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Mandible trimorphism by Yutaka IGUCHI

Male mandible trimorphism in the stag beetle Dorcus rectus (Coleoptera: Lucanidae)
YUTAKA IGUCHI
Laboratory of Biology, Yamashita-cho 1-10-6, Okaya City, Nagano Prefecture, 394-0005, Japan; e-mail: bio-igu@f8.dion.ne.jp
Key words. Lucanidae, Dorcus rectus, stag beetle, mandible, trimorphism, scaling relationship, discontinuous model.

Abstract. Males in many beetles show horn or mandible dimorphism. The stag beetle Dorcus rectus was assumed to have dimorphic males, but in this species there are not two but three visually distinct mandibular phenotypes. The aim of this study is to determine if the three phenotypes represent an allometric trimorphism in this species by studying the scaling relationship between body length and mandible length in 148 adult males and 31 adult females. The relationship was fitted using the following four statistical models; a simple line, a logistic curve, a continuous segmented line and a discontinuous line. The best-fitting model for the males was a dis- continuous line with two break points and that for the females a simple line. The male data was also well fitted by a logistic curve. The discontinuous linear model divided the males into three groups that were in good agreement with the three phenotypes. These results suggest that a subtle allometric trimorphism possibly exists in males of this species. Small males of this species have no dis- tinct teeth on their mandibles, whereas small males of D. striatipennis and D. curvidens, which are closely related to D. rectus, have a pair of distinct teeth on their mandibles. The phylogenetic relationship of these Dorcus species suggests that the trimorphism in D. rectus may have arisen through the loss of teeth in small males.

INTRODUCTION
Males in many beetle species show great variation in the expression of secondary sexual traits such as horns or mandibles. Such variation in males is often discontinuous and males are either large or small with respect to their horn or mandible size (Inukai, 1924; Clark, 1977; Eber- hard, 1982; Goldsmith, 1985; Cook, 1987; Rasmussen, 1994; Siva-Jothy, 1987; Eberhard & Gutierrez, 1991; Kawano, 1995, 1997; Iguchi, 1998; Emlen & Nijhout, 2000; Moczek & Emlen, 2000; Shiokawa & Iwahashi, 2000; Tatsuta et al., 2001, 2004). Recently, however, Rowland & Emlen (2009) indicated that several families of the Coleoptera (e.g., Scarabaeidae and Lucanidae) con- sidered to be male dimorphic actually contain species that are trimorphic in terms of their horns or mandibles. Nev- ertheless, there are very few reports of such trimorphism in beetles (but see Eberhard et al., 2000; Iguchi, 2002).
Males of Dorcus rectus (Motschulsky) are considered to be dimorphic with respect to mandible length (Iguchi, 2001a). However, they also show three mandible types with respect to the number of teeth (Fig. 1a–c; Kurosawa et al., 1988; Iguchi, 1992), whereas females have only one type of mandible (Fig. 1d). As mandible length increases, the number of teeth seems to increase in males (Iguchi, 1992). However, the relationship between man- dible length and mandible shape has not yet been exam- ined in detail. Moreover, there are no morphometric studies on females of this species.
This paper uses the following four models for the scaling relationship between body length and mandible length in D. rectus; a simple line, a logistic curve (Fig. 2a), a continuous segmented line (Fig. 2b) and a discon- tinuous line (Fig. 2c). These models have been used to

determine horn or mandible dimorphism. However, there are very few studies that compare these models in detail (Knell, 2009). In this paper the scaling relationship is determined using these models and the possibility of male allometric trimorphism in D. rectus discussed. Rowland & Emlen (2009) suggest that trimorphism will be difficult to detect using current methods. However, this paper shows that the comparison of these models, especially the use of the discontinuous model, might help detect a sub- tle allometric trimorphism. This paper presents the best- fitting models for males and females and then discusses the evolution of their mandibles on the basis of the phylo- genetic relationship of the species of Dorcus.

MATERIAL AND METHODS Sampling and measurement
A total of 148 adult males and 31 adult females of D. rectus were collected at sap sites on oak trees on 22 days between 20 July and 5 September 2002 in Nirasaki City, Yamanashi Prefec- ture, Japan. For each living male and female, body length (from the front of the head excluding the mandibles to the tip of the elytra) and mandible length (the greatest length of the left or right mandible measured in a straight line) were measured to the nearest 0.1 mm with a slide caliper in the laboratory. Voucher specimens are deposited in the Laboratory of Biology, Okaya City, Japan.
Classification of the mandible types
The mandibles of large males differ in shape from those of small males (Fig. 1). Males can be visually divided into three types, as suggested in previous studies (Kurosawa et al., 1988; Iguchi, 1992); males with two pairs of teeth (Fig. 1a; n = 43), males with one pair (Fig. 1b; n = 75) and males with no teeth on their mandibles (Fig. 1c; n = 30). On the other hand, females only ever have one pair of teeth on their mandibles (Fig. 1d; n = 31). 

Fig. 1. Mandibles of Dorcus rectus of different shapes. (a) Male mandibles with two pairs of teeth (arrows). (b) Male mandibles with one pair of teeth (arrows). (c) Male mandibles with no teeth. (d) Female mandibles with one pair of teeth (arrows).

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