Is Allometric Variation in the Cephalic Horn on Male Rhinoceros Beetles Discontinuously Dimorphic?

Evolution of horn length and lifting strength in the Japanese rhinoceros beetle Trypoxylus dichotomus

What limits the size of nature's most extreme structures? For weapons like beetle horns, one possibility is a tradeoff associated with mechanical levers: as the output arm of the lever system-the beetle horn-gets longer, it also gets weaker. This "paradox of the weakening combatant" could offset reproductive advantages of additional increases in weapon size. However, in contemporary populations of most heavily weaponed species, males with the longest weapons also tend to be the strongest, presumably because selection drove the evolution of compensatory changes to these lever systems that ameliorated the force reductions of increased weapon size. Therefore, we test for biomechanical limits by reconstructing the stages of weapon evolution, exploring whether initial increases in weapon length first led to reductions in weapon force generation that were later ameliorated through the evolution of mechanisms of mechanical compensation. We describe phylogeographic relationships among populations of a rhinoceros beetle and show that the "pitchfork" shaped head horn likely increased in length independently in the northern and southern radiations of beetles. Both increases in horn length were associated with dramatic reductions to horn lifting strength-compelling evidence for the paradox of the weakening combatant-and these initial reductions to horn strength were later ameliorated in some populations through reductions to horn length or through increases in head height (the input arm for the horn lever system). Our results reveal an exciting geographic mosaic of weapon size, weapon force, and mechanical compensation, shedding light on larger questions pertaining to the evolution of extreme structures.

Continuous phenotypic modulation explains male horn allometry in three dung beetle species

Many dung beetle species show male horn polyphenism, the ability of males to develop into distinct phenotypes without intermediate forms as a response to the larval growth environment. While males with long (majors) and rudimentary (minor) horn have been widely reported in literature, little is known about the existence of individuals with intermediate horn length. Here we investigate the occurrence of intermediates in natural populations of three dung beetle species (Onthophagus furcatus, Copris lunaris and C. hispanus). We analysed the body size-horn length relationship using linear, exponential, and sigmoidal models with different error structures. We inferred the number of individuals in the minor, intermediate, and major groups by combining changepoint analysis and simulation from fitted allometric models. The sigmoidal equation was a better descriptor of the body size-horn length relationship than linear or exponential equations in all the three studied species. Our results indicated that the number of intermediates equals or exceeds the number of minor and major males. This work provides evidence that, at least in the studied species, males with intermediate horn length exist in natural populations. For similar cases we therefore suggest that continuous phenotypic modulation rather than discrete polyphenism can explain variation in male horn allometry.

When perception isn’t reality: allometric variation in the exaggerated mandibles of male stag beetles (Coleoptera: Lucanidae)

A variety of protocols have been used to study allometric variation in size of the exaggerated mandibles on male stag beetles. Many of these protocols entail logarithmic transformation of the original measurements followed by numerical analysis of the transformations by linear regression or some conceptual extension thereof. I reanalysed data from four such studies to show how these protocols can lead investigators to conclusions that are not well supported by the original observations. One of the data sets was originally reported to conform to simple loglinear allometry, with untransformed observations that presumably follow the path of a two-parameter power function; one was said to represent biphasic, loglinear allometry, with two distinctive morphs having different scaling relationships on the arithmetic scale; and two were originally described as cases of discontinuous, loglinear allometry caused by dimorphisms. My analyses, which were based on graphical analysis and nonlinear regression of untransformed observations, revealed that all the data sets form S-shaped distributions and that each of the distributions is well described by a four-parameter sigmoid function. None of the bivariate distributions reveals a discontinuity or dimorphism. Thus, the original authors unknowingly offered descriptions and interpretations for patterns of variation that do not exist in their data.