vol. 163, no. 5 the american naturalist may 2004  Persistence and Fluctuation of Lateral Dimorphism in Fishes Mifuyu Nakajima, 1,* Hiroyuki Matsuda, 1,† and Michio Hori 2,‡ 1. Ocean Research Institute, University of Tokyo, 1-15-1 Minamidai, Nakano-ku, Tokyo 164-8639, Japan; 2. Department of Animal Ecology, Faculty of Science, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan Submitted May 27, 2003; Accepted December 3, 2003; Electronically published May 4, 2004 Online enhancements: appendixes, table, literature cited. abstract: Two morphological types (“righty” and “lefty”) have been discovered in several fish species and are referred to as a typical example of antisymmetry. It has been suggested, first, that this di- morphism (called laterality) is inheritable; second, that the frequen- cies of laterality in each species fluctuate around 0.5; and third, that predators mainly exploit prey of the opposite laterality; that is, lefty and righty predators prey on righties and lefties, respectively. The latter is defined as “cross predation”; the antonym “parallel preda- tion” means predation within the same laterality. We hypothesized that cross predation drives alternation of the survival and repro- ductive advantages between two morphological types, leading to frequency-dependent selection that maintains the dimorphism. To investigate this, we constructed mathematical models of population dynamics of one prey/one predator systems and three-trophic-level systems with omnivory. Mathematical analysis and computer sim- ulations explained the behavior of the laterality frequency in nature well, insofar as cross predation dominated over parallel predation. Furthermore, the simulations showed that when only one of the morphological types exists in a species, the other type can invade. This suggests that dimorphism is maintained in all interacting species. Keywords: laterality, antisymmetry, prey-predator system, omnivory, dimorphism, frequency-dependent selection. Although one of the factors known to maintain poly- morphism is frequency-dependent selection, this has not * E-mail: mifuyu@ori.u-tokyo.ac.jp. † Present address: Faculty of Environment and Information Sciences, Yoko- hama National University, Tokiwadai, Hodogaya-ku, Yokohama 240-8501,Ja- pan; e-mail: matsuda@ynu.ac.jp. ‡ E-mail: hori@terra.zool.kyoto-u.ac.jp. Am. Nat. 2004. Vol. 163, pp. 692–698.  2004 by The University of Chicago. 0003-0147/2004/16305-30205$15.00. All rights reserved. been clearly demonstrated in field data. Hori (1991, 1993) found two morphological types in a population of scale- eating cichlids Perissodus microlepis in Lake Tanganyika: one type has its mouth opening to the right, causing the left side of its head to more or less face the front (termed “lefty”), while the other type has its mouth to the left, causing the right side of the head to face frontward (“righty”). Note that Hori (M. Hori, unpublished man- uscript) has changed the definitions of lefty and righty to those described above; in previous works (Hori 1991, 1993), he considered an individual with its mouth opening to the left to be “left-handed” or “sinistral.” As Mboko et al. (1998) and Seki et al. (2000) mentioned, this asymmetry in laterality differs from fluctuating asymmetry (see the definition in Van Valen 1962) in that there are no “middle” or “normal” individuals with little deviation from sym- metry. It is a typical example of “antisymmetry” (Palmer 1996), which has a bimodal distribution of signed differ- ences on both sides (Van Valen 1962). Hori (1991, 1993) has described several features of this type of dimorphism. First, the laterality is inheritable in a Mendelian one locus/two allele fashion, with lefties dom- inating; second, the proportion of lefties in the population over 11 yr showed a periodical oscillation around 0.5; and third, lefty scale eaters in Lake Tanganyika attacked only the left flanks of their prey, whereas righty scale eaters attacked only the right flanks of prey. Recently, laterality has been found not only in populations of the scale eaters P. microlepis and Perissodus straeleni (Hori 1993, 2000; Takahashi and Hori 1998) but also in other Lake Tangan- yika cichlids (Telmatochromis temporalis: Mboko et al. 1998; 19 other species: M. Hori, unpublished manuscript) and even in a freshwater goby Rhinogobius flumineus in a Japanese river (Seki et al. 2000). In addition, laterality appears in both prey and predator fish species, and pred- ators usually attack prey of the opposite morphological type (Hori 2000). Here we define “cross predation” as predation when predators exploit prey of the opposite laterality, that is, when lefties and righties of the same predator species feed on righties and lefties, respectively, of the prey species. Conversely, we define “parallel pre- dation” as a situation in which predators feed on prey of the same laterality. To explain the mechanism that main-