mathematics

Rank abundance curve

Rank abundance curve is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Rank abundance curve rather than just read about it. In short: A rank abundance curve or Whittaker plot is a chart used by ecologists to display relative species abundance, a component of biodiversity. It can also be used to visualize species richness and species evenness.

Key takeaways

Rank abundance curve belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Rank abundance curve to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Rank abundance curve from memory before moving on to harder problems.

Reference excerpt

A rank abundance curve or Whittaker plot is a chart used by ecologists to display relative species abundance, a component of biodiversity. It can also be used to visualize species richness and species evenness. It overcomes the shortcomings of biodiversity indices that cannot display the relative role different variables play in their calculation. The curve is a 2D chart with relative abundance on the Y-axis and the abundance rank on the X-axis.

X-axis: The abundance rank. The most abundant species is given rank 1, the second most abundant is 2 and so on. Y-axis: The relative abundance. Usually measured on a log scale, this is a measure of a species abundance (e.g., the number of individuals) relative to the abundance of other species. The figure above, however, does not have a log scale, despite the fact that the label says '(log)'. If it did have a log scale, the shape would be quite different.

Interpretation The rank abundance curve visually depicts both species richness and species evenness. Species richness can be viewed as the number of different species on the chart i.e., how many species were ranked. Species evenness is reflected in the slope of the line that fits the graph (assuming a linear, i.e. logarithmic series, relationship). A steep gradient indicates low evenness as the high-ranking species have much higher abundances than the low-ranking species. A shallow gradient indicates high evenness as the abundances of different species are similar.

Quantitative comparison of rank abundance curves Quantitative comparison of rank abundance curves of different communities can be done using RADanalysis package in R. This package uses the max rank normalization method in which a rank abundance distribution is made by normalization of rank abundance curves of communities to the same number of ranks and then normalize the relative abundances to one.

References

Magurran, Anne E. (2004). Measuring biological diversity. Oxford: Blackwell. ISBN 0-632-05633-9. Whittaker, R. H. (1965). "Dominance and Diversity in Land Plant Communities: Numerical relations of species express the importance of competition in community function and evolution". Science. 147 (3655): 250–260. doi:10.1126/science.147.3655.250. PMID 17788203. S2CID 22414021.

External links Whittaker Diagram, Procedural Content Generation Wiki - use of Whittaker diagrams in procedural content generation RADanalysis package in R, Package in CRAN contain functions for quantitative comparison of rank abundance curves

Illustrations

Worked examples

Example 1 — a first encounter with Rank abundance curve

Start with the simplest possible case. Write down what Rank abundance curve claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Rank abundance curve before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Rank abundance curve ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Rank abundance curve

In research: Rank abundance curve appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Rank abundance curve in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Rank abundance curve is common in secondary-school and first-year university syllabi. It links to neighbouring topics Biodiversity, Statistical charts and diagrams, Systems ecology, so understanding it makes those chapters shorter.
In everyday life: Look for Rank abundance curve outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Rank abundance curve in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Rank abundance curve means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Rank abundance curve out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Rank abundance curve in simple terms?

Why does Rank abundance curve matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Rank abundance curve?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Rank abundance curve.