Can the form of sexual selection explain patterns of static weapon allometry expressed by alternative mating morphotypes?

The regime of selection acting on a trait is expected to shape its static allometry. Few studies, however, have quantified the form of sexual selection acting on a trait in the wild to test whether the trait allometrically scales as predicted. Even fewer studies have tested these predictions using males expressing weapon polymorphism as part of their alternative mating strategies. Here, I use field data to test how sexual selection shapes scaling allometries of male weaponry in the Wellington tree wētā (H. crassidens), a male-trimorphic and harem-polygynous insect endemic to New Zealand. Contrary to the prediction that 10th instar males' large weaponry would scale hyperallometrically because it is under direct sexual selection, I found that 10th instar weaponry is not subject to direct sexual selection and scales hypoallometrically. Similarly, neither 8th nor 9th instar male weaponry experiences direct sexual selection, and their weaponry scales hyperallometrically and hypoallometrically, respectively. My study suggests that disentangling competing hypotheses for the evolution of scaling patterns of sexually selected traits must go beyond a simple viability-sexual selection dichotomy by also considering weapon function and the ecological context within which the weapon is used.