Modeling the temporal periodicity of growth increments based on harmonic functions

Age estimation methods based on hard structures require a process of validation to confirm the periodical pattern of growth marks. Among such processes, one of the most used is the marginal increment ratio (MIR), which was stated to follow a sinusoidal cycle in a population. Despite its utility, in most cases, its implementation has lacked robust statistical analysis. Accordingly, we propose a modeling approach for the temporal periodicity of growth increments based on single and second order harmonic functions. For illustrative purposes, the MIR periodicities for two geoduck species (Panopea generosa and Panopea globosa) were modeled to identify the periodical pattern of growth increments in the shell. This model identified an annual periodicity for both species but described different temporal patterns. The proposed procedure can be broadly used to objectively define the timing of the peak, the degree of symmetry, and therefore, the synchrony of band deposition of different species on the basis of MIR data.