrictedP-T-Xstabilityranges.Therefore,
physical properties.
the demarcation point wherein a mineral species is
definedasbeingrarebecomessubjective.Thefactthat The Mineral Evolution Database (MED). The
a mineral species has been discovered at many Mineral Evolution Database (Golden et al. 2016),
geographic localities cannot be considered a valid designed primarily for supporting mineral evolution
indicatorastowhetheramineralmaybeconsideredas and ecology studies, is another resource freely
endemic or not and thus is insufficient to completely accessible through RRUFF Project (https://RRUFF.
address the taxonomy issue. In this context, a new, info/Evolution). The MED contains mineral locality
alternative point of view on the issue is provided, data extracted from mindat.org. As of November 14,
including the presentation of a taxonomy proposal 2021,theMEDdataon810,907mineral-localitypairs
based on the study of mineral rarity as an absolute isavailable.Additionally,thedatabaseallowsretrieval
measure and deciphering the similarities within the of subsets of mineral-locality pairs through years
rarityclassesusingmachine-learning(ML)techniques. between 2016 and 2020. The latter is extremely
Downloaded from http://pubs.geoscienceworld.org/canmin/article-pdf/60/5/731/5721758/i1499-1276-60-5-731.pdf
by Mineralogical Association of Canada user
on 17 November 2022
734 THECANADIANMINERALOGIST
helpful in assessing the evolution of rarity and within the defined rarity groups. They are: (1) data
endemicitywithtime. cleaning,(2)datatransformation,and(3)dataparsing
Athena.TheAthenamineraldatabasewasthefirst and normalization to at least a second normal form
completemineraldatabaseontheweb,createdduring (2NF) where appropriate. In addition, two unsuper-
1986–1987 at the Department of Mineralogy at the visedmachinelearning(ML)techniqueswereusedfor
Geneva Natural History Museum. In 1994, the testing the hypotheses in regard to data distribution:
database was published online; since then, it has (1) k-means clustering and kernel density estimation
become accessible to the geoscientific community. (KDE) of unlabeled one-dimensional data for data
The Nickel-Strunz classification used in the current classification and (2) ordinary least-squares linear
research was kindly provided by Pierre Perroud, the regression models with second- and third-degree
founder of Athena (https://athena.unige.ch/athena/), polynomial feature transforms for predicting the
withhiswritten permission. ‘‘true’’ rate of mineral discoveries. Furthermore, a
HandbookofMineralogy.HandbookofMineralogy network analysis of element co-occurrences was
(http://www.handbookofmineralogy.org) is another employed to encode the interactions between mineral
web resource for accessing data on 4988 IMA- associationsof severalrarity groups.
approved minerals (as of December 2, 2021), main- Networkcommunitystructureswerecomputedand
tained by the Mineralogical Society of America measured through agglomerative and division com-
(MSA) since 2001. A variety of data is stored under munity detection algorithms known as the Girvan-
the website: crystal data, physical properties, optical Newman algorithm and a greedy modularity maximi-
properties, unit-cell data, occurrence, association, zationbasedontheClauset-Newman-Moorealgorithm
distribution,name origins,and references. (Clausetetal.2004).Greedymodularitymaximization
Mindat. In rare cases, the number of occurrences focusesonidentifyingthosecommunitiesthatproduce
andmineralformulaeofsomeraremineralswascross- the greatest increase in modularity, beginning with
checked with the online mineral database Mindat each node in its community. On the other hand, the
(www.mindat.org) in November 2021. The localities Girvan-Newman algorithm detects communities by
returned were then screened visually and analyzed steadily removing edges from the original graph. At
through external resources to decide whether these eachstep,thealgorithmremovesthe‘‘mostvaluable’’
localitiesconstitute differentgeological units ornot. edge of the network, traditionally this being the edge
All web resources cited above, other sources used with the highest betweenness centrality. The number
in research negligibly, and online and hard-copy ofelementsco-occurrencewasusedastheattributeto
publications used to develop the core analytics of the measuretheweight ofeachedge.
research, were accessed under ‘‘fair use’’ conditions The work follows PEP-8 rules of Rossum et al.
governed by The Copyright Act of 1976 — a United (2001) as much as possible, and the authors recom-
States copyright law (17 USC § 107) and what is mend that other developers in geoscientific areas
known as ‘‘fair dealing’’ in other countries (Canada, follow generally accepted code quality guides. A
Australia, UK, EU, and its Member States). All the standardizedwayofbuildingthedatawarehousesand
datausedinthisresearchresidesinthepublicdomain analyticspipelinesisnotonlyasuggestion,butrather
andisfreely accessiblethrough webinterfaces. ademanddictated byprogrammingethics. Moreover,
All the code developed during the research is storing the code and history of commits in version-
provided under MIT license in the public GitHub control systems (e.g., GitHub, GitLab, or Bitbucket)
repository ‘‘mineral-rarity’’, accessible through an under open-access conditions to track and to manage
open-source geoscientific computing organization changes to code developed within the scope of
called ‘‘mineralogy-rocks’’ (https://github.com/ research, is strongly encouraged. The code repository
mineralogy-rocks/mineral-rarity). providedherecouldbetreatedasaguidetosettingup
the local development environment, analyzing miner-
Methodology alogicaldatausingmoderntools,andwritingdescrip-
tiveand meaningful commitshistory.
Python3.10.1wasusedalongwithsharedscientific
libraries (NumPy, Pandas, scikit-learn, NetworkX, Key definitions
matplotlib) to build up the analytics warehouse and
compute the dependencies within the collected data. Afewkeydefinitionsareprovidedinthissectionto
Several data analysis algorithms were employed for emphasize the importance of understanding the
parsing text data like mineral formulae, encoding terminologyused inthis paper.
categorical data into binary (‘‘one-hot encoding’’ or Rarity. While rarity is considered as an absolute,
OHE), and calculating the co-occurrence matrices notrelative,metric,anideaisputforwardthatoncea
Downloaded from http://pubs.geoscienceworld.org/canmin/article-pdf/60/5/731/5721758/i1499-1276-60-5-731.pdf
by Mineralogical Association of Canada user
on 17 November 2022
THETAXONOMYOFMINERALOCCURRENCERARITYANDENDEMICITY 735
species’ rarity status is assigned, it can shift toward a similar in terms of rarity. For instance, charoite is
more common category (case 1) and, in very rare recorded from only three localities, and abramovite
cases,towardararerone(case 2)withtime.Forcase occurs only at Kudriavy volcano, Kuril Islands,
1, the rarity of a mineral follows a ‘‘normal rarity Russian Federation. Both are considered rare species
flow’’, which is typical behavior of the majority of and are therefore similar from a taxonomical point of
species.Whenamineralisdiscoveredatnlocalities,it view.
may subsequently be discovered at other localities However, charoite’s abundance at the recorded
(nþ1), thus shifting its rarity index toward that of a localitiesissohighthatthename‘‘charoitite’’hasbeen
morecommonmineral.However,inexceptionalcases, appliedtothoserocksconsistingofmorethan50%of
a mineral recorded at n localities may have been charoite, along with variable proportions of quartz,
erroneously reported from one locality, meaning that aegirine, and K-feldspar. In contrast, abramovite
theabsolutenumberoflocalitieswherethemineralis occurs as tiny elongated lamellar-shaped crystals, up
recorded from is n–1. For instance, in 2011, jacutin- to 130.2 mm in size, that are barely visible to the
gaite was erroneously reported from Libsˇta´t copper naked eye. Therefore, while charoite and abramovite
mines (Kosˇˇta´lov, Semily District, Liberec Region, aresimilarintermsofthelocality-countsmetric,they
Czech Republic), due to a mistake developed during
are different in terms of their relative abundances in
thin-section polishing (Malecetal.2012).
the upper crust. A rarity taxonomy must consider the
Another example is samarskite-(Yb), an endemic
overallabundanceofamineralinadditiontoitsspatial
mineralthatwaserroneouslyreportedasoccurringata
distributiontobeasrobustandcompleteasispossible.
secondary locality in the Pryor Mountains (Big Horn
However, an abundance parameter could not be
Co., Montana, USA). Upon detailed examination, it
introduced into the research due to a lack of data
was demonstrated that the chemical composition did
relating to the relative size or morphology of all the
notinfactmatchthatofsamarskite-(Yb).Assuch,the
minerals considered. Of course, these discrepancies
mineral rarity index would necessarily shift toward
impactmoregreatlyonrelativelyraremineralspecies
that of a rarer one, i.e., following an ‘‘inverse rarity
thanthosethat are widespread.
flow’’.
Discoveryyear.Inordertoassesstherateatwhich
Locality. Particular attention should be drawn to
minerals have been discovered, which can then be
what defines a mineral locality, especially when one
employed to develop regression models, the year in
has notyetbeen standardized. Insome instances,this
whichamineralwasfirstdiscoveredwasconsideredas
termcanhaveaminimalmeaning,suchasalocalityof
aparameter.Importantly,thediscoveryyearisdefined
a mineral found in a thin section from a sample
as the year of the first publication or report about the
collectedatasetofexactcoordinates.Othertimes,this
mineral,not theIMAapproval orredefinition year.
termhasamuchbroaderandlessdefinedmeaning,for
Mineral abundance. When comparing the abun-
example,anoutcrop,amine,orageologicformation.
danceofelementsintheEarth’scrusttothenumberof
Thelatterintroducesbiasinthedataset,whichprefers
mineralswhereagivenelementispresentinessential
microlocalities,theseoftencorrespondingtodifferent
quantities, a simple rule was followed: if a chemical
outcrops of the same rock formation or to a different
element is present in a stoichiometric formula, it is
levelwithin an undergroundmine.
considered an essential constituent. This metric is
The data modeling presented in this paper is
dependent on the correct number of the localities for calleda‘‘mineralclarke’’(Krivovichevetal.2018),a
a given mineral species and other data used in proportion of minerals containing a specific element
conjunction with the locality counts. While the relative to all those minerals present in the data set.
localities used in this research constitute a data point TheKrivovichevetal.(2018)approachwasfollowed,
(geographical location of mineral occurrence), it also and this parameter was calculated as a proportion of
introducesanimmeasurablebiasintotheresultsforthe minerals containing the element but only within the
reasons mentionedabove. Additional caveats include: members of a specific rarity group, called ‘‘mineral
(1) the number of occurrences does not necessarily abundance’’forclarity(i.e.,amineralabundanceofSi
reflecttheabundanceofagivenmineralintheEarth’s meansaproportionofmineralswhereSiispresentin
crust; (2) the abundance of a single phase at the all minerals within the rarity group under consider-
locality is not considered, and (3) frequently, a few ation). Technically, the mineral abundance of each
localities represent different portions of a given element was calculated using a regular expression
quarry, open pit, or mine, all related to the same ore extraction of unique elements from every IMA-
body,geologicalformation,orstratigraphicunit.Inthe approved mineral formula. This data, grouped by
firstcase,whenconsideringtwodifferentrarespecies mineral species, was used to calculate co-occurrence
recorded at fewer than five localities, they are very matrices of elements within each rarity group and
Downloaded from http://pubs.geoscienceworld.org/canmin/article-pdf/60/5/731/5721758/i1499-1276-60-5-731.pdf
by Mineralogical Association of Canada user
on 17 November 2022
736 THECANADIANMINERALOGIST
FIG.1.Mineral-localitypairsusing:(a)rawdataand(b)log-transform(base10).
compare their crustal abundance to the observed within this type of data, and to further interpret the
distributionwithin minerals. resultsinlightof theclassification obtained.
Themineralversuslocalitycountspairswereused
Dataclusteringandclassification asentrydatafortheanalysis,sincethegoalduringthis
step was to find the similarities within localities data
The raw localities data is hard to visualize and
ratherthantesthypotheses.Datapreparationinvolved
interpretbecauseofitscomplexityandavastspreadof
data cleaning and transformation, including feature
data(Fig.1)—somemineralsarerecordedatonlyone
scaling—a common requirement for many machine
locality (gaotaiite) while others are recorded at
learning estimators, so that individual features look
.60,000 localities (quartz). A common technique to
likestandardnormallydistributeddata(e.g.,Gaussian
delineate raw one-dimensional data into categories is
withzeromean and unit variance).
to calculate the frequency distribution over the 25%,
Twowaysto placethedata attributes onthesame
50%, and 75% quantiles. In the case of mineral-
scale were considered: so-called min-max scaling
localitypairs,25%correspondstoonelocality,50%to
(normalization) and standardization. Considering that
4, and 75% to 18 localities. The latter appears
mineral-localitycountpairsareleft-skewed(owingto
reasonableenoughandsuggestsapreliminaryskeleton
a large group of minerals occurring at only a few
forthetaxonomy asfollows:
localities), log-transformation (base 10), furthered by
standardization, was employed to achieve the unit
(1) mineralsoccurringat1–4localitiesmakeup46%
variance and to reduce the impact of outliers on the
of the data volume. All of these species are rare,
clustering. The standardization component included
while those found at exactly one locality are
removingthemean and scalingto unit-variance.
endemic;
K-means is an unsupervised machine learning
(2) mineralsfoundat5–18localitiesconstitutenearly
technique commonly used to organize a sizable
26% of data volume and could be regarded as
multivariatedatasetintoclassesandrecognizestypical
transitional betweenrare and commonminerals;
characteristics. For the k-means algorithm, often
(3) mineralsrecordedat.18localitiesmakeup28%
referred to as Lloyd’s algorithm (Lloyd 1982), there
of data volumeand are relatively common.
arethreeprincipalhyperparameterstosetuptodefine
Based on the preliminary examination of the themodel’sconfiguration:(1)initialvaluesofclusters,
quartiles, a set of clustering techniques of unlabeled (2) distance measures, and (3) the number of clusters
data was employed to separate samples into n groups (k value). The k-meansþþ initialization was used to
of equal variance, to identify similar rarity groups select initial cluster centers for clustering, with 10 as
Downloaded from http://pubs.geoscienceworld.org/canmin/article-pdf/60/5/731/5721758/i1499-1276-60-5-731.pdf
by Mineralogical Association of Canada user
on 17 November 2022
THETAXONOMYOFMINERALOCCURRENCERARITYANDENDEMICITY 737
FIG. 2. Visual representation of the Elbow method: within- FIG.3.KDEplotscalculatedusingtheEpanechnikov(1969)
cluster sum of squares (WCSS) and the number of
method on one-dimensional standardized and scaled
clusters.
localitycountswithvariousbandwidths.
thenumberoftimesthek-meansalgorithmwillberun
in the analysis. Results coming from this choice
withdifferentcentroidseeds,and300asthemaximum
suggest the existence of the following clusters within
number of iterations of the k-means algorithm for a
thedata:
single run. In addition, the k-meansþþ allows the
initialization of the centroids distant from each other. (1) highly dense cluster with minerals occurring at 1
The number of clusters (k) is the most critical locality;
hyperparameter in k-means clustering. In order to (2) 2–4localities;
calculate the optimal k, both elbow and silhouette (3) 5–16localities;
(Rousseeuw 1987) methods wereused.
(4) 17–70localities;
Severalk-meanswererun,incrementedkwitheach
(5) mineralsoccurring at .70localities.
iteration, and recorded the sum of the squared
distances(within-clustersumofthesquare)witheach Another powerful method to identify intervals
run to perform the empirical elbow method (Fig. 2). within a one-dimensional array of data is KDE, often
The‘‘elbowpoint’’iswherethewithin-clustersumof referred to as the Parzen-Rosenblatt window method
square (WCSS) curve starts to bend. The x-value of (Rosenblatt1956,Parzen1962),anon-parametricway
thispointfortheuseddatasetisbetweenk¼4andk¼ to estimate the probability density function of a
7,meaningthattheoptimalnumberofclusterswould random variable. The KDE method is also regarded
be within thisrange. as an unsupervised clustering approach and is
Thesilhouettecoefficientisanothermethodtofind instrumental in estimating the class-conditional mar-
the optimal number of clusters and measures cluster ginal densities of data. During the study, Gaussian,
cohesion and separation. The technique allows the Epanechnikov,andtophat(rectangular)methodswere
identification of how well each object has been used to calculate KDE over various bandwidth
classified based on two factors: (1) how similar the parameters from 0.1 to 0.9 at 0.05 step. The
dataobjectistootherobjectsinitscluster(cohesion) Epanechnikov (1969) method revealed the highest
and(2)howdifferentthedataobjectisfromobjectsin performance and data fit (Fig. 3). The bandwidth
other nearestcluster (separation). affects how ‘‘smooth’’ the resulting KDE curve is,
Despitealloftheclustersbeingabovetheaverage controlling the tradeoff between bias and variance in
silhouettescores,thesilhouetteanalysisshowsthatthe the result. This approach was taken to determine the
cluster values of 2–4 are a poor choice for the given optimal number of clusters by first finding dense
data,duetowidefluctuationsinthesizeoftheclusters regions in data and focusing on features described by
that result. Silhouette analysis is more ambivalent in localmaxima(modes)andlocalminima(anti-modes)
decidingbetween5and7.Whentheclusternumberis (Bugrien et al. 2014). Accordingly, KDE using the
equal to 5, all the clusters are more or less of similar Epanechnikovmethodimpliestheexistenceofatleast
thickness. For this study, and to better differentiate 6 margins within the data: 1, 2, 4, 5, and between 12
mineralsoccurringatpreciselyonelocality,akvalue and 20 localities, depending on the bandwidth
¼5wasselectedfortheinitialnumberofclustersused parameter.
Downloaded from http://pubs.geoscienceworld.org/canmin/article-pdf/60/5/731/5721758/i1499-1276-60-5-731.pdf
by Mineralogical Association of Canada user
on 17 November 2022
738 THECANADIANMINERALOGIST
TABLE1.THETAXONOMYOFRARITYGROUPS ofmineraldiscoveryandthediscoveryyear.Thelatter
iscovered inthefollowing subsection ofthepaper.
Rarity Rarity Numberof Numberof
group subgroup Index localities minerals b) R:rare subgroup
Rare Endemic RE 1 1232 These minerals are not endemic anymore, but are
Rare RR 2–4 1473 stillvery rare,taxonomically.
Transitional Rare TR 5–16 1313
Ubiquitous TU 17–70 840 2. T: transitional group – minerals occurring at 5–70
localities (2153 minerals):
Ubiquitous U .70 701
The term ‘‘transitional species’’ designates those
speciesthatarenolongerrarebutarenotyetcommon
THE TAXONOMY OF MINERAL RARITY enough at the same time, i.e., they are transitional
betweenthesetwocategories.Generally,thesespecies
It must be noted that the categorization based on can relatively quickly transform through a ‘‘normal
the k-means clustering results, the KDE implications, rarityflow’’,duetotheirdiscoveryatnewlocationsor
and quantile assessment broadly intersects, especially the intensive application of new analytical methods.
intherangeofrarerspecies,sincemorethanahalfof For instance, more than 4500 IMA-approved species
thedatavolumeisconcentratedwithintherangeof1– were discovered during the period 1950–2021. Once
4 localities. Therefore, all the results were taken into discovered, almost every mineral was regarded as
account, and the locality counts data were classified endemic or rare. However, some of them were later
into the following groups (Table 1), each of which discovered at enough additional localities to shift the
represents therarity taxonomy ofa mineralspecies: rarity status of these species toward a more common
state, into a ‘‘transitional state’’, in this case. The
1. R:raregroup–mineralsoccurringat,5localities transitionalspeciesaredividedintotwosubcategories,
(2705 minerals) delineatingthetypeof thetransition:
This group is well-described byHazen & Ausubel a) R:rare subgroup
(2016),whodefined‘‘rare’’mineralsasthoserecorded
fromfiveorfewerlocalities.Whiletheywerethefirst Themineralsofthissubgroupshouldbeconsidered
to make an in-depth analysis of mineral rarity and to rarewithinabroaderextent.However,theyarehighly
likely to become common and transfer into the next
pose the question in regard to taxonomy, this paper
stage withthecontinuation ofmineral exploration.
recommends limiting this range to 1–4, since all
algorithms, especially the KDE, detect an extremum
b) U: ubiquitoussubgroup
between4and5localities.Additionally,theraregroup
is further split into two distinct and dense subcatego- In contrast, the minerals of this subgroup are no
ries: longerconsideredrare.Theyarenotlikelytobecome
rareby‘‘inverserarityflow’’,andtheytendtobecome
a) E:endemicsubgroup ubiquitous.
Once a new mineral is discovered, it is often 3. U: ubiquitous group – minerals occurring at .70
reported as endemic unintentionally. For instance, of localities (701 intotal).
65 minerals approved by IMA in 2021, 57 were
reported from only one locality (as of November 11, Thesemaybeconsideredasrock-formingminerals
thatare relatively widespread in distribution.
2021) and thus constitute endemic species. However,
nitscheite, a new endemic mineral with a uranyl-
‘‘True’’ endemicity
sulfatesheet,wasfirstreportedfromtheGreenLizard
Mine(Utah,USA)andsubsequentlydiscoveredatthe Itisnotedthattheproportionofobservedendemic
Krunkelbach Valley Uranium deposit (Freiburg Re- minerals has increased steadily since 1800 (Fig. 4),
gion, Germany), shortly after the discovery of the increasingfrom12.5%in1839to87.6%in2021,with
mineral at the type locality. The latter indicates the only slight deviations from the general trend prior to
importance of finding the criteria to discriminate 2011.Asteepincreaseisobservedstartingfrom2012.
betweennewlydiscoveredspeciesthatare‘‘endemic’’ Thelattercouldbeattributedtoageneralclimbinrate
conventionally (RE) and ‘‘true’’ endemic minerals of mineral discovery during this period. However,
(tRE). Accordingly, two more factors should be uponcloserexamination,itcanbeseenthatdespitea
consideredwhenassessing‘‘trueendemicity’’:therate similarrateofmineraldiscoveryovertheperiod2009–
Downloaded from http://pubs.geoscienceworld.org/canmin/article-pdf/60/5/731/5721758/i1499-1276-60-5-731.pdf
by Mineralogical Association of Canada user
on 17 November 2022
THETAXONOMYOFMINERALOCCURRENCERARITYANDENDEMICITY 739
2011, the proportion of endemic minerals was
relatively lower compared to that over the period
2012–2021. Considering the principle of ‘‘normal
rarity flow’’, a hypothesis can be made that a portion
oftheobservedREmineralsdiscoveredduringthelast
decade will become RR over the next few years. To
decipher the discovery rate of ‘‘true’’ endemicity and
determine the optimal features required for training,
the ML model was trained, and several linear
regression models were tested, using four different
spans of years: (1) 1900–1990, (2) 1900–2000, (3)
1900–2011, and (4) 1900–2021. The presumption is
that the discovery year and the number of minerals
discovered during a specific year are independent
features during this analysis, while the number of
FIG.4.Discoveryrateofendemicminerals. endemicmineralsdiscovereddependsonthem.Before
trainingthemodels,thenonlinearfeatureoftheinput
datawasconsidered,and asecond-degreepolynomial
feature transformation was applied. After the models
were trained, the results were compared with those
trained with third-degree polynomial transformed
features (Fig. 5).
FIG.5.Polynomialregressionmodelpredictionswith95%confidenceintervalsofendemicmineraldiscoveryratesusing2nd
and3rddegreepolynomialtransform.
Downloaded from http://pubs.geoscienceworld.org/canmin/article-pdf/60/5/731/5721758/i1499-1276-60-5-731.pdf
by Mineralogical Association of Canada user
on 17 November 2022
740 THECANADIANMINERALOGIST
TABLE2.EFFICIENCYOFPOLYNOMIALREGRESSIONMODELSWITHDIFFERENT
TRAININGSETS
Modelestimates
2nddegreepolynomialtransform 3rddegreepolynomialtransform
Explained Explained
Trainingset R2 RMSE variance R2 RMSE variance
1900–1990 0.6444 1.1685 0.6444 0.7519 0.9759 0.7659
1900–2000 0.9432 0.7781 0.9432 0.9360 0.8259 0.9360
1900–2011 0.6889 2.7114 0.6900 0.6805 2.7477 0.6824
1900–2021 0.7527 12.4175 0.7556 0.7940 11.3352 0.7977
In some cases, models trained on third-degree COMPOSITION OF RARITY GROUPS
polynomial transformed features lead to ‘‘overfit-
RaregroupR(RE,RR,TR)
ting’’, specifically when training is performed using
data over the range of 1900–2021. Additionally, Over the period 1800–1950, 323 rare (20 RE, 75
modelingissomewhatdependentonthesetofinitial RR, and 228 TR) minerals were discovered, and
featuresthatwereused.Therefore,theinitialdatafor another 3639 (1165 RE including 276 tRE, 1306 RR,
each run was split into a training set (90% of data) and 1168 TR) were discovered after 1950. The
and a testing set (10%), which was followed by majority of rare group minerals are silicates (RE:
features shuffling, model training, running the 317 including 78 tRE, RR: 379, TR: 332), along with
predictions, and finally, evaluating the efficiency of phosphates,arsenates,andvanadates(RE:286includ-
the model (Table 2). ing 72 tRE, RR: 264, TR: 212). The most uncommon
Takingintoaccounttheresultsofmodelfitsanda are so-called organic minerals (RE: 24 including 12
general presumption that the number of endemic tRE; RR: 16, TR: 12) and those containing native
minerals observed during the last decade has been elements (RE: 29 including 5 tRE, RR: 37, TR: 34)
overestimated, the features set for the period 1900– (Fig.6).EachgroupofRE,RR,andTRexhibitssimilar
2000 transformed to a second-degree polynomial was distributions of those minerals representing different
chosenforestimatingthepreliminarygapbetweenthe crystal-chemical groups, thus suggesting a general
values of ‘‘true’’ endemicity and those observed. The homogeneitywithin values for(RE,RR,TR).
Nearly 70% of RE, RR, and TR mineral species
predictedtargetvaluesfortheperiodof2000–2021are
exhibit low symmetry, i.e., belonging to the triclinic,
17–33 for ‘‘true’’ endemic minerals, with ~550 total
monoclinic, and orthorhombic crystal systems, with
endemicspecies.Thisnumberisonlyapproximate,but
only7.3%ofthosemineralsintheREandRRgroups
theapproach and theresultsobtained generallyimply
being cubic, rising slightly to 8.9% in the TR group
that: (1) the ‘‘true’’ endemicity rate follows the same
(Fig. 7). As in the case of chemical groups, the
generaltrendasrateofdiscovery,butwithatendency
distribution patterns in the RE, RR, and TR groups
to increase at a rate lower in magnitude, and (2) the
follow similar patterns when the proportions of those
~380 minerals discovered after 2000 are more likely
minerals with different crystal systems are compared.
to be classified as RR rather than RE, taxonomically.
Following the approach used by Urusov (2002), the
The latter indicates that the total number of tRE
symmetryindexisdefinedas(HþM)/L,whereHisthe
mineralsmightbelowerthanthatofRE(~850versus
percentage of species with the highest symmetry
1232), while the number of RR could be higher
category and M and L are the percentages of the
(~1750versus1473).However,theseobservationsdo intermediateandlowestcategories.Applyingthis,the
not influence the proposed classifications, since any symmetry indices vary between 0.47 and 0.48 for RE
deviations only relate to rare group species, specifi- and RR groups, respectively, while TR exhibits a
callyREandtRE.Takingintoaccountthatthe‘‘true’’ slightly higher value of 0.54. The latter is still below
discovery rate of endemic mineral species clearly theindexof0.55calculatedbyUrusov(2007)for3314
deviatesfromtheobservedrateofdiscovery,separate rare species.
data analytics are provided for all endemic minerals Taking into account the chemical similarities
(RE),alongwithdataforthosediscoveredbefore2000 among values for R(RE,RR,TR) and the difference in
(tRE),where appropriate. symmetry indices between R(RE,RR) and TR, further
Downloaded from http://pubs.geoscienceworld.org/canmin/article-pdf/60/5/731/5721758/i1499-1276-60-5-731.pdf
by Mineralogical Association of Canada user
on 17 November 2022