piCurve: an R package for modeling photosynthesis-irradiance curves
Authors:
Mohammad M. Amirian,
Andrew J. Irwin
Abstract:
Photosynthesis-irradiance (PI) curves are foundational for quantifying primary production, parameterizing ecosystem and biogeochemical models, and interpreting physiological acclimation to light. Despite their broad use, researchers lack a unified, reproducible toolkit to fit, compare, and diagnose the many PI formulations that have accumulated over the last century. We introduce piCurve, an R pac…
▽ More
Photosynthesis-irradiance (PI) curves are foundational for quantifying primary production, parameterizing ecosystem and biogeochemical models, and interpreting physiological acclimation to light. Despite their broad use, researchers lack a unified, reproducible toolkit to fit, compare, and diagnose the many PI formulations that have accumulated over the last century. We introduce piCurve, an R package that standardizes the modeling of PI relationships, with a library of widely used light-limited, light-saturated, and photoinhibited formulations and a consistent statistical framework for estimation and comparison. With the total of 24 PI models, piCurve supports mean squared error (MSE) and maximum likelihood estimation (MLE), provides uncertainty quantification via information matrix (Hessian), and includes automated, data-informed initialization to improve convergence. Utilities classify PI data into light-limited, light-saturated, and photoinhibited regions, while plotting and 'tidy' helpers streamline workflow and reporting. Together, these features enable reproducible analyses and fair model comparisons, including for curves exhibiting a plateau followed by photoinhibition.
△ Less
Submitted 9 September, 2025; v1 submitted 19 August, 2025;
originally announced August 2025.
Extending the Monod Model of Microbial Growth with Memory
Authors:
Mohammad M. Amirian,
Andrew J. Irwin,
Zoe V. Finkel
Abstract:
Monod's model describes the growth of microorganisms using a hyperbolic function of extracellular resource concentration. Under fluctuating or limited resource concentrations this model performs poorly against experimental data, motivating the more complex Droop model with a time-varying internal storage pool. We extend the Monod model to incorporate memory of past conditions, adding a single para…
▽ More
Monod's model describes the growth of microorganisms using a hyperbolic function of extracellular resource concentration. Under fluctuating or limited resource concentrations this model performs poorly against experimental data, motivating the more complex Droop model with a time-varying internal storage pool. We extend the Monod model to incorporate memory of past conditions, adding a single parameter motivated by a fractional calculus analysis. We show how to interpret the memory element in a biological context and describe its connection to a resource storage pool. Under nitrogen starvation at non-equilibrium conditions, we validate the model with simulations and empirical data obtained from lab cultures of diatoms (T. pseudonana and T. weissflogii) and prasinophytes (Micromonas sp. and O. tauri), globally influential phytoplankton taxa. Using statistical analysis, we show that our Monod-memory model estimates the growth rate, cell density, and resource concentration as well as the Droop model while requiring one less state variable. Our simple model may improve descriptions of phytoplankton dynamics in complex earth system models at a lower computational cost than is presently achievable.
△ Less
Submitted 28 December, 2022; v1 submitted 5 July, 2022;
originally announced July 2022.