Mechanical limits to maximum weapon size in a giant rhinoceros beetle

Abstract

The horns of giant rhinoceros beetles are a classic example of the elaborate morphologies that can result from sexual selection. Theory predicts that sexual traits will evolve to be increasingly exaggerated until survival costs balance the reproductive benefits of further trait elaboration. In Trypoxylus dichotomus, long horns confer a competitive advantage to males, yet previous studies have found that they do not incur survival costs. It is therefore unlikely that horn size is limited by the theoretical cost -benefit equilibrium. However, males sometimes fight vigorously enough to break their horns, so mechanical limits may set an upper bound on horn size. Here, I tested this mechanical limit hypothesis by measuring safety factors across the full range of horn sizes. Safety factors were calculated as the ratio between the force required to break a horn and the maximum force exerted on a horn during a typical fight. I found that safety factors decrease with increasing horn length, indicating that the risk of breakage is indeed highest for the longest horns. Structural failure of oversized horns may therefore oppose the continued exaggeration of horn length driven by male-male competition and set a mechanical limit on the maximum size of rhinoceros beetle horns.

Structural adaptations to diverse fighting styles in sexually selected weapons

“…Results from the finite element models indicate that the highest stresses generated in a horn during fights occur in the middle of the shaft, which matches the actual location of horn fractures for beetles in the field (39). Our finite element models therefore accurately predict the responses of horns to the forces incurred during fights.…”

“…Specifically, to compare performance in terms of model stress (σ = F=A, where F is force and A is cross-sectional surface area) in the vertical and lateral bending models, we maintained the same force-to-surface area ratios (36). The three models were therefore scaled to the same surface area (723 mm 2 , or the surface area of the Trypoxylus model), and the same total force (4 N) was applied to the horn tip, based on field estimates of the forces exerted by Trypoxylus males during fights (39). Similarly, to compare stress in our twisting models, we maintained the same torque-tovolume ratios.…”

Role of stag beetle jaw bending and torsion in grip on rivals

“…As a result, males manage to retain their safety factor at approximately the same level as that of female jaws, despite their strongly increased bite muscle force. The safety factors that we measured (5.2-7.2) are comparable to other measurements of male C. metallifer stag beetle jaws (2.05-12.7) and to those of rhinoceros beetle horns (6.5) [17,18].…”

Functional mechanics of beetle mandibles: Honest signaling in a sexually selected system

“…An important possible trade off between reproductive benefits and survival costs is the mechanical or structural strength of the weapon. Studies on the structural strength of horns on the rhinoceros beetle, Trypoxylus dichotomus , suggested that as the horn length increased, so did the force that was required to break the horn, indicating that longer horns can withstand higher forces and that there is increased material reinforcement in longer horns (McCullough, ). Our findings show that the force required to break a mandible did not increase with mandible length, but rather stayed relatively constant across mandible lengths.…”

“…It has been suggested that there are mechanical limits to the size of the horn in rhinoceros beetles, resulting in decreased safety factors as the horn length increases (McCullough, ). This same trend was found in our data.…”