Environmental conditions experienced by aquatic organisms are archived in biogenic carbonates such as fish otoliths, bivalve shells and coral skeletons. Like tree rings, these calcified structures present an accretionary growth and variations in optical properties - color or opacity - that are used to reconstruct time. Full and reliable exploitation of the information from these structures is, however, often limited as the metabolic processes that control their growth and their optical properties are poorly understood. Here, we propose a new modeling framework that couples both the growth of a biogenic carbonate and its optical properties with the metabolism of the organism. The model relies on well-tested properties of Dynamic Energy Budget (DEB) theory, here applied to the formation of fish otoliths. The model reproduces well-known otolith patterns and thus provides us with mechanisms for the metabolic control of otolith size and opacity at the scale of an individual lifespan. Two original contributions using this framework are demonstrated. First, we show that non-seasonal checks can be discriminated from seasonal checks, which is a well-recognized problem when interpreting fish otoliths. Second, we demonstrate that the model reveals the history of temporal variations in the food assimilated by an individual fish. Reconstructing food conditions of past and present aquatic species in their natural environment is key ecological information, essential for better understanding which individual traits determine population dynamics.