Abstract
Determining how microbial communities organize and function at the ecosystem level is essential to understanding and predicting how they will respond to environmental change. Mathematical models can be used to describe these communities, but properly representing all the biological interactions in extremely diverse natural microbial ecosystems in a mathematical model is challenging. We examine a complementary approach based on the maximum entropy production (MEP) principle, which proposes that systems with many degrees of freedom will likely organize to maximize the rate of free energy dissipation. In this study, we develop an MEP model to describe biogeochemistry observed in Siders Pond, a phosphate limited meromictic system located in Falmouth, MA that exhibits steep chemical gradients due to density-driven stratification that supports anaerobic photosynthesis as well as microbial communities that catalyze redox cycles involving O, N, S, Fe and Mn. The MEP model uses a metabolic network to represent microbial redox reactions, where biomass allocation and reaction rates are determined by solving an optimization problem that maximizes entropy production over time, and a 1D vertical profile constrained by an advection-dispersion-reaction model. We introduce a new approach for modeling phototrophy and explicitly represent oxygenic photoautotrophs, photoheterotrophs and anoxygenic photoautotrophs. The metabolic network also includes reactions for aerobic organoheterotrophic bacteria, sulfate reducing bacteria, sulfide oxidizing bacteria and aerobic and anaerobic grazers. Model results were compared to observations of biogeochemical constituents collected over a 24 hour period at 8 depths at a single 15 m deep station in Siders Pond. Maximizing entropy production over long (3 day) intervals produced results more similar to field observations than short (0.25 day) interval optimizations, which support the importance of temporal strategies for maximizing entropy production over time. Furthermore, we found that entropy production must be maximized locally instead of globally where energy potentials are degraded quickly by abiotic processes, such as light absorption by water. This combination of field observations and modeling results indicate that natural microbial systems can be modeled by using the maximum entropy production principle applied over time and space using many fewer parameters than conventional models.
Highlights
Mass and energy flow associated with the growth and predation of bacteria, archaea and eukaryotes in microbial food webs, coupled with abiotic reactions and transport processes, define biogeochemical cycles that occur in ecosystems ranging in size from less than a liter (Marino et al, 2016) to the entire planet
Our results focus on how these two solutions compare to observations in the Simulations Compared to Observations section as well as how the short and long interval optimization windows differ from each other in the Comparison Between short interval optimization (SIO) and LIO Simulations section
While improvements could be made with explicit data assimilation (Edwards et al, 2015), the maximum entropy production (MEP) model did a reasonable job at simulating biogeochemistry in Siders Pond with few adjustable parameters, and the better fit of the long interval optimization (LIO) simulation to 6 out of 9 observations indicates that the microbial community has evolved to function over time scales that are longer than 0.25 days (Table 3)
Summary
Mass and energy flow associated with the growth and predation of bacteria, archaea and eukaryotes in microbial food webs, coupled with abiotic reactions and transport processes, define biogeochemical cycles that occur in ecosystems ranging in size from less than a liter (Marino et al, 2016) to the entire planet. Because organisms are responsible for most observed biogeochemical transformations, it is customary and natural to focus on the bioenergetics of growth and predation of organisms that constitute food webs in order to understand and predict biogeochemical transformations. This organismal focus has a long history and has advanced our understanding and prediction of ecosystem dynamics and the mass and energy flow through them (Riley, 1946; Fasham et al, 1990; Le Quere et al, 2005; Friedrichs et al, 2007; Schartau et al, 2017). We believe the reductionist approach is essential, but there is a complementary approach to understanding microbial biogeochemistry that is less studied and uses a more thermodynamic, or whole systems, approach
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