Abstract. Although it has been the subject of verbal theory since Darwin, the evolution of morphological trait allometries remains poorly understood, especially in the context of sexual selection. Here we present an allocation trade-off model that predicts the optimal pattern of allometry under different selective regimes. We derive a general solution that has a simple and intuitive interpretation and use it to investigate several examples of fitness functions. Verbal arguments have suggested cost or benefit scenarios under which sexual selection on signal or weapon traits may favor larger individuals with disproportionately larger traits (i.e., positive allometry). However, our results suggest that this is necessarily true only under a precisely specified set of conditions: positive allometry will evolve when the marginal fitness gains from an increase in relative trait size are greater for large individuals than for small ones. Thus, the optimal allometric pattern depends on the precise nature of net selection, and simple examples readily yield isometry, positive or negative allometry, or polymorphisms corresponding to sigmoidal scaling. The variety of allometric patterns predicted by our model is consistent with the diversity of patterns observed in empirical studies on the allometries of sexually selected traits. More generally, our findings highlight the difficulty of inferring complex underlying processes from simple emergent patterns.Key words. Allometry, display traits, evolution, exaggerated traits, morphology, sexual selection, signaling, weapons.Received April 7, 2003. Accepted June 5, 2003 An organism's shape is defined by the sizes of its body parts (traits) in relation to the size of the whole (body size), with the scaling pattern relating trait size to body size known as the trait allometry. Although a great deal of work has been devoted to the mathematical analysis of observed allometric patterns (e.g., Brody 1945;Gould 1966;Sprent 1972;Eberhard and Gutiérrez 1991) and the effects of biomechanical constraints (e.g., McMahon 1975;Pennycuick 1992;Ravosa et al. 2000), much less is known about how allometry is shaped by selection. This last question is of particular interest in the context of sexually selected traits, which sometimes exhibit spectacular elaboration and enlargement (e.g., Darwin 1871;Gould 1974;Simmons and Tomkins 1996;Emlen and Nijhout 2000). In this paper, we use a resource allocation trade-off model to investigate how the form of selection acting on a trait and body size affects the evolution of static allometry, trait scaling with body size among conspecific individuals at the same developmental stage (Cock 1966). The model yields some intuitively appealing predictions as well as counterintuitive insights that challenge the validity or generality of verbal theories.Allometries are usually modeled using the allometric equation (Brody 1945), Y ϭ aX b . When log-transformed, this becomes the linear equation log(Y) ϭ log(a) ϩ blog(X), where b is the allometric slope. Although, in pra...