Equifinality, sloppiness and emergent minimal structures of biogeochemical models

Process-based biogeochemical models consider increasingly the control of microorganisms on biogeochemical processes. These models are used for a number of important purposes, from small-scale (mm-cm) controls on pollutant turnover to impacts of global climate change. A major challenge is to validate mechanistic descriptions of microbial processes and predicted emergent system responses against experimental observations. The validity of model assumptions for microbial activity in soil is often difficult to assess due to the scarcity of experimental data. Therefore, most complex biogeochemical models suffer from equifinality, i.e. many different model realizations lead to the same system behavior. In order to minimize parameter equifinality and prediction uncertainty in biogeochemical modeling, a key question is to determine what can and cannot be inferred from available data. My thesis aimed at solving the problem of equifinality in biogeochemical modeling. Thereby, I opted to test a novel mathematical framework (the Manifold Boundary Approximation Method) that allows to systematically tailor the complexity of biogeochemical models to the information content of available data.Prozessbasierte Modelle des Kohlenstoffumsatzes im Boden berücksichtigen zunehmend direkt die Dynamik von mikrobiellen Gruppen und deren Auswirkung auf biogeochemische Prozesse. Der Einsatzbereich dieser Modelle reicht von kleinskaliger Modellierung (mm-cm) von Schadstoffumsätzen im Boden bis hin zu globalen Simulationen der Folgen des Klimawandels. Eine große Herausforderung ist es, mechanistische Beschreibungen mikrobieller Prozesse und das beobachtbare emergente Systemverhalten zu validieren. Besonders schwierig ist die Validierung von Modellannahmen zur Aktivität einzelner mikrobieller Gruppen im Boden, weil direkte Messungen fehlen. Die meisten komplexen biogeochemischen Modelle zeigen Äquifinalität, d.h. viele unterschiedliche Parameterkombinationen führen zu identischen Simulationen. Um die Parameter-Äquifinalität und die Vorhersageunsicherheit biogeochemischer Modelle zu minimieren, ist es wichtig, den Informationsgehalt verfügbarer Messdaten für die Modellparametrisierung zu quantifizieren. Ziel meiner Dissertation war es, das Problem der Äquifinalität zu lösen und einen allgemeingültigen mathematischen Formalismus zu finden, in dessen Rahmen die Komplexität biogeochemischer Modelle systematisch an den Informationsgehalt verfügbarer Daten angepasst werden kann

Modeling microbial dormancy in soils

Dormancy is a very effective trait of microorganisms in soil to cope with varying environmental conditions (e.g. substrate availability or moisture) that leads to a graded, switch-like microbial response to fluctuations in environmental parameters. Microbial dormancy strategies vary from rapid to delayed response to environmental change and the activation from dormant to active state is typically faster than the transition to dormant state (Blagodatskaya, E., & Kuzyakov, Y. 2013). Dormancy is typically represented in models by explicitly considering active and dormant biomass pools or by introducing a physiological state variable that describes the active fraction of the total biomass. Existing modeling approaches mainly differ in the description of the transformation process between active and dormant states and disregard the classification into active, potentially active and dormant microbial states. The growth rate, death rates and the transition rate from active to dormant state are represented by generic functions. The question arises of gauging the sensitivity of model predictions for the temporal evolution of active and dormant bacteria not only to perturbations in constants of proportionality (parameter sensitivity), but to perturbations in uncertain or assumed expressions (functional sensitivity). Instead of postulating a particular description, the functional form of the transition function can be tested by fitting a type of free-form function as a linear combination of shape functions to the experimental dataset used in Wang et al. 2014. Depending on the form of the transition function, we observe that simple SOM turnover models show qualitatively different dynamical behavior. We aim to generalize existing modeling approaches to account for diversity in dormancy strategies and to understand which strategies for transiting between dormant and active states are favoured under which environmental conditions

Conceptualizing Biogeochemical Reactions With an Ohm's Law Analogy

In studying problems like plant-soil-microbe interactions in environmental biogeochemistry and ecology, one usually has to quantify and model how substrates control the growth of, and interaction among, biological organisms (and abiotic factors, e.g., adsorptive mineral soil surfaces). To address these substrate-consumer relationships, many substrate kinetics and growth rules have been developed, including the famous Monod kinetics for single-substrate-based growth and Liebig's law of the minimum for multiple-nutrient-colimited growth. However, the mechanistic basis that leads to these various concepts and mathematical formulations and the implications of their parameters are often quite uncertain. Here, we show that an analogy based on Ohm's law in electric circuit theory is able to unify many of these different concepts and mathematical formulations. In this Ohm's law analogy, a resistor is defined by a combination of consumers’ and substrates’ kinetic traits. In particular, the resistance is equal to the mean first passage time that has been used to derive the Michaelis-Menten kinetics under substrate replete conditions for a single substrate as well as the predation rate of individual organisms. We further show that this analogy leads to important insights on various biogeochemical problems, such as (a) multiple-nutrient-colimited biological growth, (b) denitrification, (c) fermentation under aerobic conditions, (d) metabolic temperature sensitivity, and (e) the legitimacy of Monod kinetics for describing bacterial growth. We expect that our approach will help both modelers and nonmodelers to better understand and formulate hypotheses when studying certain aspects of environmental biogeochemistry and ecology

Predictions of rhizosphere microbiome dynamics with a genome-informed and trait-based energy budget model.

Soil microbiomes are highly diverse, and to improve their representation in biogeochemical models, microbial genome data can be leveraged to infer key functional traits. By integrating genome-inferred traits into a theory-based hierarchical framework, emergent behaviour arising from interactions of individual traits can be predicted. Here we combine theory-driven predictions of substrate uptake kinetics with a genome-informed trait-based dynamic energy budget model to predict emergent life-history traits and trade-offs in soil bacteria. When applied to a plant microbiome system, the model accurately predicted distinct substrate-acquisition strategies that aligned with observations, uncovering resource-dependent trade-offs between microbial growth rate and efficiency. For instance, inherently slower-growing microorganisms, favoured by organic acid exudation at later plant growth stages, exhibited enhanced carbon use efficiency (yield) without sacrificing growth rate (power). This insight has implications for retaining plant root-derived carbon in soils and highlights the power of data-driven, trait-based approaches for improving microbial representation in biogeochemical models

Kinetic Properties of Microbial Exoenzymes Vary With Soil Depth but Have Similar Temperature Sensitivities Through the Soil Profile.

Current knowledge of the mechanisms driving soil organic matter (SOM) turnover and responses to warming is mainly limited to surface soils, although over 50% of global soil carbon is contained in subsoils. Deep soils have different physicochemical properties, nutrient inputs, and microbiomes, which may harbor distinct functional traits and lead to different SOM dynamics and temperature responses. We hypothesized that kinetic and thermal properties of soil exoenzymes, which mediate SOM depolymerization, vary with soil depth, reflecting microbial adaptation to distinct substrate and temperature regimes. We determined the Michaelis-Menten (MM) kinetics of three ubiquitous enzymes involved in carbon (C), nitrogen (N) and phosphorus (P) acquisition at six soil depths down to 90 cm at a temperate forest, and their temperature sensitivity based on Arrhenius/Q 10 and Macromolecular Rate Theory (MMRT) models over six temperatures between 4-50°C. Maximal enzyme velocity (V max) decreased strongly with depth for all enzymes, both on a dry soil mass and a microbial biomass C basis, whereas their affinities increased, indicating adaptation to lower substrate availability. Surprisingly, microbial biomass-specific catalytic efficiencies also decreased with depth, except for the P-acquiring enzyme, indicating distinct nutrient demands at depth relative to microbial abundance. These results suggested that deep soil microbiomes encode enzymes with intrinsically lower turnover and/or produce less enzymes per cell, reflecting distinct life strategies. The relative kinetics between different enzymes also varied with depth, suggesting an increase in relative P demand with depth, or that phosphatases may be involved in C acquisition. V max and catalytic efficiency increased consistently with temperature for all enzymes, leading to overall higher SOM-decomposition potential, but enzyme temperature sensitivity was similar at all depths and between enzymes, based on both Arrhenius/Q 10 and MMRT models. In a few cases, however, temperature affected differently the kinetic properties of distinct enzymes at discrete depths, suggesting that it may alter the relative depolymerization of different compounds. We show that soil exoenzyme kinetics may reflect intrinsic traits of microbiomes adapted to distinct soil depths, although their temperature sensitivity is remarkably uniform. These results improve our understanding of critical mechanisms underlying SOM dynamics and responses to changing temperatures through the soil profile