Background: Since oleic acid (OA, 18:1 c9) and arachidonic acid (AA, 20:4 n6) may have antagonistic actions, it is of interest to assess their relative abundances. We previously reported an inverse correlation between % OA and %AA. However, percentages of the same sum may be correlated without involving biology. We now investigate whether random numbers, generated within the true concentration distributions for OA and AA, may be correlated.
Methods: We reanalysed data from a previous diet trial in chickens. Breast muscle was collected, and the concentration of fatty acids in muscle lipids was determined using gas chromatography. We computed R = S - OA - AA, where S is the sum of all fatty acids (g/kg) and R is concentration of all fatty acids, except OA and AA. From histograms we found physiological distributions of OA, AA and R. Then we generated random numbers for each of 3 variables (n = 163), within the distributions (g/kg) for OA (1-7), AA (0.25-0.39), and R (4-10). Next we made scatterplots of % OA vs. % AA, and studied how a narrowing or broadening of distributions might change the relationship.
Results: Also with random numbers, generated within true concentration distributions for OA and AA, we found an inverse relationship between their percentages (r = - 0.356, p < 0.001; r = 163); however, the points were not close to the regression line. The %OA vs. %AA relationship changed appreciably in response to slightly altering concentration distributions of OA and AA, and a negative association could be changed to become positive.
Conclusion: Using random numbers, generated within the biological distributions for OA, AA, and sum of the remaining fatty acids, we found an inverse relationship between "% OA" and "% AA", but the scatterplot was poor compared with that obtained with real values. The association between relative abundances of random numbers of OA and AA was very sensitive to changes in distributions, and a negative association could be changed to become positive by slightly altering the distributions. Thus, the association between relative abundances of OA and AA could be partly caused by the particular distribution of the fatty acid concentration: a Distribution Dependent Correlation.
Keywords: Arachidonic acid; Chickens; Oleic acid; Random numbers.