Covarying Shell Growth Parameters and the Regulation of Shell Shape in Marine Bivalves: A Case Study on Tellinoidea

Abstract

Specific parameters characterising shell shape may arguably have a significant role in the adaptation of bivalve molluscs to their particular environments. Yet, suchfunctionally relevantshape parameters (shell outline elongation, dissymmetry, and ventral convexity) are not those parameters that the animal may directly control. Rather than shell shape, the animal regulates shell growth. Accordingly, an alternative,growth-baseddescription of shell-shape is best fitted to understand how the animal may control the achieved shell shape. The key point is, in practice, to bring out the link between those two alternative modes of shell-shape descriptions, that is, to derive the set of equations which connects thegrowth-basedshell-shape parameters to thefunctionally relevantshell-shape parameters. Thus, a preliminary object of this note is toderivethis set of equations as a tool for further investigations. A second object of this work is to provide an illustrative example of implementation of this tool. I report on an unexpected negative covariance between growth-based parameters and show how this covariance results in a severe limitation of the range of interspecific variability of the degree of ventral convexity of the shell outline within the superfamily Tellinoidea. Hypotheses are proposed regarding the constraints possibly at the origin of this limitation of interspecific variability.

Unexpected Covariances between Shell Growth Parameters are Controlling the Range of Interspecific Variations of Shell shape in the Deep-Sea Clams Genus Calyptogena (Bivalvia: Veneroida)

“…Previous studies analysing the interspecific variations of shell shape within a series of bivalves genus (Tellina, Donax, Gari, Abra, Macoma) [1,2] have shown that, among the six types of covariances that may exist a priori between the three growth-related parameters α, ρ and δ, only the negative covariance between α and ρ was systematically recorded. In addition, recent (unpublished) work on interspecific variations within Mactridae, including clams species with high levels of shell-growth dissymmetry (δ up to 3.1) also confirms the occurrence of the negative covariance between α and ρ.…”

“…-From developmental constraints (other than the purely geometrical constraints which do not exist, as already mentioned, see [1,2]) applying directly on the growth process and then, controlling only indirectly the achieved shell shape, or, -From selective constraints applying now directly to functionally-relevant shell shape parameters, resulting in the selective sorting of the more appropriate, best adapted shell shapes, according to the preferred environmental contexts of each species (the recorded covariances between growth parameters being, thus, the indirect result of these selective pressures applying directly to shell-shape).…”

“…As for the three growth-related parameters α, ρ, δ above, these three functionally-relevant parameters E, D, K, are, intrinsically, free from any geometrical constraint a priori and thus mutually independent also. Yet, E, D, K are entirely dependent, a posteriori, upon α, ρ, δ, according to three, geometrically-based equations, provided in Appendix: equations A.1, A.2, A.3 and Table A.2 (see references [1][2] for the derivation of these equations and further details).…”

“…An alternative solution, however, may arise from the thorough analysis of crude field data. Due to rigid geometrical relationships between shell-growth parameters and shellshape parameters in bivalves, it has been demonstrated [1][2] that any significant modification of amplitude of the range of variations of a given shell-shape parameter (either expansion or restriction) mathematically implies the appearance of a specific kind of covariation between shell-growth parameters. Conversely, the unexpected occurrence of a given covariance between shell-growth parameters calls for the likely existence of a constraint, that either expands or contracts the range of variation of one or another shell-shape parameters ("unexpected occurrence" being understood in the sense that no other alternative origin for this covariance -developmental in particular [3] -might arguably be admitted).…”

“…Based on this procedure, a series of investigations conducted on a variety of groups of clams ( [1,2] and also still unpublished data) have provided evidence for the repeated occurrence of either expansion or restriction of the interspecific ranges of variation of several functionally-relevant shell-shape traits ("expansion or restriction" being understood as compared to what would be the amplitudes of theses ranges of variation in the absence of covariance). More precisely, the following trends have been highlighted [2] as regards three major, functionally-relevant shell-shape traits (more precisely defined below, in section Methods):…”