Intended Ranges and Correlations between Relative Amounts: a Review

Abstract

The present article is a review of our previously suggested concepts of “Distribution Dependent Correlations” (DDC), and “Intended Ranges”. DDC concern associations between relative amounts of positive scale variables, in unit systems where sum of the percentages is 100%. Such correlations arise mathematically on the condition that the variables in question have particular (“intended”) ranges. For example, with three variables, two of which (A, B) having very low variability relative to a third one (C), we should expect a positive association between percent A and percent B, the slope being estimated by the B/A ratio. In addition, we should anticipate a negative relationship between %C and %A (%B). On the other hand, if A and B have high numbers and variability relative to C, then %A should relate inversely to %B. Furthermore, alterations in the ranges may have appreciable effects to change the associations. We present examples from physiology, where ranges seem to give strong DDC (positive and negative). The examples relate to body fatty acids, and white blood cell counts. Possibly, Intended Ranges could represent a case of evolutionary selection, to ensure proper balance between particular metabolites.