75 years since Monod: It is time to increase the complexity of our predictive ecosystem models (opinion)

Cost-benefit analysis of ecosystem modeling to support fisheries management

Mathematical and statistical models underlie many of the world's most important fisheries management decisions. Since the 19th century, difficulty calibrating and fitting such models has been used to justify the selection of simple, stationary, single-species models to aid tactical fisheries management decisions. Whereas these justifications are reasonable, it is imperative that we quantify the value of different levels of model complexity for supporting fisheries management, especially given a changing climate, where old methodologies may no longer perform as well as in the past. Here we argue that cost-benefit analysis is an ideal lens to assess the value of model complexity in fisheries management. While some studies have reported the benefits of model complexity in fisheries, modeling costs are rarely considered. In the absence of cost data in the literature, we report, as a starting point, relative costs of single-species stock assessment and marine ecosystem models from two Australian organizations. We found that costs varied by two orders of magnitude, and that ecosystem model costs increased with model complexity. Using these costs, we walk through a hypothetical example of cost-benefit analysis. The demonstration is intended to catalyze the reporting of modeling costs and benefits.

Multiscale models driving hypothesis and theory-based research in microbial ecology

Hypothesis and theory-based studies in microbial ecology have been neglected in favour of those that are descriptive and aim for data-gathering of uncultured microbial species. This tendency limits our capacity to create new mechanistic explanations of microbial community dynamics, hampering the improvement of current environmental biotechnologies. We propose that a multiscale modelling bottom-up approach (piecing together sub-systems to give rise to more complex systems) can be used as a framework to generate mechanistic hypotheses and theories (in-silico bottom-up methodology). To accomplish this, formal comprehension of the mathematical model design is required together with a systematic procedure for the application of the in-silico bottom-up methodology. Ruling out the belief that experimentation before modelling is indispensable, we propose that mathematical modelling can be used as a tool to direct experimentation by validating theoretical principles of microbial ecology. Our goal is to develop methodologies that effectively integrate experimentation and modelling efforts to achieve superior levels of predictive capacity.

Assessing the validity and sensitivity of microbial processes within a hydrodynamic model

Eutrophication due to excess anthropogenic nutrients in waterways is a significant issue worldwide. The pressure-stressor-response of a waterway to excessive nutrient loading is reliant on numerous physical and biological factors, including hydrodynamics and microbial processing. While substantial progress has been made towards simulating these mechanisms there are limited multi-disciplinary studies that relate the physical hydrodynamics of a site with the ecological response from linked laboratory and field studies. This paper presents the development of a coupled hydrodynamic and aquatic ecosystem response model, expanded to include an integrated microbial loop, that allows the explicit representation of heterotrophic bacteria growth and dissolved organic nutrient mineralisation. A unique long-term water quality dataset at an estuary in south-eastern Australia was used to validate and assess the model's sensitivity to complex biophysical processes driving the observed water quality variability. Results indicate that explicit time-varying bacterial mineralisation rates provide a substantially improved understanding of the broader aquatic ecosystem response than assigned fixed bulk rate parameter values, which are typically derived from non-local literature. Implementation of a microbial loop at the study site indicated that the model is sensitive to the boundary conditions, in particular catchment loads, with both net transport rates and the net growth rates of heterotrophic bacteria demonstrating different responses. Under average flow conditions, a smaller net transport and reduced nutrient availability has a pronounced effect of lowering net growth rates through the applied limitation factors. During high flow conditions, freshwater inflows increased net transport and nutrient loads, which resulted in higher net growth rates. Further, temporal variability in water temperature had a compounding effect on the model's response sensitivity. This approach has broader application in other riverine systems subject to eutrophication, and in interrogating linkages in hydrodynamic and microbial mediated processes (e.g., productivity). Future studies are recommended to better understand the sensitivity of aquatic ecosystem response models to microbial net growth rate kinetics at different temperatures and from top-down predation (e.g., zooplankton grazing).

Limited Mechanistic Link Between the Monod Equation and Methanogen Growth: a Perspective from Metabolic Modeling

The Monod equation has been widely applied as the general rate law of microbial growth, but its applications are not always successful. By drawing on the frameworks of kinetic and stoichiometric metabolic models and metabolic control analysis, the modeling reported here simulated the growth kinetics of a methanogenic microorganism and illustrated that different enzymes and metabolites control growth rate to various extents and that their controls peak at either very low, intermediate, or very high substrate concentrations. In comparison, with a single term and two parameters, the Monod equation only approximately accounts for the controls of rate-determining enzymes and metabolites at very high and very low substrate concentrations, but neglects the enzymes and metabolites whose controls are most notable at intermediate concentrations. These findings support a limited link between the Monod equation and methanogen growth, and unify the competing views regarding enzyme roles in shaping growth kinetics. The results also preclude a mechanistic derivation of the Monod equation from methanogen metabolic networks and highlight a fundamental challenge in microbiology: single-term expressions may not be sufficient for accurate prediction of microbial growth. IMPORTANCE The Monod equation has been widely applied to predict the rate of microbial growth, but its application is not always successful. Using a novel metabolic modeling approach, we simulated the growth of a methanogen and uncovered a limited mechanistic link between the Monod equation and the methanogen's metabolic network. Specifically, the equation provides an approximation to the controls by rate-determining metabolites and enzymes at very low and very high substrate concentrations, but it is missing the remaining enzymes and metabolites whose controls are most notable at intermediate concentrations. These results support the Monod equation as a useful approximation of growth rates and highlight a fundamental challenge in microbial kinetics: single-term rate expressions may not be sufficient for accurate prediction of microbial growth.

Implications of bacterial mineralisation in aquatic ecosystem response models

Widespread wastewater pollution is a major barrier to the sustainable management of freshwater and coastal marine ecosystems worldwide. Integrated multi-disciplinary studies are necessary to improve waterway management and protect ecosystem integrity. This study used the Generalised Likelihood Uncertainty Estimation (GLUE) methodology to link microbial community ecotoxicology laboratory data to a mechanistic aquatic ecosystem response model. The generic model provided good predictive skill for major water quality constituents, including heterotrophic bacteria dynamics (r2 = 0.91). The model was validated against observed data across a gradient of effluent concentrations from community whole effluent toxicity (WET) laboratory tests. GLUE analysis revealed that a combined likelihood measure increased confidence in the predictive capability of the model. This study highlights the importance of calibrating aquatic ecosystem response models with net growth rates (i.e., sum of the growth minus loss rate parameter terms) of biological functional groups. The final calibrated net growth rate value of heterotrophic bacteria determined using the GLUE analysis was selected to be 0.58, which was significantly greater than the average literature value of -0.15. This finding demonstrated that use of literature parameter values without a good understanding of the represented processes could create misleading outputs and result in unsatisfactory conclusions. Further, fixed bulk mineralisation rate literature values are typically higher than realistically required in aquatic ecosystem response models. This indicates that explicitly including bacterial mineralisation is crucial to represent microbial ecosystem functioning more accurately. Our study suggests that improved data collection and modelling efforts in real-world management applications are needed to better address nutrients released into the natural environment. Future studies should aim to better understand the sensitivity of aquatic ecosystem response models to bacterial mineralisation rates.

Dynamic carbon flux network of a diverse marine microbial community

The functioning of microbial ecosystems has important consequences from global climate to human health, but quantitative mechanistic understanding remains elusive. The components of microbial ecosystems can now be observed at high resolution, but interactions still have to be inferred e.g., a time-series may show a bloom of bacteria X followed by virus Y suggesting they interact. Existing inference approaches are mostly empirical, like correlation networks, which are not mechanistically constrained and do not provide quantitative mass fluxes, and thus have limited utility. We developed an inference method, where a mechanistic model with hundreds of species and thousands of parameters is calibrated to time series data. The large scale, nonlinearity and feedbacks pose a challenging optimization problem, which is overcome using a novel procedure that mimics natural speciation or diversification e.g., stepwise increase of bacteria species. The method allows for curation using species-level information from e.g., physiological experiments or genome sequences. The product is a mass-balancing, mechanistically-constrained, quantitative representation of the ecosystem. We apply the method to characterize phytoplankton-heterotrophic bacteria interactions via dissolved organic matter in a marine system. The resulting model predicts quantitative fluxes for each interaction and time point (e.g., 0.16 µmolC/L/d of chrysolaminarin to Polaribacter on April 16, 2009). At the system level, the flux network shows a strong correlation between the abundance of bacteria species and their carbon flux during blooms, with copiotrophs being relatively more important than oligotrophs. However, oligotrophs, like SAR11, are unexpectedly high carbon processors for weeks into blooms, due to their higher biomass. The fraction of exudates (vs. grazing/death products) in the DOM pool decreases during blooms, and they are preferentially consumed by oligotrophs. In addition, functional similarity of phytoplankton i.e., what they produce, decouples their association with heterotrophs. The methodology is applicable to other microbial ecosystems, like human microbiome or wastewater treatment plants.

Spatiotemporal metabolic modeling of bacterial life in complex habitats

The combination of genome-scale metabolic networks with spatially explicit representation of microbial habitats (spatiotemporal metabolic network modeling) paves the way to predict complex metabolic landscapes to a hitherto unparalleled detail, thus providing new insights into trophic interactions occurring at different scales. Placing detailed bacterial metabolism in realistic physical environment highlights the roles of physical barriers and diffusional bottlenecks on bacterial community interactions, structure and stability. We review recent advances in spatiotemporal metabolic network modeling using a few illustrative examples that highlight the immense potential of these novel approaches to interpret and design metabolic mediated interactions in structures (natural and engineered) environments.

Fresh Ideas Bloom in Gut Healthcare to Cross-Fertilize Lake Management

Harmful bacteria may be the most significant threat to human gut and lake ecosystem health, and they are often managed using similar tools, like poisoning with antibiotics or algicides. Out-of-the-box thinking in human microbiome engineering is leading to novel methods, like engineering bacteria to kill pathogens, "persuade" them not to produce toxins, or "mop up" their toxins. The bacterial agent can be given a competitive edge via an exclusive nutrient, and they can be engineered to commit suicide once their work is done. Viruses can kill pathogens with specific DNA sequences or knock out their antibiotic resistance genes using CRISPR technology. Some of these ideas may work for lakes. We critically review novel methods for managing harmful bacteria in the gut from the perspective of managing toxic cyanobacteria in lakes, and discuss practical aspects such as modifying bacteria using genetic engineering or directed evolution, mass culturing and controlling the agents. A key knowledge gap is in the ecology of strains, like toxigenic vs nontoxigenic Microcystis, including allelopathic and Black Queen interactions. Some of the "gut methods" may have future potential for lakes, but there presently is no substitute for established management approaches, including reducing N and P nutrient inputs, and mitigating climate change.

Modelling microbial communities using biochemical resource allocation analysis

To understand the functioning and dynamics of microbial communities is a fundamental challenge in current biology. To tackle this challenge, the construction of computational models of interacting microbes is an indispensable tool. There is, however, a large chasm between ecologically motivated descriptions of microbial growth used in many current ecosystems simulations, and detailed metabolic pathway and genome-based descriptions developed in the context of systems and synthetic biology. Here, we seek to demonstrate how resource allocation models of microbial growth offer the potential to advance ecosystem simulations and their parametrization. In particular, recent work on quantitative resource allocation allow us to formulate mechanistic models of microbial growth that are physiologically meaningful while remaining computationally tractable. These models go beyond Michaelis-Menten and Monod-type growth models, and are capable of accounting for emergent properties that underlie the remarkable plasticity of microbial growth. We outline the utility and advantages of using biochemical resource allocation models by considering a coarse-grained model of cyanobacterial growth and demonstrate how the model allows us to address specific questions of relevance for the simulation of marine microbial ecosystems, including the physiological acclimation of protein expression to different environments, the description of co-limitation by several nutrients and the differential use of alternative nutrient sources, as well as the description of metabolic diversity based on our increasing knowledge about quantitative cell physiology.

Modelling eutrophication in lake ecosystems: A review

Eutrophication is one of the main causes of the degradation of lake ecosystems. Its intensification during the last decades has led the stakeholders to seek for water management and restoration solutions, including those based on modelling approaches. This paper presents a review of lake eutrophication modelling, on the basis of a scientific appraisal performed by researchers for the French ministries of Environment and Agriculture. After a brief introduction presenting the scientific context, a bibliography analysis is presented. Then the main results obtained with process-based models are summarized. A synthesis of the scientist recommendations in order to improve the lake eutrophication modelling is finally given before the conclusion.

A model of optimal protein allocation during phototrophic growth

Photoautotrophic growth depends upon an optimal allocation of finite cellular resources to diverse intracellular processes. Commitment of a certain mass fraction of the proteome to a specific cellular function typically reduces the proteome available for other cellular functions. Here, we develop a semi-quantitative kinetic model of cyanobacterial phototrophic growth to describe such trade-offs of cellular protein allocation. The model is based on coarse-grained descriptions of key cellular processes, in particular carbon uptake, metabolism, photosynthesis, and protein translation. The model is parameterized using literature data and experimentally obtained growth curves. Of particular interest are the resulting cyanobacterial growth laws as fundamental characteristics of cellular growth. We show that the model gives rise to similar growth laws as observed for heterotrophic organisms, with several important differences due to the distinction between light energy and carbon uptake. We discuss recent experimental data supporting the model results and show that coarse-grained growth models have implications for our understanding of the limits of phototrophic growth and bridge a gap between molecular physiology and ecology.

Digital Image Analysis of Yeast Single Cells Growing in Two Different Oxygen Concentrations to Analyze the Population Growth and to Assist Individual-Based Modeling

Nowadays control of the growth of Saccharomyces to obtain biomass or cellular wall components is crucial for specific industrial applications. The general aim of this contribution is to deal with experimental data obtained from yeast cells and from yeast cultures to attempt the integration of the two levels of information, individual and population, to progress in the control of yeast biotechnological processes by means of the overall analysis of this set of experimental data, and to assist in the improvement of an individual-based model, namely, INDISIM-Saccha. Populations of S. cerevisiae growing in liquid batch culture, in aerobic and microaerophilic conditions, were studied. A set of digital images was taken during the population growth, and a protocol for the treatment and analyses of the images obtained was established. The piecewise linear model of Buchanan was adjusted to the temporal evolutions of the yeast populations to determine the kinetic parameters and changes of growth phases. In parallel, for all the yeast cells analyzed, values of direct morphological parameters, such as area, perimeter, major diameter, minor diameter, and derived ones, such as circularity and elongation, were obtained. Graphical and numerical methods from descriptive statistics were applied to these data to characterize the growth phases and the budding state of the yeast cells in both experimental conditions, and inferential statistical methods were used to compare the diverse groups of data achieved. Oxidative metabolism of yeast in a medium with oxygen available and low initial sugar concentration can be taken into account in order to obtain a greater number of cells or larger cells. Morphological parameters were analyzed statistically to identify which were the most useful for the discrimination of the different states, according to budding and/or growth phase, in aerobic and microaerophilic conditions. The use of the experimental data for subsequent modeling work was then discussed and compared to simulation results generated with INDISIM-Saccha, which allowed us to advance in the development of this yeast model, and illustrated the utility of data at different levels of observation and the needs and logic behind the development of a microbial individual-based model.

Variation within and between cyanobacterial species and strains affects competition: Implications for phytoplankton modelling

Cyanobacteria Microcystis aeruginosa and Cylindrospermopsis raciborskii are two harmful species which co-occur and successively dominate in freshwaters globally. Within-species strain variability affects cyanobacterial population responses to environmental conditions, and it is unclear which species/strain would dominate under different environmental conditions. This study applied a Monte Carlo approach to a phytoplankton dynamic growth model to identify how growth variability of multiple strains of these two species affects their competition. Pairwise competition between four M. aeruginosa and eight C. raciborskii strains was simulated using a deterministic model, parameterized with laboratory measurements of growth and light attenuation for all strains, and run at two temperatures and light intensities. 17 000 runs were simulated for each pair using a statistical distribution with Monte Carlo approach. The model results showed that cyanobacterial competition was highly variable, depending on strains present, light and temperature conditions. There was no absolute 'winner' under all conditions as there were always strains predicted to coexist with the dominant strains, which were M. aeruginosa strains at 20°C and C. raciborskii strains at 28°C. The uncertainty in prediction of species competition outcomes was due to the substantial variability of growth responses within and between strains. Overall, this study demonstrates that within-species strain variability has a potentially large effect on cyanobacterial population dynamics, and therefore this variability may substantially reduce confidence in predicting outcomes of phytoplankton competition in deterministic models, that are based on only one set of parameters for each species or strain.

Modelling food-web mediated effects of hydrological variability and environmental flows

Environmental flows are designed to enhance aquatic ecosystems through a variety of mechanisms; however, to date most attention has been paid to the effects on habitat quality and life-history triggers, especially for fish and vegetation. The effects of environmental flows on food webs have so far received little attention, despite food-web thinking being fundamental to understanding of river ecosystems. Understanding environmental flows in a food-web context can help scientists and policy-makers better understand and manage outcomes of flow alteration and restoration. In this paper, we consider mechanisms by which flow variability can influence and alter food webs, and place these within a conceptual and numerical modelling framework. We also review the strengths and weaknesses of various approaches to modelling the effects of hydrological management on food webs. Although classic bioenergetic models such as Ecopath with Ecosim capture many of the key features required, other approaches, such as biogeochemical ecosystem modelling, end-to-end modelling, population dynamic models, individual-based models, graph theory models, and stock assessment models are also relevant. In many cases, a combination of approaches will be useful. We identify current challenges and new directions in modelling food-web responses to hydrological variability and environmental flow management. These include better integration of food-web and hydraulic models, taking physiologically-based approaches to food quality effects, and better representation of variations in space and time that may create ecosystem control points.