Understanding how abundance is defined and computed can vary greatly by domain. Below, we explore several fields – Chemistry, Ecology, Linguistics, Astronomy, Economics/Demographics, and Bioinformatics – explaining what abundance means in each context, how it’s measured (units, formulas), and giving example applications.
Chemistry (Isotopic and Elemental Abundance)
Definition: In chemistry, abundance often refers to the proportion of a particular isotope or element within a mixture or sample. For example, each chemical element may have multiple isotopes with different natural abundances. Mercury has seven stable isotopes with percent abundances ranging from 0.146% up to ~29.8%, which all sum to 100% . The most abundant isotope of Hg (≈29.8%) occurs far more frequently than the rarest (~0.15%) in natural samples .
Units/Representation: Isotopic abundance is typically expressed as a percentage (%) or fraction of the total amount of that element. Elemental abundance in a larger context (like in Earth’s crust or atmosphere) is often given in mass fraction (e.g. mg/kg or parts per million by mass, where 10,000 ppm = 1%) . For instance, oxygen constitutes about 46.1% of the Earth’s crust by mass (≈461,000 ppm) . In a compound or mixture, elemental abundance might be given as a weight percent or mole fraction.
Computation Methods: Abundances in chemistry are usually determined via analytical techniques. Mass spectrometry is a key method for isotopic abundance: a sample is ionized and separated by mass-to-charge ratio, producing a spectrum of peaks. The relative intensity of each isotope’s peak is proportional to its abundance . By comparing peak heights, chemists compute the fraction of each isotope (e.g., a ^35Cl:^37Cl peak ratio of 3:1 corresponds to 75% ^35Cl and 25% ^37Cl) . In elemental analysis, techniques like spectroscopy or chemical assays measure how much of each element is present, often calibrated against standards. The formulas involved are typically weighted averages. For example, the average atomic mass of an element is calculated by summing the mass of each isotope times its fractional abundance :
\text{Average Atomic Mass} = \sum_i (\text{mass of isotope}_i \times \text{fractional abundance}_i)\,.\ [oai_citation:9‡chem.libretexts.org](https://chem.libretexts.org/Courses/University_of_Arkansas_Little_Rock/Chem_1402%3A_General_Chemistry_1_(Kattoum)/Text/2%3A_Atoms%2C_Molecules%2C_and_Ions/2.03%3A_Isotopic_Abundance_and_Atomic_Weight#:~:text=atoms%20of%20an%20element%20taking,done%20through%20the%20following%20formula)
Example Applications: Knowing isotopic abundances is crucial in calculating atomic weights on the periodic table and in techniques like radiometric dating. For instance, carbon-14’s abundance in a sample (relative to carbon-12) is used to determine age in carbon dating. In chemistry and geochemistry, elemental abundance data help identify material composition. As an example, the isotopic composition of strontium can be determined from its mass spectrum, which shows four isotopes:
| Isotope (Sr) | Mass Number | Relative Abundance (%) |
| ^84Sr | 84 | 0.56% |
| ^86Sr | 86 | 9.86% |
| ^87Sr | 87 | 7.00% |
| ^88Sr | 88 | 82.58% |
Table: Naturally occurring isotopes of strontium and their approximate abundances . In this example, ^88Sr is by far the most abundant (≈82.6% of all Sr atoms), which influences the average atomic mass of strontium (around 87.6 amu in this case). Such isotopic abundance data are applied in geological sourcing (strontium isotope ratios can trace origin of rocks) and in medical diagnostics (enriched isotopes in tracers).
Ecology (Species Abundance in Populations)
Definition: In ecology, abundance refers to the number of individuals of a species in a given area or ecosystem. It is essentially the population size of the species in the context of the study. For example, one might talk about the abundance of deer in a forest (e.g. 50 deer in a 10 km² area). More formally, local abundance is “the relative representation of a species in a particular ecosystem,” usually measured as the count of individuals per sample or unit area . The term can also be used comparatively: a species that has many individuals in an area is abundant, whereas one with few individuals is rare.
Units/Representation: The simplest unit is a count of individuals. This can be an absolute count (e.g. 200 oak trees in a plot) or a density (e.g. 50 oaks per hectare). Abundance can be expressed in relative terms as well – relative abundance is the proportion of the total community that a given species represents . For instance, if in a sample of 100 organisms, 30 are of species A, then A’s relative abundance is 0.30 (30%). Both absolute and relative measures are important: absolute abundance shows population size, while relative abundance indicates how common a species is compared to others in the community.
Computation Methods: Ecologists employ various sampling methods to estimate abundance. For animals, methods include direct counts (sightings, camera traps), transect surveys, mark-and-recapture techniques, or indices like footprint or track counts and roadkill counts as proxies . For plants or sessile organisms, abundance might be measured via percent cover (the area occupied by the species in a quadrat) as an analog to count . When it’s impractical to count every individual, statistical estimates are used. A simple formula for relative species abundance in a sample is:
\text{Relative Abundance of species } i = \frac{N_i}{N_{\text{total}}},
where $N_i$ is the number of individuals of species i and $N_{\text{total}}$ is the total individuals of all species counted . This yields a fraction or percentage for each species. Ecologists also summarize community abundance patterns via diversity indices. For example, the Shannon index uses the proportion $p_i = N_i/N_{\text{total}}$ (where $N_i$ is the abundance of species $i$) in its formula, and $N_i$ itself is termed the abundance of species $i$ .
Example Applications: Species abundance data are fundamental in conservation biology and wildlife management. For instance, tracking the abundance of an endangered bird species over time allows assessment of recovery efforts. In community ecology, species abundance distributions are studied to understand ecosystem structure; typically a few species are very abundant while many others are rare . As an example, in a tidepool survey you might find 100 organisms consisting of 85 mussels, 10 barnacles, 3 crabs, and 2 starfish. The mussel is overwhelmingly dominant (85% of individuals), indicating a skewed abundance distribution common in many ecosystems . Such information helps in biodiversity assessments, identifying keystone species (often highly abundant or with high impact), and monitoring environmental changes (e.g. a sudden drop in the abundance of insect pollinators could signal an ecological problem).
Linguistics or Text Analysis (Word Frequency)
Definition: In linguistics and text analysis, abundance usually refers to how frequently a given word or term appears in a text or corpus. Essentially, it’s the word frequency. For example, in English text the word “the” is extremely abundant (occurring very often), whereas a rare word like “quagmire” has low abundance. Frequency can be considered for single words or phrases, and it can be defined for a specific document or across a large corpus of documents. In computational linguistics, a frequency list is a list of word types alongside their frequencies (number of occurrences) in a corpus .
Units/Representation: The simplest measure is the raw count of occurrences of a word. This is often called the absolute frequency . For instance, in a novel, a common word like “and” might have an absolute frequency of 1,000 (appears 1,000 times). To compare frequencies across texts of different lengths or across corpora, normalized frequencies are used. A common normalization is per million words (instances per million, i.p.m.) . This expresses how many times a word would occur if the text had one million tokens. The formula for frequency per million is:
f_{\text{per million}} = \frac{\text{raw count of word}}{\text{total tokens in corpus}} \times 1,000,000,
so that frequencies can be compared independent of corpus size . For example, if a word appears 50 times in a corpus of 500,000 words, that’s 100 occurrences per million words. Linguists also talk about relative frequency (the proportion of text comprised by that word) which is essentially the same concept expressed as a probability or percentage.
Methods of Computation: Computing word frequency is straightforward with modern tools: one simply tokenizes the text and counts occurrences of each token. Tools in corpus linguistics and natural language processing (NLP) can output frequency lists. In the past, this might be done manually or with simple scripts; now, large corpora (billions of words) are analyzed using software to get frequency distributions. More advanced metrics like TF-IDF (term frequency–inverse document frequency) combine raw frequency with adjustments, but the basic term frequency is just the count . Lexicographers (dictionary makers) often use word frequency (often normalized as per million) to decide which words are common (e.g., OED marks words by frequency band).
Example Applications: Word frequency information is used in many ways. In language learning and lexicography, high-frequency words (e.g., “the”, “of”, “and” in English) are taught first or noted as common vocabulary. Frequency lists help researchers study language usage patterns and even cognitive processing (common words are recognized faster by readers). As an example, in one corpus analysis of modern English text, the most frequent word “the” appeared 3,789,654 times, and the second-ranked word “he” appeared 2,098,762 times . By contrast, a moderately common noun like “boy” occurred about 56,975 times (outside the top 1,000 words) , and many words appeared only once (called hapax legomena ). These frequency statistics follow a Zipf’s law distribution – a few words are extremely abundant, while the majority are rare. In text mining, such frequency counts form the basis of keyword extraction and topic modeling. In computational linguistics, understanding term abundance is key for building language models (where very frequent words might be treated differently from rare ones).
Astronomy or Astrophysics (Elemental Abundances in Stars and Galaxies)
Definition: In astrophysics, abundance refers to the prevalence of an element or isotope in an astronomical object or environment (such as a star, galaxy, or the universe as a whole). It most commonly denotes the chemical composition of stars and gas clouds in terms of elements like hydrogen, helium, iron, etc. Because hydrogen is the most common element in the universe, abundances are often given relative to hydrogen. Astronomers use a logarithmic scale for reporting elemental abundances: by convention hydrogen’s abundance is defined as 12.00 (as a reference), and other elements are given by log₁₀ of their number ratio relative to hydrogen . This is sometimes called the “dex” scale. For example, in the Sun’s photosphere, helium has an abundance around 10.5 on this scale, meaning He is about 10^(-1.5) times as numerous as H atoms; oxygen is about 8.7, and iron about 7.6 . These logarithmic numbers correspond to actual number ratios. An element X with abundance 7.0 (in the H=12 system) means: \log_{10}(N_X/N_H) + 12 = 7.0, so N_X/N_H = 10^{-5} (i.e., 1 part of X per 100,000 parts H).
Another common notation is “square bracket” abundance ratios. For example, [Fe/H] is used to compare a star’s iron abundance to that of the Sun. By definition, [Fe/H] = \log_{10}(N_{Fe}/N_H)_{\text{star}} – \log_{10}(N_{Fe}/N_H)_{\odot}. If a star has [Fe/H] = 0, it has the same iron-to-hydrogen ratio as the Sun; [Fe/H] = +1.0 indicates ten times the iron abundance of the Sun, while [Fe/H] = –1.0 means one-tenth the solar iron content . This notation is used to classify stars by metallicity (overall metal content). For instance, metal-poor Population II stars might have [Fe/H] ≈ –3, meaning 1/1000 of the iron that the Sun has .
Units/Representation: As noted, abundances by number are often given on a log scale relative to H. Alternatively, mass fractions can be used (especially in stellar models), denoted X, Y, Z for mass fraction of hydrogen, helium, and “everything else” (metals). For example, a typical young star might have X ≈ 0.70, Y ≈ 0.28, Z ≈ 0.02 (i.e. ~70% of mass hydrogen, 28% helium, 2% heavier elements). In cosmology, primordial abundances from Big Bang nucleosynthesis are given as ratios (e.g., helium was about 25% of the mass of the early universe). In interstellar gas, abundances can also be given in “parts per million” by number relative to hydrogen (for trace elements).
Methods of Measurement: Elemental abundances in stars and gas are deduced from spectroscopy. Each element absorbs or emits light at characteristic wavelengths. By observing the spectral lines in starlight, astronomers can infer which elements are present and in what amounts. The depth or strength of an absorption line (after careful modeling of temperature and pressure) indicates the abundance of that element’s atoms in the stellar atmosphere. Because this process requires astrophysical models, obtaining precise abundances is challenging . For stellar atmospheres like the Sun’s, detailed spectral analysis yields the abundances mentioned above. In galaxies or nebulae, scientists often look at emission lines in ionized gas (e.g. in H II regions). Stronger line intensities generally mean higher abundances of the element that produces those lines . For example, the brightness of certain oxygen emission lines in a nebula can be used to estimate the oxygen-to-hydrogen ratio in that gas cloud . These measurements are sometimes calibrated against known standards (like the Sun or laboratory spectra). In practice, astronomers report uncertainties and use the term “metallicity” as an overall gauge of heavy-element abundance in stars and galaxies.
Example Applications: Elemental abundance calculations are fundamental in astronomy. They inform us about stellar evolution and the history of nucleosynthesis. For example, a star with very low metal abundance ([Fe/H] ≪ 0) is recognized as an old star, formed when the galaxy had fewer heavy elements. Abundance ratios like [O/Fe] or [Mg/Fe] are used to study supernova yields and galactic chemical evolution. In cosmology, the measured abundances of light elements (hydrogen, helium, deuterium, lithium) are compared to Big Bang nucleosynthesis predictions, serving as a key test of the Big Bang model. In planetary science, the elemental makeup of the Sun and meteorites (where, e.g., Fe, O, Si are common) helps us understand the composition of Earth and other planets . As an illustration, the Sun’s composition by number of atoms is ~90% hydrogen and ~10% helium, with all other elements accounting for just 0.1% or less; yet those trace elements (C, N, O, Fe, etc.) are crucial for forming planets and life. Measuring abundances in distant stars also guides the search for exoplanets – higher metallicity in a star has been linked to a greater likelihood of hosting planets (especially gas giants) .
Economics and Demographics (Resource Abundance and Wealth Distribution)
Definition (Resources): In economics, abundance typically relates to the availability of resources (natural or economic) relative to demand. A resource (like water, oil, arable land) is considered abundant if it exists in plentiful supply. This is often discussed in contrast to scarcity. Resource abundance can be defined in absolute terms (total quantity available) or per capita. For example, a country might be said to have abundant oil reserves if it has a large endowment of oil relative to its population or needs. In geography and development studies, resource abundance refers to “the availability of natural resources in a given area” and how that can influence economic outcomes .
Units/Representation (Resources): Resources are quantified in domain-specific units: barrels (oil), cubic meters (natural gas or water), tons (coal, minerals), etc. Often, economists and policymakers look at per capita availability or per land area to gauge abundance. For instance, freshwater availability is measured in cubic meters per person per year; a country with >10,000 m³ per person/year is water-rich, whereas below 1,000 m³ per person/year indicates water scarcity . As another example, the abundance of elements in Earth’s crust is tabulated in mg/kg or ppm as noted earlier , which tells us, say, aluminum is about 8.23% of the crust by mass while copper is only 0.006% . In economic terms, one might also measure resource abundance by its contribution to GDP or exports (e.g. a “resource-rich” economy where a large share of GDP comes from oil).
Computation (Resources): Computing resource abundance often involves summing up reserves or stocks and then normalizing by some factor (population, area, etc.). For renewable resources like water, it could mean annual renewable supply per capita . For non-renewables like minerals, it could be total proven reserves. No single formula applies to all resources, but an illustrative calculation is:
\text{Resource per capita} = \frac{\text{Total available quantity}}{\text{Population}}.
For example, if a country has 50 billion cubic meters of freshwater runoff annually and a population of 10 million, that’s 5,000 m³ per person per year. Another measure is the reserves-to-production ratio for fossil fuels, which estimates how many years a resource will last at current production rates (a higher ratio can imply more abundance relative to current use). It’s worth noting that economic abundance also depends on accessibility and demand – a resource can be abundant in the ground but economically scarce if extraction is difficult or expensive.
Example (Resources): An application of these concepts is in discussing the “resource curse” in development economics. Paradoxically, countries with abundant natural resources (like oil or diamonds) have sometimes experienced slower economic growth or governance issues. Here, quantifying abundance might involve noting that a country’s oil exports per capita are very high (indicating resource wealth) but looking at outcomes like GDP growth or income distribution to see if that abundance translates to broad benefits . On a more everyday level, understanding resource abundance guides policy: a region with abundant agricultural land per farmer might support biofuel production, whereas a region with scarce land must prioritize food crops.
Definition (Wealth Distribution): In demographics and economics, abundance can also refer to the distribution of wealth or income in a population – essentially, who has how much wealth. While we don’t usually say a person has “abundant wealth” in technical terms, we do analyze how wealth is concentrated. A highly unequal wealth distribution means a small portion of people hold the majority of resources (so wealth is abundant only among the rich). Conversely, in an egalitarian distribution, wealth is spread more evenly. The Lorenz curve is a tool to represent this: it plots the cumulative percentage of population (x-axis) against the cumulative percentage of wealth they hold (y-axis) . If wealth were perfectly equal, the Lorenz curve would be a 45° line (each x% of people holds x% of wealth). The more it bends toward the bottom-right, the more unequal the distribution (i.e., large abundance of wealth is concentrated in a small top fraction).
Units/Representation (Wealth): Wealth distribution is often summarized by inequality indices, the most famous being the Gini coefficient. The Gini index ranges from 0 (perfect equality – everyone has the same wealth) to 1 (perfect inequality – one person has all the wealth) . It is derived from the Lorenz curve: if we denote area A as the area between the line of perfect equality and the Lorenz curve, and B as the area under the Lorenz curve, then Gini = \frac{A}{A+B} . A higher Gini means more inequality (fewer people hold most wealth). Wealth distribution can also be described by percentile shares (e.g., “the top 10% of households own 70% of the wealth”). For example, many countries report that the top 1% owns a significant fraction of total wealth – an indication of wealth abundance at the top.
Computation (Wealth): To compute a Gini coefficient from data, one typically orders all individuals by wealth, calculates the cumulative share of wealth held at various population percentages, plots the Lorenz curve, and then uses the formula G = \frac{A}{A+B} (which can be calculated via summation or integration methods from the income/wealth data). The Lorenz curve itself is computed by sorting the population from poorest to richest and then finding, for each percentage (or decile, etc.), what share of total wealth that fraction of population possesses . If the bottom 50% of people have only 10% of the wealth, and the top 10% have, say, 60% of the wealth, that indicates a highly unequal, skewed abundance of wealth. Such calculations are often done using survey or tax data. In practical reports, a Gini coefficient might be given in percentage form (e.g., Gini = 40 means 0.40 in the 0–1 scale, or 40%). Wealth Gini is usually higher than income Gini, since wealth (assets) tends to be more concentrated than annual income .
Example Applications (Wealth): Measures of wealth abundance and distribution are crucial for economic policy and social science. For instance, a country like Norway might have a Gini around 0.25, indicating a relatively even distribution, whereas South Africa might have a Gini around 0.63, indicating extreme inequality . This tells policymakers how abundance (in terms of wealth) is shared or hoarded. High inequality might prompt discussions of taxation or redistribution. On a global scale, wealth distribution analyses show that a small fraction of the global population holds a majority of assets – a trend that has intensified in recent decades . The Lorenz curve visualization helps to grasp this: for example, the bottom 50% of the world’s population might own just a single-digit percentage of global wealth, whereas the richest 10% own well over half. Figure 1 below illustrates a typical Lorenz curve for income or wealth:
Figure 1: A typical Lorenz curve used in economics to depict wealth (or income) distribution. The straight diagonal line represents perfect equality (each proportion of the population owning an equal proportion of wealth). The curved line shows an actual distribution where inequality exists. Area A (between the equality line and the Lorenz curve) and area B (under the Lorenz curve) are used to compute the Gini coefficient G = A/(A+B) . A larger area A (more bowing of the curve) indicates higher inequality.
Such analysis of abundance and its distribution in economics informs debates on resource allocation, poverty, and policy measures (like whether an abundance of natural resources is being managed to benefit the whole population or just a few).
Bioinformatics or Molecular Biology (Gene/Transcript Abundance)
Definition: In molecular biology, abundance often refers to the amount of a specific molecular species present in a sample. Commonly, this is used in the context of gene expression – i.e., how many copies of an mRNA (transcript) are present as a measure of gene activity. Transcript abundance is essentially the expression level of a gene, measured by the quantity of its RNA transcript in the cell or tissue. For example, in an RNA sequencing (RNA-seq) experiment, one might say “Gene X has high abundance in liver tissue” meaning there are many mRNA reads for Gene X, indicating high expression. Similarly, one can speak of protein abundance for how much of a protein is present, though nucleic acid (DNA/RNA) abundance is easier to quantify at large scale.
Units/Representation: There are multiple units used to represent gene/transcript abundance. Raw data from RNA-seq is in read counts (an integer count of sequencing reads mapped to each gene). However, raw counts depend on sequencing depth and gene length, so they are usually normalized. Two widely used normalized units are RPKM/FPKM and TPM:
- RPKM (Reads Per Kilobase of transcript per Million mapped reads) and its variant FPKM (Fragments Per Kilobase per Million, for paired-end data) are classic RNA-seq expression units. RPKM normalizes the raw read count by both the gene’s length (so longer transcripts don’t automatically get higher counts) and the total sequencing depth (so samples with more total reads can be compared) . In formula form, for single-end sequencing:
RPKM = \frac{\text{read count} \times 10^9}{(\text{gene length in bases}) \times (\text{total reads})}\,.
The factor $10^9$ (10^3 * 10^6) accounts for kilobases and per million scaling . The result is a number that represents relative transcript abundance in the sample. FPKM is essentially the same but accounts for paired-end reads so that a pair counting as one fragment doesn’t double-count . - TPM (Transcripts Per Million) is a newer preferred unit. It is calculated slightly differently: first normalize read counts by gene length, then scale so that the sum of all transcript abundances equals one million . The key property of TPM is that within each sample, all TPM values sum to 1,000,000, which makes TPM values comparable across samples (if Gene A is 5 TPM in both Sample 1 and Sample 2, it means the same fraction of the transcript pool in each) . This is not true for RPKM, where the totals can differ between samples, complicating comparisons . By construction, TPM = RPKM * (some common scaling factor per sample) and is interpreted as: if you had one million transcripts, TPM is how many out of that million would be from a given gene .
Other contexts use different measures: microarray fluorescence intensity (arbitrary units) was an older measure of transcript abundance; quantitative PCR (qPCR) yields a C_t value (cycle threshold) which is inversely related to abundance (lower C_t = higher starting abundance) and can be converted to an absolute or relative quantity using standard curves. In metagenomics or transcriptomics, sometimes CPM (counts per million) is used, which is similar to TPM but without length normalization (suitable for comparing overall expression of a gene across samples, assuming length is constant for that gene).
Computation Methods: High-throughput techniques provide the data to compute molecular abundances. For gene expression, RNA-seq is the predominant method: RNA is extracted, converted to cDNA and sequenced, yielding millions of reads. Bioinformatics tools then count how many reads map to each gene. These raw counts are then fed into the above formulas for RPKM/FPKM or TPM to get normalized abundances . The normalization adjusts for two major biases: (1) sequencing depth (more total reads would inflate all counts linearly if not corrected) and (2) gene length (longer transcripts naturally accumulate more reads) . By dividing by total reads (per million) and length (per kilobase), RPKM/FPKM addresses these biases . TPM does the same but in a different order, yielding more directly comparable values across datasets .
In quantitative proteomics, abundance might be computed via spectral counts or intensity in mass spectrometry, often normalized to produce measures like iBAQ or label-free quantification values. In DNA sequencing (e.g., measuring abundance of a species in a metagenomic sample), similar normalized counts (reads per million or per base) can indicate how abundant a sequence is.
Example Applications: Quantifying gene abundance is fundamental in understanding biology. For example, in cancer research, one might find that an oncogene has much higher transcript abundance in tumor tissue versus normal tissue, indicating upregulation. This could be reported as, say, 120 FPKM in the tumor vs 5 FPKM in normal tissue, or a 24-fold increase. In a typical RNA-seq result, housekeeping genes like GAPDH might show very high TPM (~1,000 TPM, for instance) because they are highly expressed, whereas a transcription factor gene might have 5 TPM, indicating low expression. These numbers help compare genes: a gene at 50 TPM is ten times more abundant than one at 5 TPM in the same sample.
As a concrete example, suppose in a sample of yeast cells you have the following TPM results: Gene1 = 500 TPM, Gene2 = 50 TPM, Gene3 = 5 TPM. This means Gene1’s mRNA makes up 0.05% of the transcript pool, which is 10× more than Gene2 (0.005%) and 100× more than Gene3 (0.0005%). Such differences are biologically meaningful; Gene1 might be a ribosomal protein gene (needed in large quantities), while Gene3 might be a regulatory gene expressed at low levels. Tools like differential expression analysis use these abundance measures (with statistical models) to find genes that are significantly up- or down-regulated under different conditions. Transcript abundance is also crucial in bioinformatics pipelines for genome annotation (high-abundance transcripts often correspond to important, conserved genes) and in systems biology to model metabolic and signaling networks based on how much of each component is present.
In summary, across domains, “abundance” always ties to the idea of how much of something is present, but the specifics of its measurement – be it percentage of isotopes, counts of organisms, frequency of words, stellar element ratios, economic resources, or gene expression units – differ widely. Understanding these measures in context allows experts in each field to compare, quantify, and draw insights from the data, whether it’s determining the average atomic mass of an element, the biodiversity of an ecosystem, the commonality of a word, the chemical makeup of a star, the equity of wealth in a society, or the activity of a gene in a cell.
Sources:
- Chemistry (isotopic abundance & atomic mass): Chemistry LibreTexts
- Chemistry (elemental abundance example): Wikipedia – Abundance of elements in Earth’s crust
- Ecology (species abundance definitions): Wikipedia – Abundance (ecology)
- Ecology (sampling methods): Wikipedia – Abundance (ecology)
- Linguistics (frequency definition): SketchEngine glossary
- Linguistics (frequency per million normalization): SketchEngine glossary
- Linguistics (frequency list example): Wikipedia – Word list (corpus linguistics)
- Astronomy (stellar abundances log scale): Wikipedia – Abundance of elements (Sun example)
- Astronomy (metallicity [Fe/H] notation): Wikipedia – Metallicity
- Astronomy (spectroscopic measurement): Research on H II regions
- Economics (resource abundance concept): Fiveable AP Geography glossary
- Economics (water per capita metric): World Bank / OurWorldInData
- Economics (Gini coefficient explanation): Investopedia and Lorenz curve (Wikipedia)
- Bioinformatics (RNA-seq normalization): RNA-Seq Blog / StatQuest explainer and Novogene blog .