Does the handicap principle explain the evolution of dimorphic ornaments?

Many species are sexually dimorphic and, interestingly, males in some species are dimorphic themselves: some males develop weapons and ornaments, whereas others express rudimentary ornaments or none at all (horned beetles, Onthophagus taurus: Emlen, Lavine, & Ewen-Campen, 2007; Moczek & Emlen, 2000; bluegill sunfish, Lepomis macrochirus: Dominey, 1980; Gross & Charnov, 1980; ruffs, Philomachus pugnax: Lank, Smith, Hanotte, Burke, & Cooke, 1995; for a review see Simpson, Sword, & Lo, 2011). Males can be so extremely dimorphic that the morphs have been misclassified as different species. The selective maintenance of such male dimorphisms has been difficult to understand (Simpson et al., 2011). Yet, a recent paper by Clifton et al. (2016) concluded the evolution of male dimorphisms can be explained solely by the handicap principle (Zahavi, 1975). It is not intuitively obvious how the handicap principle can selectively maintain male dimorphisms, and no verbal explanations were provided. Here, we raise several caveats about this recent study and, in particular, we show that the findings are not generated by the handicap principle, but by an unrelated assumption of the model. This assumption is not unreasonable, but its stability needs to be examined before