Mineral Species Frequency Distribution Conforms to a Large Number of Rare Events Model: Prediction of Earth’s Missing Minerals

Abstract

A population model is introduced to describe the mineral species frequency distribution. Mineral species coupled with their localities conform to a large number of rare events (LNRE) distribution: 100 common mineral species occur at more than 1,000 localities, whereas 34 % of the approved 4,831 mineral species are found at only one or two localities. LNRE models formulated in terms of a structural type distribution allow the estimation of Earth's undiscovered mineralogical diversity and the prediction of the percentage of observed mineral species that would differ if Earth's history were replayed.

Statistical analysis of mineral diversity and distribution: Earth's mineralogy is unique

“…However, many terrestrial planets will not possess key traits of Earth, such as a hydrosphere and plate tectonics. Consequently, a compelling definition of Earth-like planets remains elusive (Brownlee and Ward, 2004;Segura et al, 2005;Sotin et al, 2007;Svedhem et al, 2007;Kaltenegger and Traub, 2009). We suggest that mineralogical criteria-specifically the diversity and distribution of near-surface mineral species-provide robust indicators of geochemical and tectonic environments that influence the evolution of a terrestrial planet, including its oceans, atmosphere, and life.…”

Data Science for Geoscience: Leveraging Mathematical Geosciences with Semantics and Open Data

“…The project proposed to deploy a data-driven abductive approach to discover patterns in the evolution of Earth's environment. (Hystad et al 2015). The work used the records of mineral species, localities and observations (species-locality pairs) from mindat.org and discovered the LNRE pattern.…”

Earth’s “missing” minerals

“…More than half of all mineral species are recorded from 5 or fewer localities, with 22% of species known from only 1 locality (data recorded in mindat.org as of February 1, 2014). Hystad et al (2015a) discovered that the relationship between mineral diversity and distribution is analogous to the frequency distribution of words in a book-i.e., a few words such as "a", "and", and "the" are very common, but most words are used infrequently. Idiosyncratic combinations of rare words and phrases can be used to identify the genre and authorship of an unsigned text, and they usually conform to a Large Number of Rare Events (LNRE) frequency distribution (Baayen 2001;Evert and Baroni 2008).…”

“…In this work we employ two types of Large Number of Rare Events models-both Generalized Inverse Gauss-Poisson (GIGP) and finite Zipf-Mandelbrot (fZM) distribution functions (Hystad et al 2015a(Hystad et al , 2015b; see Supplementary Materials 1 ). These frequency distributions use an empirical three-parameter fit to model the number of mineral species found at m localities, typically for 1 ≤ m ≤ 15.…”

“…1 ; Hazen et al 2015;Hystad et al 2015a). We used a LNRE model to calculate an "accumulation curve," which documents the rates of discovery of new mineral species as more mineral species-locality data are recorded.…”