Fatty acids are important in nutrition and health.  Previously, we reported that the concentration range per se may explain positive and negative correlations between percentages of fatty acids. We now present additional data to explain such correlations. With 3 positive scale variables, A, B, and C, dependency between their percentages is:  %A + %B + %C = 100, or %B = - %A + (100 - %C), each variable with a particular range. The equation may be simplified by making the expression (100 - %C) approach zero (high %C, low %A and %B values), i.e.  %B = %A (giving positive %A vs. %B), and by making %C approach zero, giving %B = - %A + 100 (giving negative %A vs. %B). In the current work we present data showing that skewness of the %A (B, C) histograms may serve as a mediator of correlations between %A and %B.

With reference to diet and fatty acid metabolism, we previously suggested that the relative amount of positive scale variables (e.g. fatty acids) can be positively associated as a consequence of their particular concentration distribution/variability, suggesting Distribution Dependent Regulation of the fatty acid metabolism [1 - 5]. Variability of concentrations could be related to differences between subjects, but also depend on intra-individual variations, for example related to diet, time, and environment in general, implying that this type of regulation might take place both between and within subjects. Furthermore, we suggested that evolution might possibly use differences in the concentration range/variability to ensure that relative amounts of some variables must be positively correlated whereas others will be negatively associated, as recently observed for the positive correlation between % EPA and

In previous works [1, 2], we investigated the association between the relative amount of the n6 fatty acid AA,  and percentages of n3 fatty acids (EPA, DPA, DHA). From histograms, we found physiological concentration distributions (g/kg wet weight) for the fatty acids. Next we computed the sum (g/kg wet weight) of all fatty acids, and the remaining sum when omitting the couple of fatty acids under investigation. We then had 3 scale variables only. With these variables, and with surrogate random number variables generated within the true distributions, we did analyses as shown below. For the purpose of the present work, we name the 3 variables A, B, and C. Our previous analyses suggested that the question of whether e.g.

An algebraic approach to assess whether percentages are correlated

We define three positive scale variables, A, B and C, giving %A + %B + %C = 100, i.e.

%B = - %A + (100 - %C).  Since the slope of the %B vs. %A regression line is determined by the ranges of A(%A) and B(%B), a more appropriate  equation would be: %B (p - q) = - %A (r - s) + (100 - %C (t – u)) where the subscript parentheses indicate ranges of A, B, and C. A crude slope estimate of the linear relationship between %A vs. %B may be calculated manually by the minimum and maximum values of the A (%A) and B (%B) ranges: i.e. by (max - min) of

Fatty acids are important in nutrition and health. The present results suggest that skewness of the frequency distribution of percentages of positive scale variables (like fatty acids) may govern whether the relative amounts will be positively or negatively associated, or not correlated. The driving force of the skewness is differences in range/distribution between the variables, and might - at least partly - serve to explain the previously suggested phenomenon of Distribution Dependent Correlation, which could be a novel regulatory mechanism in physiology.  However, skewness is not an absolute requirement to obtain such correlations.