Supporting information for Rensch’s rule – definitions and statistics

Issue: Sexual size dimorphism is thought to vary 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. Evidence: We 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 literature data, we show that RMA and ordinary least square
(OLS) methods of line fitting can produce conflicting results, suggesting
that RMA is less conservative a way to test the rule. Conclusion: We
recommend that both line fitting methods are used to estimate Rensch’s
rule with strong support claimed only when results of both agree with each
other. Alternatively, we suggest tests are conducted in a way that agree
with the rule’s definition, i.e. that size dimorphism is regressed on the
mean size of males and females of species.