Convergent evolution is a phenomenon whereby similar traits evolved independently in not closely related species, and is often interpreted in functional terms. Spines in mollusk seashells are classically interpreted as having repeatedly evolved as a defense in response to shell-crushing predators. Here we consider the morphogenetic process that shapes these structures and underlies their repeated emergence. We develop a mathematical model for spine morphogenesis based on the mechanical interaction between the secreting mantle edge and the calcified shell edge to which the mantle adheres during shell growth. It is demonstrated that a large diversity of spine structures can be accounted for through small variations in control parameters of this natural mechanical process. This physical mechanism suggests that convergent evolution of spines can be understood through a generic morphogenetic process, and provides unique perspectives in understanding the phenotypic evolution of this second largest phylum in the animal kingdom.H omoplasy, the appearance of similar traits in separate evolutionary lineages as a result of convergence, parallelism, or evolutionary reversals, is a major concern in phylogenetic analysis for which it is viewed as noise. However, over the past two decades, homoplasy has also become a subject of increasing interest, stimulated by the rise of evolutionary developmental biology (evo devo) and the wish to uncover the developmental basis of this phenomenon (1-3). Spines constitute the most prominent ornamentation of mollusk shells and have evolved in many distantly related fossil and current mollusk species (at least 55 genera and 21 families of current gastropods; 10 genera and 8 families of current bivalves; 11 genera and 8 families of ammonoids; and 6 fossil nautiloid genera; see Fig. 1 for examples). Convergent evolution of spines in mollusks has been addressed in functional terms, these structures being interpreted as having evolved as a defense in response to shell-crushing predators (4-6). This hypothesis is itself the basis of the widely cited "escalation hypothesis," according to which long-term trends in the fossil record were caused by the evolutionary response of prey to predation pressure (7). The idea that convergent evolution of similar mollusk ornamentations might be fully explained in functional terms is based on the premise that similar characters, perceived as well designed for a presumed function, cannot conceivably have independently evolved fortuitously. Therefore, natural selection is thought to have repeatedly shaped similar functional traits out of random variations.Over the past two decades, there has been an increasing awareness that selectionist hypotheses on their own have partial explanatory value for understanding the evolution of biological form, because they do not address the origin of traits thought to increase reproductive success (8-10). In other words, even if spines act in some species as protection against predators, to hypothesize that this feature has sprea...

This article explores the close relationships between growth rate and allometries of molluscan shells. After reviewing the previous theoretical approaches devoted to the understanding of shell form and its morphogenesis, we present a free-form vector model which can simulate apertural shape changes and nonlinear allometries. Shell morphology is generated by iteratively adding a growth increment onto the last computed aperture. The first growth increment defines so-called growth vectors which are assumed to be constant in direction (relative to the last computed aperture position) during a simulation of a shell (ontogeny). These growth vectors are uniformly scaled at each time step according to various growth rate curves that are used to simulate the mantle growth over time. From the model, we derive morphometric variables that illustrate the ontogenetic trajectories in time-size-shape space. We investigate the effects of changing the growth curves types, growth rate parameters and growth vector maps on the direction, speed and patterns of ontogenetic allometries. Because this model focuses the issue on time, it highlights a plausible effect of growth rate on shell shape and illustrates some fundamental geometrical properties of the logarithmic spiral, in particular the close relationship between the size and the geometry of growth increments. This model could be used to develop a mathematically data-driven approach where experimentally obtained growth curves could be used as inputs in the model. More generally, our study recalls the role of growth rates in the generation of allometries.

In recent years, developmental plasticity has received increasing attention. Specifically, some studies highlighted a possible association between shell shape and growth rates in intertidal gastropods. We use a growth vector model to study how hypothetical growth processes could underlie developmental plasticity in molluscs. It illustrates that variation in instantaneous shell growth rate can induce variability in allometric curves. Consequently, morphological variation is time-dependent. Basing our model parameters on a study documenting the results of transplants experiments of three gastropods ecomorphs, we reproduce the main aspects of the variation in size, shape, and growth rates among populations when bred in their own habitat or transplanted to another ecotype habitat. In agreement with empirical results, our simulation shows that a flatter growth profile corresponds to conditions of rapid growth. The model also allows the comparison of allometric slopes using different subdata sets that correspond to static and ontogenetic allometry. Our model highlights that depending on subdata sets, the "main effects" could be attributed to source population or environment. In addition, convergence or divergence of allometric slopes is observed depending on the subdata sets. Although there is evidence that shell shape in gastropods is to some extent growth rate dependent, gaining a general overview of the issue is challenging, in particular because of the scarcity of studies referring to allometry. We argue that the dynamics of development at the "phenotypic level" constitute a non-reducible level of investigation if one seeks to relate the observed amount of phenotypic variation to variability in the underlying factors.