MoGroFunGen: A numerical model for reconstructing intra-annual growth rates of bivalve molluscs

Bivalve mollusc shells contain valuable archives of biological and environmental information. For example, periodic microgrowth increments record intra-annual growth rates that vary, in large part, as a function of temperature. Unfortunately, these increments are often not preserved, or were deposited at equivocal intervals, especially in fossils or shells with obscure increments. Here we present a new numerical model that reconstructs intra-annual growth rates by relating linear growth and time using oxygen isotopes from shell carbonate. The model involves converting observed oxygen isotope values from shell carbonate (δ18Ocarb) to temperatures, which requires knowledge of the oxygen isotope composition of water (δ18Owater). Then calculated temperatures are converted to dates using temporally calibrated temperature records. Next, dates are plotted versus sample distance (measured from sampled shells), fit with a monotonic cubic spline, and finally the first derivative of this function is evaluated yielding the growth function. The variance of this function is estimated through resampling by incorporating the uncertainty associated with δ18O measurement (e.g., ± 0.08‰). This numerical model produces a distribution of growth functions, from which we calculate the average growth function. Modeled growth functions agree well with independently derived growth functions, which suggests our modeling procedure produces reliable estimates of intra-annual growth rates. These data can, in turn, provide valuable ecological information, such as the timing of highest intra-annual growth rates, growth-limiting temperatures, and optimal growth temperatures. This final parameter is particularly important because optimal growth temperatures can now be estimated without any a priori knowledge of growth rates.