An empirically based minimalistic model for 1 representing seasonal phytoplankton dynamics

Supported by chl-a satellite data in the North Atlantic (and phytoplankton division rate computed from therein), the disturbance-recovery hypothesis for the initiation of phytoplankton blooms posits that the change in chl-a concentration is proportional to the rel18 ative change in the phytoplankton division rate. Here, we use this hypothesis introduced by Behrenfeld as a principal model assumption and construct a non-autonomous ordinary differential equation model for seasonally varying chl-a concentration. Our quantitative comparison between model simulations and in situ measurements of chl-a and primary production collected from a Swedish fjord is two-fold: First, by using approximate Bayesian computation, we find distributions of values for the three model parameters that best describe the chl-a data. Then, we validate our model by comparing the simulated (not fitted)1 division rate to the data on division rate. Our minimalistic model is able to capture (1) the yearly trend in the chl-a concentration, (2) the pattern of growth and decline in the phytoplankton division rate, and (3) the decreasing trend in the relative change of the division rate exhibited in the data for several individual years. Moreover, the modeling efficiency (which is a measure of the goodness of fit of a (deterministic) model and nearly identical to R2 for statistical models) is positive (between 0.3 and 0.9 with an average of 0.63) for all 11 years included in this study. Thus, we conclude that the change in chl-a concentra8 tion being proportional to the relative change in the division rate is a possible explanation for the bloom dynamics in the Gullmar fjord. In addition, our work provides a simple and empirically based differential equation for representing yearly dynamics of primary
production, e.g., for generating ecological hypotheses using models of other trophic levels.