AN EMPIRICALLY BASED MODEL OF VARIATION IN ROTATIONAL ELEMENTS IN CENTRIC DIATOMS WITH COMMENTS ON RATIOS IN PHYCOLOGY1

Abstract

ABSTRACTRatios are commonly used to relate taxonomic, physiological and ecological properties of algal cells to variation in cell shape and size. However, ratios can be more difficult to interpret than the original variables. A detailed example of a ratio commonly used in diatom taxonomy is presented. The abundance of a reported rotational element on a centric diatom valve is often expressed as density (e.g. number of marginal spines per μm of circumference), rather than simply as total number. It is empirically demonstrated that density if often curvilinearly related to diameter, whereas total number is linearly related (when related at all) to diameter. This linear relationship is the basis for an empirical model which accounts for variation in density in real examples. Under this model, densitywill be a poorer taxonomic character than total number except under rare occasions (e.g. when the slope of the total element versus diameter regression in zero and variance in the numerator is not dependent on the denominator). Other ratios are similarly difficult to interpret. Length/width (or width/length) is often curvilinearly related to width (or width/lenght) is often curvilinearly related to width (Length) because variation is compounded from several sources. Surface/volume has been employed to investigate the relative contributions of size and shape to phytoplankton sinking. However, the properties of this ratio have not been fully investigated, and the relationship between size, shape and sinking rate has not been fully elucidated for the data set in question.