Such growth style as the expansion of body size stops at some point during the life (at the time of maturation, in general) and the size never increases after that time is called "determinate growth". In contrast, body size continues to increase after maturation in "indeterminate growth". Separately from this distinction, I newly name such growth style in shelled organisms as body size and shell thickness increase at the same time "simultaneous shell growth". On the other hand, "sequential shell growth" is characterized by somatic expansion preceding shell thickening.

Although many shelled-molluscs adopt "simultaneous shell growth" with allometric increase of body size and shell thickness, some molluscan families including the family Cypraeidae (Mollusca; Gastropoda) are determinate growers with "sequential shell growth". I raise a question of which is the optimal growth strategy, "simultaneous shell growth" or "sequential shell growth", in a given environment.

In this seminar, I firstly introduce the results of field research that demonstrate that thicker shell prevents shell-breaking predation by crabs or other shell-breakers more effectively. Secondly, I will exhibit the results of calculation for a mathematical model tolerant of dynamic optimization on the assumptions that predation pressure keeps constant throughout life and that thick callus reduces predation pressure. The result indicates that the lifetime reproductive success of the optimal schedule in "sequential shell growth" is smaller than that in "simultaneous shell growth". This suggests the sequential growth pattern found in cowries is not optimal in terms of resource allocation. Finally, I will show the most likely candidate for the optimal growth schedule of the same model through the use of "Pontryagin's Maximum Principle".