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.