Covariations between Shell-Growth Parameters and the Control of the Ranges of Variation of Functionally Relevant Shell-Shape Parameters in Bivalves: A Theoretical Approach
Major traits of shell shape in bivalves may alternatively be described in terms of (i) functionally relevant parameters, assumed to play a significant role in the adaptation of bivalves molluscs to their environments (such as the shell-outline elongation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>E</mml:mi></mml:mrow></mml:math>, ventral convexity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:math>, and dissymmetry <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math>), or (ii) growth-based parameters, directly controlled by the animal. Due to the geometrical linkage between functionally-relevant and growth-based parameters, adaptive constraints that may either widen or narrow the respective ranges of variations of the functional parameters lead to the onset of specific covariations (either positive or negative) between the growth-based parameters. This has practical interest since adaptive constraints are often difficult to identify directly, while they can be conveniently inferred indirectly via the easily recorded patterns of covariances between growth-based parameters. Hereafter, I provide the theoretical background of this tool, including (1) establishing the geometrical relationships between growth-based and functionally relevant parameters and (2) then specifying the correspondences between the different patterns of adaptive constraints, widening or narrowing the variations of the functional parameters and the corresponding patterns of covariations between the growth-based parameters. Illustrative examples of the practical use of this tool are provided, considering both interspecific and intraspecific variations within marine and fresh-water clams.