Rensch’s rule—Definitions and statistics

Abstract

AbstractIssueSexual size dimorphism is thought to vary in a predictable manner with overall body size, a pattern named “Rensch's rule”. The rule is thought to suggest different predictions for taxa with female‐ and male‐biased dimorphism. This leaves taxa where both types of dimorphism are common in limbo. Rensch's rule is usually estimated using the reduced major axis (RMA) slope of a regression of male size on female size. A slope steeper than one shows support for the rule.EvidenceWe show that the predictions of Rensch's rule for male‐ and female‐biased taxa are, in fact, the same and offer a unified definition of the rule. Using numerical examples and data from the literature, we show that RMA and ordinary least squares (OLS) methods of line fitting can produce conflicting results, suggesting that RMA is a less conservative way to test the rule.ConclusionWe recommend that both line‐fitting methods are used to estimate Rensch's rule, with strong support being claimed only when the results of both agree with each other. Alternatively, we suggest that tests are conducted in a way that agrees with the definition of the rule (i.e., that size dimorphism is regressed on the mean size of males and females of the species).