Life‐history invariants with bounded variables cannot be distinguish from data generated by random processes using standard analyses

Abstract

A dimensionless approach to the study of life-history evolution has been applied to a wide variety of variables in the search for life-history invariants. This approach usually employs ordinary least squares (OLS) regressions of log-transformed data. In several well-studied combinations of variables the range of values of one parameter is bounded or limited by the value of the other. In this situation, the null hypothesis normally applied to regression analysis is not appropriate. We generate the null expectations and confidence intervals (CI) for OLS and reduced major axis (RMA) regressions using random variables that are bounded in this way. Comparisons of these CI show that, for log-transformed data, the patterns generated by random data and those predicted by life history invariant theory often could not be distinguished because both predict a slope of 1. We recommend that tests based on the putative invariant ratios and not the correlations between the two variables be used in the exploration of life-history invariants using bounded data. Because empirical data are often not normally distributed randomization test may be more appropriate than standard statistical tests.