Adaptive significance of critical weight for metamorphosis in holometabolous insects

Holometabolous insect larvae become committed to metamorphosis when they reach a critical weight. Although the physiological mechanisms involved in this process have been well-studied, the adaptive significance of the critical weight remains unclear. Here, we developed a life history model for holometabolous insects and evaluated it from the viewpoint of optimal energy allocation. We found that, without a priori assumptions about critical weight, the optimal growth schedule is always biphasic: larval tissues grow predominately until they reach a certain threshold, after which the imaginal tissues begin rapid growth, suggesting that the emergence of a critical weight as a phase-transition point is a natural consequence of optimal growth scheduling. Our model predicts the optimal timing of critical-weight attainment, in agreement with observations in phylogenetically-distinct species. Furthermore, it also predicts the scaling of growth scheduling against environmental change, i.e., the relative value and timing of the critical weight should be constant, thus providing a general interpretation of observed phenotypic plasticity. This scaling relationship allows the classification of adaptive responses in critical weight into five possible types that reflect the ecological features of focal insects. In this manner, our theory and its consistency with experimental observations demonstrate the adaptive significance of critical weight.