Workshop 6: Microbial Ecology

(May 15,2006 - May 19,2006 )

Organizers


George Jackson
Oceanography, Texas A & M University

Microbial ecology is the study of how micro-organisms interact with each other and with their environment. The whole field is thus a study of a dynamic system where properties of the system emerge from the constraints imposed by the chemistry of the environment, physical laws, and the biological strategies that have evolved in the interacting micro-organisms. The struggle to understand these interactions implies the analysis of phenomena occurring on spatial scales from that of viruses (10-8m) to that of ocean chlorophyll distributions (106m) and on time scales from milliseconds to a few billion years; for example, from the biophysical processes of photosynthesis to those of biological evolution. Such analysis creates an interface that demands insight into both biology and mathematics.

Microbial ecology is also a field that evolves rapidly. Molecular techniques have allowed experimentalists to address questions concerning, for example, microbial diversity, unanswerable with traditional methods. Micro-organisms unknown a few decades ago have been shown to be among the most abundant organisms on earth such as, for example, the tiny cyanobacteria dominating primary production in large parts of the ocean, and SAR11, a bacterium which is probably the most abundant organism on earth, but whose function in the ecosystem is still obscure.

The objective of this workshop is to describe areas in microbial ecology where the tools of mathematics have been used to provide insight into the phenomena.

Accepted Speakers

Michael Dowd
Mathematics and Statistics, Dalhousie University
Bernard Boudreau
Oceanography, Dalhousie University
Tom Curtis
Civil Engineering and Geosciences, University of Newcastle upon Tyne
Jarl Giske
biology, University of Bergen
James Grover
Biology, University of Texas
Daniel Grunbaum
Oceanography, University of Washington
Åke Hagstrøm
Univ Kalmar
Jef Huisman
Aquatic Microbiology , University of Amsterdam
George Jackson
Oceanography, Texas A & M University
Peter Jumars
School of Marine Sciences, University of Maine at Orono
Thomas Kiørboe
Danish Institute for Fisheries Research
Mary Lunn
Statistics , St Hugh's College
Laurent Seuront
Station Marine de Wimereux, Observatoire National de Besanc con (CNRS)
Joe Vallino
Marine Biological Laboratory
Dick Van Oevelen
NIOO-KNAW, Centre for Estuarine and Marine Ecology
Alain Vézina
Ecosystem Research Division, Bedford Institute of Oceanography
Andy Visser
Marine Ecology and Aquaculture , Danish Institute for Fisheries Research
Monday, May 15, 2006
Time Session
10:15 AM
11:15 AM
James Grover - Stoichometry in Microbial Food Webs

The law of mass conservation constrains the dynamics of interacting microbial populations. These stoichiometric constraints facilitate theoretical studies of how species interactions relate to dynamics of nutrients and other substances. In theory, stoichiometry affects the coexistence and stability of populations interacting through mechanisms such as competition for resources, allelopathy, commensalism, mutualism, and predation. Experimental studies support many predictions of stoichiometric theory as applied to interacting microbial populations. Stoichiometric signatures are also predicted for the assembly of diverse communities. Although existing theory is largely limited to steady state analyses of systems with two growth-limiting substances, current research extends the stoichiometric approach to three growth-limiting substances and non-steady conditions.

01:00 PM
02:00 PM
Jarl Giske - The Use of Individual Based Models (IBMs)

At the outset of population modeling, an individual was seen as a number among other equals in the population. Later, extensions have been introduced to account for individual variability within population models. These extensions may be classified into community ecology models, game theory, state-dependent models and age-dependent models. We show that the individual-based approach can be used to merge these traditions. We will show how the ING concept and hedonic modeling can be used to combine genetic variation and density- and frequency-dependency with trade-offs linked to age and state. We will also present simulations of evolution in a microbial community. Our work is done in collaboration with Frede Thingstad.


This presentation is made in collaboration with Espen Strand, also at the Department of Biology, University of Bergen.

02:30 PM
03:30 PM
Michael Dowd - Statistical Methods in Modelling (MCMC etc.)

Estimating the time evolution of ocean biogeochemical variables requires both models and data. Mathematical models for ocean biogeochemistry are based on nonlinear (ordinary and partial) differential equations, and exhibit complex dynamical behaviour and high dimensionality. Observations come from a variety of sources and are characterized by being noisy, sparse and non-Gaussian, and with complex spatial and temporal structure. This talk considers some emerging statistical approaches for estimating the time evolution of the biogeochemical state of the ocean (along with relevant parameters). These use a state space framework which incorporates nonlinear (stochastic) dynamical models and available data. Solutions are probabilistic and rely on sampling based (sequential Monte Carlo) methods. Application and illustration of these approaches is presented using models of pelagic ocean biogeochemistry (e.g. PZND models: phytoplankton, zooplankton, nutrient, detritus).

Tuesday, May 16, 2006
Time Session
09:00 AM
10:00 AM
Tom Curtis - Microbial Distributions Math Perspective

The nature and extent of bacterial diversity is a frontier in science of astronomical dimensions and profound practical importance. Bacterial diversity is unknown at any scale in any environment. Debates about the nature of a species contribute to but do not actually cause this confusion. Rather the scale and inscrutable nature of the microbial world, combined with a paucity of theory, prevents us from gaining a clear picture of bacterial diversity. For example, in most environments we are confronted with exponentially increasing numbers of taxa at exponentially decreasing abundances. Random sampling often reveals the same taxa again and again and we cannot therefore distinguish between rarity and absolute lack of taxa. Unfortunately, sample sizes are dictated by budgets not statistics. The usual alternative to counting is to infer the numbers from a taxa abundance curve which one can either guess, or infer by fitting curves from samples. Unfortunately, the biggest samples are very small with respect to the community and the fitted parameters can be so uncertain as to yield quite variable estimates of diversity. Theory can lend a hand. We believe that fundamental, and hopefully universal, aspects of community assembly can be expressed mathematically, and that therefore diversity can, in principle, be predicted. Unfortunately, these predictions must be made in a world we can barely perceive and in which meaningful quantitative studies are expensive, laborious and prone to failure. Consequently complex and unparameterised models must be eschewed for they are potentially very misleading. We need theory which is simple and amenable to calibration using small samples. In our hands stochastic, birth death and invasion models can fulfil this role (especially if they can be complemented by deterministic models to determine the number of individuals). These neutral models are conceptually analogous to MacArthur and Wilson's "Theory of Island Biogeography" and will describe, inter alia, taxa abundance curves, and thus diversity. Theory is not a substitute for the empirical measurement of diversity but it could prove an invaluable ally in this task. It will allow us to design the large scale sequencing programmes that are required for definitive studies on microbial diversity in some communities which could in turn permits the confident prediction of bacterial diversity in others.


This work was done in collaboration with Mary Lunn, Stephen Woodcock, and I.M Head William T. Sloan.

10:30 AM
11:30 AM
Åke Hagstrøm - Microbial Distributions, Biological Perspective

For most eukaryotic organisms a species is defined as an interbreeding population. But bacteria don't have sex. Instead they acquire DNA fragments for recombination in several direct ways (i.e. horizontal gene transfer). Thus, the traditional Biological Species concept makes little sense in relation to bacterial speciation. To overcome this problem the concept of ecotypes defined as populations of bacterial cells that show genetic cohesion and are ecologically distinct has been introduced. In this presentation the "species" issue will be discussed in relation to current estimates of total marine bacterioplankton diversity. Also, bacterial cosmopolitanism, widely accepted by microbiologists, confronts recent reports of endemic species and restricted distributions. Because of their small size, huge abundance and easy dispersal, it is assumed that marine planktonic microorganisms may show an ubiquitous distribution that prevents any structured assembly into local communities. Currently a global picture of the bacterioplankton distribution in surface layer is emerging showing a marine bacterioplankton community that follows a latitudinal gradient of diversity and that includes few truly cosmopolitan species. The structure of the bacterioplankton community that leads to these results will be discussed as well as the implications of a structured bacterioplankton community for modelling biogeochemical cycles in the ocean.

01:00 PM
02:00 PM
Mary Lunn - Samples and Simulation

Given huge populations of microbes, extracting as much information as possible from small sub-samples is important. Analytic methods based on traditional likelihood calculations are difficult to use when selecting a subsample from a potentially large number of species. We present some preliminary results on how simulation may be used, applying the method to data from soil and human gut flora.

02:30 PM
03:30 PM
Andy Visser - The Role of Turbulence and Small Scale Processes

For planktonic organisms, nearly all important life processes are governed by an encounter rate. For instance, growth, reproduction, and mortality are closely linked to an individual's encounter with food, mates, and predators respectively. Understanding the distribution of resources on scales relevant for individual organisms, and how they locate and exploit these resources is central to understanding how marine ecosystems function. At these scales, the dispersion of material is controlled by molecular diffusion, turbulent straining and Richardson's law. That is, the landscape experienced by plankton (i.e. chemical patches, detrital aggregates and other organisms) is strongly controlled by small scale physics. Lagrangian models of planktonic interactions can be built up by examining (i) their small scale physical environment, (ii) their motility and behaviour, and (iii) their sensory ability in remotely detecting each other and patchily distributed resources. As an example, many aquatic organisms - from bacteria to crustaceans - use chemical plumes released by sinking particulate organic material either directly as a food source or as a signal to find potential food items (marine snow aggregates, fecal pellets). This interaction is important as it determines where, how fast and to what degree sinking detrital material is demineralised in the water column; a pivotal process in determining the vertical carbon flux in the ocean. This example highlights the interplay of abiotic aspects of the environment, in particular turbulence, with the sensory ability and motile behaviour of planktonic organisms.

Wednesday, May 17, 2006
Time Session
09:00 AM
10:00 AM
Laurent Seuront - Small Scale Distributions of Microbes

A ubiquitous feature of aquatic ecosystems is their temporal variability and spatial heterogeneity that occur over a wide range of scales. Despite the considerable amount of work devoted to the quantification of the spatial and temporal patterns of plankton distributions, their intrinsic three-dimensional and microscale properties have widely been underestimated. Here, using tools borrowed from the field of statistical physics, I will illustrate how taking into account the space-time complexity of microbial distributions at microscale and in 3D, in particular their intermittent behaviour and the related dynamics of extreme events, can provide extremely valuable ecological information. A specific attention will be given to the nature of and the interplay between turbulence intermittency, seawater viscosity, individual swimming and mating behaviour, predator/prey and virus/host interactions.

10:30 AM
11:30 AM
Thomas Kiørboe - Particle Colonization

Rich microbial communities develop on and around suspended particles in pelagic environments. Their activity may account for a significant fraction of the microbial activity in the water column and they enhance the degradation of sinking particles, thus retarding vertical material fluxes in the ocean. A combination of simple mechanistic models and experiments are used to explore the dynamics of these communities. The description considers motility behaviour and colonization of bacteria and flagellates, growth and detachment of particle-attached microbes, and trophic interactions. The models and experiments are capable of describing some gross features of particle attached microbial communities, such as how the abundances of attached microbes scale with particle size, but there are many open and unresolved questions. These include the similarity or difference of particle-attached and free microbes; the interaction between the dynamics of the particles (as they form and degrade) and the dynamics of the microbes; and the significance for ocean carbon fluxes of these microbial communities.

01:00 PM
02:00 PM
Dick Van Oevelen - The Role of Bacterial Carbon in Marine Benthic Food Webs: Integrating experimental 13C isotope data with models

Bacteria dominate biogeochemical processes in most sediments. Bacterial production and respiration processes are therefore studied in detail by biogeochemists. However, the fate of produced bacterial biomass is often not considered. The ubiquitous presence of bacteria, their high nutritional value and secondary production has lead many benthic ecologists to speculate that bacteria fulfill an important carbon transfer in the benthic food web. Recent evidence suggests that viral infection and subsequent lysis may be an important factor in bacterial loss processes in the pelagic zone, but its significance in sediments is not well established. It is clear that an integrated approach is required to understand the dynamics of bacterial in sediments.


We present, analyse and model the results of an in situ experiment, in which 13C-glucose was injected in the surface 10 cm of a marine intertidal sediment. The injected 13C-glucose was quickly incorporated by the bacterial community as evidenced by 13C enrichment of bacterial specific biomarkers (polar-lipid-derived fatty acid and D-alanine) and its fate in the food web was followed during a period of 4.5 months. Trophic transfer through grazing on bacterial was assessed through the 13C enrichment of meio- (group level) and macrobenthos (species level). Respiration was monitored through the production of 13C dissolved inorganic carbon. 13C enrichment of different sedimentary amino acids was used to gain insight in preservation of bacterial remnants in the particulate organic carbon pool of the sediment. The complete data set was evaluated with a mechanistic model to quantify the importance of exchange processes (i.e. resuspension and irrigation), bacterial grazing by benthic fauna and bacterial growth, respiration and mortality.


The interaction between bacterial and benthic fauna can be viewed from the bacterial perspective in terms of the importance of grazing as a fate of bacterial carbon production. Another interesting question is how much the grazed bacterial carbon contributes to the total carbon requirements of benthic fauna. To address this question, the relative enrichment of meio- and macrobenthic taxa was evaluated against the relative enrichement in bacteria by means of a simple isotope model. Bayesian analysis was employed in both modeling approaches to determine the constraining effect of the data - model interaction on the model parameters.


The results of this comprehensive study will be compared against the results of an inversion analysis and studies performed on other resources and in other ecosystems to give an overview of our current understanding of the role of bacteria in benthic food webs.


This work was done in collaboration with Leon Moodley, Bart Veuger, Karline Soetaert, Jack J. Middelburg and Carlo H. R. Heip.

02:30 PM
03:30 PM
Alain Vézina - Inverse Modelling and the Parsimony Principle in Investigations of Microbial Food Webs

Microbial food webs are maintained by complex flows of carbon, nutrients and biochemical compounds that cannot be fully quantified by measurements. Inverse modelling was introduced to biological oceanography and microbial ecology in the late 1980s as a way to reconstruct complete flow networks from incomplete information. The reconstructed flow network is the simplest among all plausible configurations. In other words, it is the flow network that contains no more structure than is required to explain the data. This parsimony principle has implications for the reconstructed microbial interactions that are not always realistic. This lecture will review new approaches to counter adverse effects of the parsimony principle and possible approaches to replace it completely. At this time it appears that parsimony will remain an integral part of inverse analysis but recent improvements in inverse modelling promise to decrease its impact on the results.

Thursday, May 18, 2006
Time Session
09:00 AM
10:00 AM
Mark Moore - Primary Producers from the Organism Perspective

Photosynthesis in the oceans is dominated by phytoplankton, an assemblage of organisms spanning many phyla across 2 empires. In addition to this vast genetic (adaptive) variability, phytoplankton have evolved a large capacity for physiological plasticity (acclimation). Modelling the response of primary productivity to environmental forcing thus potentially represents a major challenge. This talk will address how to confront this challenge from a mechanistic physiological view point. Initially we will consider slower timescale acclimation to temperature, light and nutrient availability, modelled in terms of adjustments in cellular constituents acting to balance the supply of energy through photosynthetic light capture, with the electron demands for biosynthesis and maintenance. Changes in the cellular chlorophyll to carbon ratio capture the essence of these models, which are likely to provide a reasonable approximation of phytoplankton photosynthesis in stratified conditions. In contrast, rapidly mixed layers often characterise the regions of the upper ocean where the highest productivity occurs (e.g. mid-high latitudes during spring). Understanding the physiological response to the high frequency variations in light occurring in this situation will likely require consideration of faster kinetic processes. Potential means of modelling these 'energy modulation' processes, which include both non-photochemical quenching and photoinhibition, will be described. The challenge of scaling back up from these physiological models to ecosystem and global scales will also be mentioned.

10:30 AM
11:30 AM
Daniel Grunbaum - Plankton Models

Plankton Models

01:00 PM
02:00 PM
Jef Huisman - Mixing and Chaos in Plankton Communities

Physical mixing processes have a major impact on species interactions in plankton communities. Here, we develop new theory to predict how changes in turbulent mixing affect the population dynamics of phytoplankton species. We apply the theory to two contrasting aquatic ecosystems, a hypertrophic lake and the oligotrophic ocean.


In hypertrophic lakes, where nutrients are in ample supply, the growth rates of phytoplankton species are often limited by light availability. The light conditions experienced by phytoplankters depend on their vertical excursions through the water column. To investigate how changes in vertical mixing affect competition for light between different species, we manipulated the turbulence structure of an entire lake using artificial mixing. Changes in turbulent mixing of the lake caused a dramatic shift in phytoplankton species composition. Consistent with our model predictions, sinking diatoms and green algae dominated during intense mixing, while buoyant and potentially toxic cyanobacteria became dominant when mixing was reduced.


In the oligotrophic ocean, phytoplankton species face two opposing resource gradients: light supplied from above and nutrients supplied from below. As a result, phytoplankton cells may achieve highest growth rates not at the water surface, but at a depth where both resources are available in sufficient supply. That is, a deep chlorophyll maximum develops. Our model predicts that reduced vertical mixing, which brings less nutrient into the euphotic zone, will generate oscillations and chaos in the phytoplankton of the deep chlorophyll maximum. These intriguing model predictions are compared with the complex species dynamics observed in deep chlorophyll maxima of the subtropical Pacific Ocean, as revealed by long-term studies of the Hawaii Ocean Timeseries program.


According to recent climate models, global warming will lead to a stronger vertical stratification of lakes and oceans, which reduces vertical mixing in the water column. The results of our plankton models, lake experiments, and ocean observations warn that changes in the vertical mixing structure, driven by climate change, can induce major shifts in the population dynamics and species composition of phytoplankton communities.


References:



  • Huisman, J., J. Sharples, J.M. Stroom, P.M. Visser, W.E.A. Kardinaal, J.M.H. Verspagen & B. Sommeijer. 2004. Changes in turbulent mixing shift competition for light between phytoplankton species. Ecology 85: 2960-2970.

  • Huisman, J., N.N. Pham Thi, D.M. Karl & B. Sommeijer. 2006. Reduced mixing generates oscillations and chaos in the oceanic deep chlorophyll maximum. Nature 439: 322-325.

02:30 PM
03:30 PM
Joe Vallino - Does non-equilibrium thermodynamics govern metabolic network expression in microbial communities?

In this presentation I take a metabolic perspective of ecosystem biogeochemistry that functions at local, region and global scales, in deep-sea hydrothermal vents and the deep biosphere, as well as in laboratory microcosms. In all these systems, a complex metabolism govern by microorganisms develops; however, instead of the metabolism being orchestrated by a single organism, metabolic function is distributed among hundreds of microbial species, yet the overall system-metabolism functions in a highly organized and coordinated manner. What governs the development and organization of this distributed metabolism? Is it governed by just happenstance depending on which organisms are present in the system at a particular instance, or are there fundamental governing laws that dictate how the system metabolism will develop? It is hypothesized that 3.5 billion years of evolution has produced biological systems so adept and efficient at producing and degrading chemical potential that the overall biogeochemistry of microbial systems can be accurately described by simple rules without requiring knowledge of the individual species that occupy a given system. Accordingly, the biogeochemistry observed on Earth, at both local and global scales, may be governed by principles derived from nonequilibrium thermodynamics with living systems being the mechanism by which the system attempts to degrade energy gradients. Using a distributed metabolic perspective constrained by nonequilibrium thermodynamics, I present a modeling framework that can predict ecosystem biogeochemistry assuming the system is sufficiently metabolically diverse. The model predicts how resources (i.e., carbon sources, nutrients, chemical electron acceptors and donors) change over time, as well as how the overall system allocates protein to metabolic processes, such as photosynthesis, nitrification, sulfate reduction, respiration, etc., as governed by the principle of maximum entropy production (MEP). The primary research objective is to demonstrate, via model comparison to experiments, that living systems tend to track the MEP objective. I will present development of the modeling framework that incorporates thermodynamic objective functions as well as model comparison to preliminary microcosm experiments in which state and microbial composition are monitored.

Friday, May 19, 2006
Time Session
09:00 AM
10:00 AM
Bernard Boudreau - Modelling Microbial Diagenesis

Most biogeochemical changes that occur to sediments after their deposition are related to organic matter decomposition, which is a microbial process. Transport-reaction modelling of this diagenesis has been extremely successful at describing and explaining the resulting distributions of solid and solute components of sediments. This lecture aims first to highlight these successes, focussing on examples from microbial mats and the transient redistribution of redox-sensitive metals. A surprising result from this modelling, confirmed by experimental results, is that the microbial population need not be modelled explicitly. The lecture explores the theoretical basis from this seemingly contradictory finding. Finally, the feedback between the macro-fauna and the microbial population in sediments is examined.

10:30 AM
11:30 AM
Peter Jumars - Unsteady Environments of Benthic Marine Microbes

Bacteria in sediments exist at a surprisingly constant 109 individuals ml-1 of pore water. Every indication, however, is that the majority of those cells are idle most of the time. Messenger compounds are one means to signal that renewed metabolic activity would be worthwhile, and signals sent or received this way have some interesting features in an environment containing diffusion-reflecting boundaries. Mechanical stresses in sediments have received less attention, but new models and measurements in sediments and sediment analogs suggest that many muds behave mechanically like linear-elastic, solid gels with fairly simply large-scale geometries. Burrowing animals produce stress and strain fields in them and fracture sediments. These stress-strain and fracture fields can provide direct mechanical stimuli and can have large influence on solute delivery by short circuiting otherwise diffusively delivered chemical signals.

Name Affiliation
Dougherty, Daniel doughe57@msu.edu Lyman Briggs School of Science, Michigan State University
Dowd , Michael mdowd@mathstat.dal.ca Mathematics and Statistics, Dalhousie University
Aguda, Baltazar bdaguda@gmail.com MBI, The Ohio State University
Andersen, Tom tom.andersen@bio.uio.no  Biology, University of Oslo
Best, Janet jbest@mbi.osu.edu
Boudreau, Bernard Oceanography, Dalhousie University
Curtis, Tom tom.curtis@ncl.ac.uk Civil Engineering and Geosciences, University of Newcastle upon Tyne
Djordjevic, Marko mdjordjevic@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Enciso, German German_Enciso@hms.harvard.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Giske, Jarl jarl.giske@bio.uib.no biology, University of Bergen
Goel, Pranay goelpra@helix.nih.gov Mathematical Biosciences Institute (MBI), The Ohio State University
Grajdeanu, Paula pgrajdeanu@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Grossart, Hans-Peter hgrossart@igb-berlin.de Inst. of Freshwater Ecology & Inland Fisheries
Grover, James grover@uta.edu Biology, University of Texas
Grunbaum, Daniel grunbaum@ocean.washington.edu Oceanography, University of Washington
Hagstrm, ke ake.hagstrom@hik.se Univ Kalmar
Huisman, Jef jef.huisman@science.uva.nl Aquatic Microbiology , University of Amsterdam
Jackson, George gjackson@tamu.edu Oceanography, Texas A & M University
Jin, Ruoming jinr@cse.ohio-state.edu Computer Science, Kent State University
Jumars, Peter jumars@maine.edu School of Marine Sciences, University of Maine at Orono
Just, Winfried just@math.ohio.edu Math, Ohio University
Kang, Yun yun.kang@asu.edu Mathematics Department, Arizona State University
Kirboe, Thomas tk@dfu.min.dk Danish Institute for Fisheries Research
Kuang, Yang kuang@asu.edu Department of Mathematics and Statistics, Arizona State University
Laurent, Arnaud arnaud.laurent@dal.ca Oceanography, Dalhousie University
Lim, Sookkyung limsk@math.uc.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Lin, Shili lin.328@osu.edu Statistics, The Ohio State University
Lombard, Fabien lombard@obs-vlfr.fr Laboratoire d'Oceanographie de , Villefranche-sur-mer
Lou, Yuan lou@math.ohio-state.edu Mathematics, The Ohio State University
Lunn, Mary mary.lunn@st-hughs.oxford.ac.uk Statistics , St Hugh's College
Mahaffy , Joe mahaffy@math.sdsu.edu Mathematical Sciences, San Diego State University
Malik, Tufail tufail@asu.edu Mathematics and Statistics, Arizona State University
Moore, Mark cmmoore@essex.ac.uk Biological Sciences, University of Essex
Nevai, Andrew anevai@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Pahlow, Markus Markus.Pahlow@Dal.ca Oceanography , Dalhousie University
Passino, Kevin passino.1@osu.edu Electrical and Computer Eng, The Ohio State University
Ross, Oliver onross@essex.ac.uk Biological Sciences, University of Essex
Schugart, Richard richard.schugart@wku.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Seuront, Laurent laurent.seuront@univ-lille1.fr Station Marine de Wimereux, Observatoire National de Besanc con (CNRS)
Smith, Hal Mathematics and Statistics , Arizona State University
Srinivasan, Partha p.srinivasan35@csuohio.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Stigler, Brandy bstigler@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Stomp, Maayke mstomp@science.uva.nl Aquatic Microbiology, University of Amsterdam
Strand, Espen espen.strand@bio.uib.no Biology , University of Bergen
Tang, Kam kamtang@vims.edu Biological Sciences , College of William and Mary
Tian, Paul tianjj@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Vallino, Joe jvallino@mbl.edu Marine Biological Laboratory
Van Oevelen, Dick D.vanOevelen@nioo.knaw.nl NIOO-KNAW, Centre for Estuarine and Marine Ecology
Vzina , Alain vezinaa@dfo-mpo.gc.ca Ecosystem Research Division, Bedford Institute of Oceanography
Visser, Andy awv@dfu.min.dk Marine Ecology and Aquaculture , Danish Institute for Fisheries Research
Wang, Hao wanghao@math.gatech.edu Mathematics and Statistics, Arizona State University
Waters, Raechel waters@ocean.washington.edu School of Oceanography, University of Washington
Zhang, Zhenbu zhenbu.zhang@jsums.edu Department of Mathematics, Jackson State University
Statistical Methods in Modelling (MCMC etc.)

Estimating the time evolution of ocean biogeochemical variables requires both models and data. Mathematical models for ocean biogeochemistry are based on nonlinear (ordinary and partial) differential equations, and exhibit complex dynamical behaviour and high dimensionality. Observations come from a variety of sources and are characterized by being noisy, sparse and non-Gaussian, and with complex spatial and temporal structure. This talk considers some emerging statistical approaches for estimating the time evolution of the biogeochemical state of the ocean (along with relevant parameters). These use a state space framework which incorporates nonlinear (stochastic) dynamical models and available data. Solutions are probabilistic and rely on sampling based (sequential Monte Carlo) methods. Application and illustration of these approaches is presented using models of pelagic ocean biogeochemistry (e.g. PZND models: phytoplankton, zooplankton, nutrient, detritus).

Modelling Microbial Diagenesis

Most biogeochemical changes that occur to sediments after their deposition are related to organic matter decomposition, which is a microbial process. Transport-reaction modelling of this diagenesis has been extremely successful at describing and explaining the resulting distributions of solid and solute components of sediments. This lecture aims first to highlight these successes, focussing on examples from microbial mats and the transient redistribution of redox-sensitive metals. A surprising result from this modelling, confirmed by experimental results, is that the microbial population need not be modelled explicitly. The lecture explores the theoretical basis from this seemingly contradictory finding. Finally, the feedback between the macro-fauna and the microbial population in sediments is examined.

Microbial Distributions Math Perspective

The nature and extent of bacterial diversity is a frontier in science of astronomical dimensions and profound practical importance. Bacterial diversity is unknown at any scale in any environment. Debates about the nature of a species contribute to but do not actually cause this confusion. Rather the scale and inscrutable nature of the microbial world, combined with a paucity of theory, prevents us from gaining a clear picture of bacterial diversity. For example, in most environments we are confronted with exponentially increasing numbers of taxa at exponentially decreasing abundances. Random sampling often reveals the same taxa again and again and we cannot therefore distinguish between rarity and absolute lack of taxa. Unfortunately, sample sizes are dictated by budgets not statistics. The usual alternative to counting is to infer the numbers from a taxa abundance curve which one can either guess, or infer by fitting curves from samples. Unfortunately, the biggest samples are very small with respect to the community and the fitted parameters can be so uncertain as to yield quite variable estimates of diversity. Theory can lend a hand. We believe that fundamental, and hopefully universal, aspects of community assembly can be expressed mathematically, and that therefore diversity can, in principle, be predicted. Unfortunately, these predictions must be made in a world we can barely perceive and in which meaningful quantitative studies are expensive, laborious and prone to failure. Consequently complex and unparameterised models must be eschewed for they are potentially very misleading. We need theory which is simple and amenable to calibration using small samples. In our hands stochastic, birth death and invasion models can fulfil this role (especially if they can be complemented by deterministic models to determine the number of individuals). These neutral models are conceptually analogous to MacArthur and Wilson's "Theory of Island Biogeography" and will describe, inter alia, taxa abundance curves, and thus diversity. Theory is not a substitute for the empirical measurement of diversity but it could prove an invaluable ally in this task. It will allow us to design the large scale sequencing programmes that are required for definitive studies on microbial diversity in some communities which could in turn permits the confident prediction of bacterial diversity in others.


This work was done in collaboration with Mary Lunn, Stephen Woodcock, and I.M Head William T. Sloan.

The Use of Individual Based Models (IBMs)

At the outset of population modeling, an individual was seen as a number among other equals in the population. Later, extensions have been introduced to account for individual variability within population models. These extensions may be classified into community ecology models, game theory, state-dependent models and age-dependent models. We show that the individual-based approach can be used to merge these traditions. We will show how the ING concept and hedonic modeling can be used to combine genetic variation and density- and frequency-dependency with trade-offs linked to age and state. We will also present simulations of evolution in a microbial community. Our work is done in collaboration with Frede Thingstad.


This presentation is made in collaboration with Espen Strand, also at the Department of Biology, University of Bergen.

Stoichometry in Microbial Food Webs

The law of mass conservation constrains the dynamics of interacting microbial populations. These stoichiometric constraints facilitate theoretical studies of how species interactions relate to dynamics of nutrients and other substances. In theory, stoichiometry affects the coexistence and stability of populations interacting through mechanisms such as competition for resources, allelopathy, commensalism, mutualism, and predation. Experimental studies support many predictions of stoichiometric theory as applied to interacting microbial populations. Stoichiometric signatures are also predicted for the assembly of diverse communities. Although existing theory is largely limited to steady state analyses of systems with two growth-limiting substances, current research extends the stoichiometric approach to three growth-limiting substances and non-steady conditions.

Plankton Models

Plankton Models

Microbial Distributions, Biological Perspective

For most eukaryotic organisms a species is defined as an interbreeding population. But bacteria don't have sex. Instead they acquire DNA fragments for recombination in several direct ways (i.e. horizontal gene transfer). Thus, the traditional Biological Species concept makes little sense in relation to bacterial speciation. To overcome this problem the concept of ecotypes defined as populations of bacterial cells that show genetic cohesion and are ecologically distinct has been introduced. In this presentation the "species" issue will be discussed in relation to current estimates of total marine bacterioplankton diversity. Also, bacterial cosmopolitanism, widely accepted by microbiologists, confronts recent reports of endemic species and restricted distributions. Because of their small size, huge abundance and easy dispersal, it is assumed that marine planktonic microorganisms may show an ubiquitous distribution that prevents any structured assembly into local communities. Currently a global picture of the bacterioplankton distribution in surface layer is emerging showing a marine bacterioplankton community that follows a latitudinal gradient of diversity and that includes few truly cosmopolitan species. The structure of the bacterioplankton community that leads to these results will be discussed as well as the implications of a structured bacterioplankton community for modelling biogeochemical cycles in the ocean.

Mixing and Chaos in Plankton Communities

Physical mixing processes have a major impact on species interactions in plankton communities. Here, we develop new theory to predict how changes in turbulent mixing affect the population dynamics of phytoplankton species. We apply the theory to two contrasting aquatic ecosystems, a hypertrophic lake and the oligotrophic ocean.


In hypertrophic lakes, where nutrients are in ample supply, the growth rates of phytoplankton species are often limited by light availability. The light conditions experienced by phytoplankters depend on their vertical excursions through the water column. To investigate how changes in vertical mixing affect competition for light between different species, we manipulated the turbulence structure of an entire lake using artificial mixing. Changes in turbulent mixing of the lake caused a dramatic shift in phytoplankton species composition. Consistent with our model predictions, sinking diatoms and green algae dominated during intense mixing, while buoyant and potentially toxic cyanobacteria became dominant when mixing was reduced.


In the oligotrophic ocean, phytoplankton species face two opposing resource gradients: light supplied from above and nutrients supplied from below. As a result, phytoplankton cells may achieve highest growth rates not at the water surface, but at a depth where both resources are available in sufficient supply. That is, a deep chlorophyll maximum develops. Our model predicts that reduced vertical mixing, which brings less nutrient into the euphotic zone, will generate oscillations and chaos in the phytoplankton of the deep chlorophyll maximum. These intriguing model predictions are compared with the complex species dynamics observed in deep chlorophyll maxima of the subtropical Pacific Ocean, as revealed by long-term studies of the Hawaii Ocean Timeseries program.


According to recent climate models, global warming will lead to a stronger vertical stratification of lakes and oceans, which reduces vertical mixing in the water column. The results of our plankton models, lake experiments, and ocean observations warn that changes in the vertical mixing structure, driven by climate change, can induce major shifts in the population dynamics and species composition of phytoplankton communities.


References:



  • Huisman, J., J. Sharples, J.M. Stroom, P.M. Visser, W.E.A. Kardinaal, J.M.H. Verspagen & B. Sommeijer. 2004. Changes in turbulent mixing shift competition for light between phytoplankton species. Ecology 85: 2960-2970.

  • Huisman, J., N.N. Pham Thi, D.M. Karl & B. Sommeijer. 2006. Reduced mixing generates oscillations and chaos in the oceanic deep chlorophyll maximum. Nature 439: 322-325.

Unsteady Environments of Benthic Marine Microbes

Bacteria in sediments exist at a surprisingly constant 109 individuals ml-1 of pore water. Every indication, however, is that the majority of those cells are idle most of the time. Messenger compounds are one means to signal that renewed metabolic activity would be worthwhile, and signals sent or received this way have some interesting features in an environment containing diffusion-reflecting boundaries. Mechanical stresses in sediments have received less attention, but new models and measurements in sediments and sediment analogs suggest that many muds behave mechanically like linear-elastic, solid gels with fairly simply large-scale geometries. Burrowing animals produce stress and strain fields in them and fracture sediments. These stress-strain and fracture fields can provide direct mechanical stimuli and can have large influence on solute delivery by short circuiting otherwise diffusively delivered chemical signals.

Particle Colonization

Rich microbial communities develop on and around suspended particles in pelagic environments. Their activity may account for a significant fraction of the microbial activity in the water column and they enhance the degradation of sinking particles, thus retarding vertical material fluxes in the ocean. A combination of simple mechanistic models and experiments are used to explore the dynamics of these communities. The description considers motility behaviour and colonization of bacteria and flagellates, growth and detachment of particle-attached microbes, and trophic interactions. The models and experiments are capable of describing some gross features of particle attached microbial communities, such as how the abundances of attached microbes scale with particle size, but there are many open and unresolved questions. These include the similarity or difference of particle-attached and free microbes; the interaction between the dynamics of the particles (as they form and degrade) and the dynamics of the microbes; and the significance for ocean carbon fluxes of these microbial communities.

Samples and Simulation

Given huge populations of microbes, extracting as much information as possible from small sub-samples is important. Analytic methods based on traditional likelihood calculations are difficult to use when selecting a subsample from a potentially large number of species. We present some preliminary results on how simulation may be used, applying the method to data from soil and human gut flora.

Primary Producers from the Organism Perspective

Photosynthesis in the oceans is dominated by phytoplankton, an assemblage of organisms spanning many phyla across 2 empires. In addition to this vast genetic (adaptive) variability, phytoplankton have evolved a large capacity for physiological plasticity (acclimation). Modelling the response of primary productivity to environmental forcing thus potentially represents a major challenge. This talk will address how to confront this challenge from a mechanistic physiological view point. Initially we will consider slower timescale acclimation to temperature, light and nutrient availability, modelled in terms of adjustments in cellular constituents acting to balance the supply of energy through photosynthetic light capture, with the electron demands for biosynthesis and maintenance. Changes in the cellular chlorophyll to carbon ratio capture the essence of these models, which are likely to provide a reasonable approximation of phytoplankton photosynthesis in stratified conditions. In contrast, rapidly mixed layers often characterise the regions of the upper ocean where the highest productivity occurs (e.g. mid-high latitudes during spring). Understanding the physiological response to the high frequency variations in light occurring in this situation will likely require consideration of faster kinetic processes. Potential means of modelling these 'energy modulation' processes, which include both non-photochemical quenching and photoinhibition, will be described. The challenge of scaling back up from these physiological models to ecosystem and global scales will also be mentioned.

Small Scale Distributions of Microbes

A ubiquitous feature of aquatic ecosystems is their temporal variability and spatial heterogeneity that occur over a wide range of scales. Despite the considerable amount of work devoted to the quantification of the spatial and temporal patterns of plankton distributions, their intrinsic three-dimensional and microscale properties have widely been underestimated. Here, using tools borrowed from the field of statistical physics, I will illustrate how taking into account the space-time complexity of microbial distributions at microscale and in 3D, in particular their intermittent behaviour and the related dynamics of extreme events, can provide extremely valuable ecological information. A specific attention will be given to the nature of and the interplay between turbulence intermittency, seawater viscosity, individual swimming and mating behaviour, predator/prey and virus/host interactions.

Does non-equilibrium thermodynamics govern metabolic network expression in microbial communities?

In this presentation I take a metabolic perspective of ecosystem biogeochemistry that functions at local, region and global scales, in deep-sea hydrothermal vents and the deep biosphere, as well as in laboratory microcosms. In all these systems, a complex metabolism govern by microorganisms develops; however, instead of the metabolism being orchestrated by a single organism, metabolic function is distributed among hundreds of microbial species, yet the overall system-metabolism functions in a highly organized and coordinated manner. What governs the development and organization of this distributed metabolism? Is it governed by just happenstance depending on which organisms are present in the system at a particular instance, or are there fundamental governing laws that dictate how the system metabolism will develop? It is hypothesized that 3.5 billion years of evolution has produced biological systems so adept and efficient at producing and degrading chemical potential that the overall biogeochemistry of microbial systems can be accurately described by simple rules without requiring knowledge of the individual species that occupy a given system. Accordingly, the biogeochemistry observed on Earth, at both local and global scales, may be governed by principles derived from nonequilibrium thermodynamics with living systems being the mechanism by which the system attempts to degrade energy gradients. Using a distributed metabolic perspective constrained by nonequilibrium thermodynamics, I present a modeling framework that can predict ecosystem biogeochemistry assuming the system is sufficiently metabolically diverse. The model predicts how resources (i.e., carbon sources, nutrients, chemical electron acceptors and donors) change over time, as well as how the overall system allocates protein to metabolic processes, such as photosynthesis, nitrification, sulfate reduction, respiration, etc., as governed by the principle of maximum entropy production (MEP). The primary research objective is to demonstrate, via model comparison to experiments, that living systems tend to track the MEP objective. I will present development of the modeling framework that incorporates thermodynamic objective functions as well as model comparison to preliminary microcosm experiments in which state and microbial composition are monitored.

The Role of Bacterial Carbon in Marine Benthic Food Webs: Integrating experimental 13C isotope data with models

Bacteria dominate biogeochemical processes in most sediments. Bacterial production and respiration processes are therefore studied in detail by biogeochemists. However, the fate of produced bacterial biomass is often not considered. The ubiquitous presence of bacteria, their high nutritional value and secondary production has lead many benthic ecologists to speculate that bacteria fulfill an important carbon transfer in the benthic food web. Recent evidence suggests that viral infection and subsequent lysis may be an important factor in bacterial loss processes in the pelagic zone, but its significance in sediments is not well established. It is clear that an integrated approach is required to understand the dynamics of bacterial in sediments.


We present, analyse and model the results of an in situ experiment, in which 13C-glucose was injected in the surface 10 cm of a marine intertidal sediment. The injected 13C-glucose was quickly incorporated by the bacterial community as evidenced by 13C enrichment of bacterial specific biomarkers (polar-lipid-derived fatty acid and D-alanine) and its fate in the food web was followed during a period of 4.5 months. Trophic transfer through grazing on bacterial was assessed through the 13C enrichment of meio- (group level) and macrobenthos (species level). Respiration was monitored through the production of 13C dissolved inorganic carbon. 13C enrichment of different sedimentary amino acids was used to gain insight in preservation of bacterial remnants in the particulate organic carbon pool of the sediment. The complete data set was evaluated with a mechanistic model to quantify the importance of exchange processes (i.e. resuspension and irrigation), bacterial grazing by benthic fauna and bacterial growth, respiration and mortality.


The interaction between bacterial and benthic fauna can be viewed from the bacterial perspective in terms of the importance of grazing as a fate of bacterial carbon production. Another interesting question is how much the grazed bacterial carbon contributes to the total carbon requirements of benthic fauna. To address this question, the relative enrichment of meio- and macrobenthic taxa was evaluated against the relative enrichement in bacteria by means of a simple isotope model. Bayesian analysis was employed in both modeling approaches to determine the constraining effect of the data - model interaction on the model parameters.


The results of this comprehensive study will be compared against the results of an inversion analysis and studies performed on other resources and in other ecosystems to give an overview of our current understanding of the role of bacteria in benthic food webs.


This work was done in collaboration with Leon Moodley, Bart Veuger, Karline Soetaert, Jack J. Middelburg and Carlo H. R. Heip.

Inverse Modelling and the Parsimony Principle in Investigations of Microbial Food Webs

Microbial food webs are maintained by complex flows of carbon, nutrients and biochemical compounds that cannot be fully quantified by measurements. Inverse modelling was introduced to biological oceanography and microbial ecology in the late 1980s as a way to reconstruct complete flow networks from incomplete information. The reconstructed flow network is the simplest among all plausible configurations. In other words, it is the flow network that contains no more structure than is required to explain the data. This parsimony principle has implications for the reconstructed microbial interactions that are not always realistic. This lecture will review new approaches to counter adverse effects of the parsimony principle and possible approaches to replace it completely. At this time it appears that parsimony will remain an integral part of inverse analysis but recent improvements in inverse modelling promise to decrease its impact on the results.

The Role of Turbulence and Small Scale Processes

For planktonic organisms, nearly all important life processes are governed by an encounter rate. For instance, growth, reproduction, and mortality are closely linked to an individual's encounter with food, mates, and predators respectively. Understanding the distribution of resources on scales relevant for individual organisms, and how they locate and exploit these resources is central to understanding how marine ecosystems function. At these scales, the dispersion of material is controlled by molecular diffusion, turbulent straining and Richardson's law. That is, the landscape experienced by plankton (i.e. chemical patches, detrital aggregates and other organisms) is strongly controlled by small scale physics. Lagrangian models of planktonic interactions can be built up by examining (i) their small scale physical environment, (ii) their motility and behaviour, and (iii) their sensory ability in remotely detecting each other and patchily distributed resources. As an example, many aquatic organisms - from bacteria to crustaceans - use chemical plumes released by sinking particulate organic material either directly as a food source or as a signal to find potential food items (marine snow aggregates, fecal pellets). This interaction is important as it determines where, how fast and to what degree sinking detrital material is demineralised in the water column; a pivotal process in determining the vertical carbon flux in the ocean. This example highlights the interplay of abiotic aspects of the environment, in particular turbulence, with the sensory ability and motile behaviour of planktonic organisms.