Is the coefficient of variation a valid measure for variability of stable isotope abundances in biological materials?

The isotopic compositions of low-mass elements such as carbon are commonly expressed on the δ scale, relative to the isotopic ratio of an international standard (RST). Carbon stable isotope measurements of plant material are interpreted with an apparently biological meaning as an estimator of water use efficiency, and this has been used widely in recent years to screen plant material for variation. To compare the observed variability with other traits, the coefficient of variation (CV) is often used as an intrinsic variability measure.

Theoretical considerations as well as an example dataset were used to test the independence of the CV from the RST on which the values of isotopic composition on the δ scale are based.

It can be shown mathematically that the CV of a dataset of δ(13)C values is directly dependent on RST. The exploration of the example dataset confirmed this but also showed that the conversion of absolute isotopic ratios into atom fraction does not change the resulting CV. Similarly, a discrimination calculated between two δ(13)C values is independent of RST, but depends on accurate knowledge of both δ(13)C values. It was also shown that results of statistics (e.g. ANOVA) are robust among different units of isotopic composition.

As CVs estimated from isotopic compositions expressed on the δ scale depend on the underlying standard, they should not be compared with those of other traits, and even comparisons of CVs among isotopic datasets should be interpreted with care.