Rensch’s Rule Applies to Clinal Variation of Body Size in the Argentine Grasshopper <I>Dichroplus pratensis</I>: Correction of Bidau and Martí

Abstract

In their article entitled “Clinal Variation of Body Size in Dichroplus pratensis (Orthoptera: Acrididae): Inversion of BergmannOs andRenschOs Rules,”Bidau and Martṍ (2007) published results in this journal about clinal population data from 1998 to 2001. In the sexual size dimorphism (SSD) analysis of the grasshopper Dichroplus pratensis Bruner, they incorrectly conclude the 19 populations studied, encompassing 22 of latitude in Argentina, exhibit the inverse of RenschOs rule (Rensch 1960). The authors explain RenschOs rule as stating “that in species where males are larger than females, sexual dimorphism increases with size” (Bidau and Martṍ 2007). Although this is correct, it is an incomplete deÞnition. In his work, Rensch (1960) describes a general pattern to relate SSD to the body size of animals: “In species of birds inwhich themale is larger than the female, the relative sexual difference increases with body size. If by way of exception, the females are larger than the males, as among many species of birds of prey, the opposite correlation applies, i.e., the greater sexual difference is found in the smaller species” (p. 159). RenschOs rule is fully deÞned as the allometry observed when SSD increases with size if males are the larger sex, butwhenSSDdecreaseswith size if females are the larger sex (Rensch 1960, Fairbairn 1990 Abouheif and Fairbairn 1997, Fairbairn 1997). Allometry consistent with RenschOs rule is represented by the slope of a model II regression being 1 ( 1) when log female size is regressed on logmale size, regardless of which sex is larger (Abouheif and Fairbairn 1997). Note that if the axes are reversed (male size regressed on female size),RenschOs rule is representedbya slope of 1 ( 1) (Fairbairn 1997). More generally, RenschOs rule occurs when more variance in male body size than female body size is observed (Fairbairn 1997, Blanckenhorn et al. 2007). The results fromBidau andMartṍ (2007) indicateD. pratensis exhibits female-biased SSD (females larger thanmales). Their data demonstrate “. . . the degree of SSD decreases as mean size of both sexes increase,” thus actually conforming to RenschOs rule. Furthermore, in Fig. 3f they regress log female on log male body length (axes similar to Þg. 1 of Abouheif and Fairbairn 1997) and Þnd a slope of 0.5718. This value is unequivocally 1, but for this study to demonstrate an inverse of RenschOs rule the slope of the regression line would need to be 1 (Abouheif and Fairbairn 1997). The authors did not state whether they used a model I or model II regression in their analyses. If a model I regression was used, reanalyzing thedatawithpropermodel IImethodsmaychange the signiÞcance of the results. The study of Bidau and Martṍ (2007) clearly demonstrates a case where empirical evidence supports RenschOs rule in D. pratensis. Due to a misinterpretation of RenschOs rule, the authors wrongly cite their work as an example of the inverse to RenschOs rule.