Where does rarefaction collide?

In ecology, rarefaction is a statistical method that estimates the species richness one would expect in a smaller random subsample of individuals (or sampling units), so that diversity can be compared fairly across samples of different size. Howard Sanders introduced it for marine benthos in his 1968 paper in The American Naturalist; Stuart Hurlbert corrected its formulation in Ecology (1971), and Gotelli and Colwell standardized its use in Ecology Letters (2001). The referent is a smooth curve of expected species versus sample size, borrowing its name, by analogy of ‘thinning out’, from the physical rarefaction of a medium, with which it shares no mechanism.[1][2][3]

Unit

One expected-species value at a given subsample size

Recovery means

Resample the abundance data without replacement and recompute expected richness

Measured by

Computed from an abundance distribution as expected species E(S_n) across subsample sizes

In acoustics and gas dynamics, rarefaction is the thinning of a medium: a region where density and pressure fall below ambient, the counterpart of compression in a longitudinal sound wave, or an expansion (‘rarefaction’) wave that spreads a gas out and lowers its pressure. Lord Rayleigh treated the compressions and rarefactions of sound in The Theory of Sound (1877), and Richard Courant and Kurt Friedrichs gave the modern theory of rarefaction waves in Supersonic Flow and Shock Waves (1948), following Riemann. The referent is a literal decrease in the density of matter, measured as a pressure or density drop, unrelated to the ecologist's subsampling curve beyond the shared meaning of ‘making less dense’.[4][5]

Unit

One region of below-ambient density/pressure

Recovery means

Detect the low-pressure phase of the wave or the expansion fan in the flow field

Measured by

Measured as a negative pressure/density deviation (e.g., by microphone or pressure transducer)