- Vallino, J.J. and Huber, J.A. (2018) Using maximum entropy production to describe microbial biogeochemistry over time and space in a meromictic pond. Frontiers in Environmental Science 6, 100, 22pp., doi: 10.3389/fenvs.2018.00100.

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 h 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.

- Vallino, J.J. and Algar, C.K. (2016) Thermodynamics of Marine Biogeochemical Cycles: Lotka Revisited. Ann. Rev. Mar. Sci. 8, 333-356, doi: 10.1146/annurev-marine-010814-015843

Nearly
100 years ago, Alfred Lotka
published two short but insightful papers describing how ecosystems may
organize. Principally, Lotka argued that ecosystems will grow in size
and that their cycles will spin faster via predation and nutrient
recycling so as to capture all available energy, and that evolution and
natural selection are the mechanisms by which this occurs and
progresses. Lotka's ideas have often been associated with the maximum
power principle, but they are more consistent with recent developments
in nonequilibrium thermodynamics, which assert that complex systems
will organize toward maximum entropy production (MEP). In this review,
we explore Lotka's hypothesis within the context of the MEP principle,
as well as how this principle can be used to improve marine
biogeochemistry models. We need to develop the equivalent of a climate
model, as opposed to a weather model, to understand marine
biogeochemistry on longer timescales, and adoption of the MEP principle
can help create such models.

- Chapman, E.J., Childers, D.L. and Vallino, J.J. (2016) How The Second Law of Thermodynamics has informed ecosystem ecology through its history. BioScience 66 (1), 27-39, doi: 10.1093/biosci/biv166

Many
attempts have been made to develop
a general principle governing how systems develop and organize in
ecology. We reviewed the historical developments that led to the
conceptualization of several goal-oriented principles in ecosystem
ecology. We focused on two prominent principles—the maximum power
principle (MPP) and the maximum entropy production principle (MEPP)—and
the literature that applies to both. Although these principles have
conceptual overlap, we found considerable differences in their
historical development, the disciplines that apply these principles,
and their adoption in the literature. These principles were more
similar than dissimilar, and the maximization of power in ecosystems
occurs with maximum entropy production. These principles have great
potential to explain how systems develop, organize, and function, but
there are no widely agreed-on theoretical derivations for the MEPP and
MPP, hindering their broader use in ecological research. We end with
recommendations for how ecosystems-level studies may better use these
principles.

- Rastetter,
E.B. and Vallino, J.J. (2015) Ecosystem's 80
^{th}and the Reemergence of Emergence. Ecosystems 18 (5), 735-739, doi: 10.1007/s10021-015-9893-6

- Using the maximum entropy production principle to understand and predict microbial biogeochemistry. Invited talk at Society for Mathematical Biology Annual Meeting, Virtual, Jun 2021

- Contributions of Microbial
Community Metabolic Expression to Biogeochemical Cycling in a Highly
Stratified Meromictic Pond over a Diel Cycle. Poster presented at ASM Microbe,
San Francisco, Jun 2019

- Comparing metagenomic and metatranscriptomic observations over time and space in a meromictic pond to predictions from a thermodynamic-based model of community metabolic expression. Presented at Ocean Sciences Meeting, AGU-ASLO, Feb 2018

- Using metagenomic and metatranscriptomic observations to test a thermodynamic-based model of community metabolic expression over time and space. UGA Marine Sciences Departmental Seminar, Nov 2016
- Updated version presented at UCI Department of Earth System Science, May 2017
- Short
version presented at the Ocean Sciences Meeting, AGU-ASLO in New
Orleans, Feb 2016

- Using thermodynamic
objective criteria for understanding distributed metabolic networks
that arise from microbial communities. URI Biological and Environmental
Sciences Departmental Seminar Mar 2016

- Also presented at: WHOI Department of Marine Chemistry & Geochemistry, Mar 2016
- And Computations in Science
Seminars, U Chicago, Apr 2015

- Metcalf Poster presentation at MBL
by Petra Byl,
Aug 2015.