A flexible Bayesian approach to estimating size-structured matrix population models
Authors: Mattern Jann Paul , Glauninger Kristof , Britten Gregory L. , Casey John , Hyun Sangwon , Wu Zhen , Armbrust E Virginia , Harchaoui Zaid , Ribalet François 
Published: July 2021

The rates of cell growth, division, and carbon loss of microbial populations are key parameters for understanding how organisms interact with their environment and how they contribute to the carbon cycle. However, the invasive nature of current analytical methods has hindered efforts to reliably quantify these parameters. In recent years, size-structured matrix population models (MPMs) have gained popularity for estimating rate parameters of microbial populations by mechanistically describing changes in microbial cell size distributions over time. And yet, the construction, analysis, and biological interpretation of these models are underdeveloped, as current implementations do not adequately constrain or assess the biological feasibility of parameter values, leading to inference which may provide a good fit to observed size distributions but does not necessarily reflect realistic physiological dynamics. Here we present a flexible Bayesian extension of size-structured MPMs for testing underlying assumptions describing the dynamics of a marine phytoplankton population over the day-night cycle. Our Bayesian framework takes prior scientific knowledge into account and generates biologically interpretable results. Using data from an exponentially growing laboratory culture of the cyanobacterium Prochlorococcus, we herein demonstrate the performance improvements of our approach over current models and isolate previously ignored biological processes, such as respiratory and exudative carbon losses, as critical parameters for the modeling of microbial population dynamics. The results demonstrate that this modeling framework can provide deeper insights into microbial population dynamics provided by flow-cytometry time-series data.

Author summary

Identifying the growth and population dynamics of marine microorganisms in their natural habitat is crucial to understanding the flow of carbon in the oceans but remains a grand challenge due to the invasive nature of current measurement methods. As time-series observations of population size structure have become more commonplace in aquatic environments, matrix population models (MPMs), which aim to mechanistically describe the change in size structure of these populations over time, have gained in popularity over the last decade. However, the underlying assumptions and behavior of MPMs have not been adequately scrutinized, and parameter values are difficult to interpret biologically, leading to inference that may not reflect plausible physiological dynamics. Here, we develop a Bayesian extension of the MPM framework to examine biological assumptions, improve interpretability of model output, and account for additional biological processes. We evaluated the performance of our models on a publicly available dataset of laboratory experiment time-series measurements of the cyanobacterium Prochlorococcus, Earth’s most abundant photosynthetic organisms, demonstrated the performance improvements of our approach over current models, and isolated previously ignored respiratory and exudative carbon losses as critical parameters for the modeling of microbial population dynamics.