Cause of bimodal distribution in the shape of a terrestrial gastropod

The distribution of a phenotypic state is often discontinuous and dispersed. An example of such a distribution can be found in the shell shapes of terrestrial gastropods, which exhibit a bimodal distribution whereby species possess either a tall shell or a flat shell. Here we propose a simple model to test the hypothesis that the bimodal distribution relates to the optimum shape for shell balance on the substrates. This model calculates the theoretical shell balance by moment and obtains empirical distribution of shell shape by compiling published data and performing a new analysis. The solution of the model supports one part of the hypothesis, showing that a low-spired shell is the best balanced and is better suited for locomotion on horizontal surface. Additionally, the model shows that both high- and low-spired shells are well balanced and suited on vertical surfaces. The shell with a spire index (shell height divided by diameter) of 1.4 is the least well balanced as a whole. Thus, spire index is expected to show a bimodal distribution with a valley at 1.4. This expectation was supported by empirical distribution of a spire index, suggesting that the bimodality of shell shape in terrestrial gastropods is related to shell balance.