Workshop 1: Sustainability and Complex Systems

(September 16,2013 - September 20,2013 )

Organizers


Chris Cosner
Mathematics, University of Miami
Volker Grimm
Ecological Modelling, Helmholtz Zentrum München (German Research Center for Enviromental Health)
Alan Hastings
Department of Environmental Science and Policy, University of California, Davis
Otso Ovaskainen
Biological and Environmental Sciences, University of Helsinki

Creating usable models for the sustainability of ecosystems has many mathematical challenges. Ecosystems are complex because they involve multiple interactions among organisms and between organisms and the physical environment, at multiple spatial and temporal scales, and with multiple feedback loops making connections between and across scales. The issue of scaling and deriving models at one scale from another is well known to lead to substantial mathematical issues, as in going from descriptions of stochastic spatial movement at the population scale from the individual scale and as in getting diffusion limits. Here, for example, recent work has focussed on alternatives to the diffusion limit. The mathematical challenges in the analysis of full ecosystems are truly great. Many modeling approaches have been used in studying ecosystems, ranging from simple dynamical systems to highly detailed computational models. Relatively simple models are essential to gain insight into fundamental features of complex systems and the mechanisms behind them, whereas highly detailed models are essential for making predictions about the specific effects that changes may have on ecosystem functioning. The complex ones include agent-based models and models that place biological models into realistic and detailed models for physical processes such as ocean dynamics. There is a need to develop new mathematical tools for making connections among different processes at different scales and thus provide a robust framework for assessing the sustainability of ecosystem processes. Understanding models at multiple scales also requires case studies of particular systems. Plankton dynamics provide a good case study. At one extreme, low dimensional Nutrient-Phytoplankton-Zooplankton (NPZ) models give insight into the balance between light penetration and nutrient upwelling that underlie patterns of plankton blooms. At the other extreme, computational models of a myriad competing plankton species, rapidly evolving in the face of changing ocean temperature and salinity, are numerically incorporated into global climate models. As a second example, forests and savanna are complex systems where organisms interact with physical processes, specifically fire and hydrology, and they have been studied from the viewpoint of individual-based modeling but also with simple models. This workshop aims to engage computational and mathematical modelers, empiricists, and mathematicians in a dialogue about how to best address the problems raised by the pressing need to understand complex ecological interactions at many scales. Its ultimate goal is to initiate transformative research that will provide new approaches and techniques, and perhaps new paradigms, for modeling complex systems and for connecting different types of models operating at different levels of detail. An important feature of the workshop will be afternoon sessions devoted to case studies rather than lectures with the goal of starting new collaborations and new research directions.

Accepted Speakers

Karen Abbott
Biology, Case Western Reserve University
Priyanga Amarasekare
Ecology and Evolutionary Biology, University of California Los Angeles
Chris Cosner
Mathematics, University of Miami
Volker Grimm
Ecological Modelling, Helmholtz Zentrum München (German Research Center for Enviromental Health)
Alan Hastings
Department of Environmental Science and Policy, University of California, Davis
Mac Hyman
Department of Mathematics, Tulane University
Yoh Iwasa
Biology, Kyushu University
Yannis Kevrekidis
Chemical and Biological Engineering, Princeton University
Mark Lewis
Canada Research Chair in Mathematical Biology, University of Alberta
Otso Ovaskainen
Biological and Environmental Sciences, University of Helsinki
Sergei Petrovskii
Mathematics, University of Leicester
Carl Simon
Ford School of Public Policy, University of Michigan
Sebastian Wieczorek
Mathematics, University of Exeter
Damaris Zurell
Institute for Biochemistry and Biology, University of Potsdam
Monday, September 16, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:15 AM

Greetings and info from MBI

09:15 AM
09:30 AM

Introduction by organizers

09:30 AM
10:30 AM
Mark Lewis - Aquaculture and Sustainability of Coastal Ecosystem

Aquaculture and Sustainability of Coastal Ecosystem

10:30 AM
11:00 AM

Break

11:00 AM
12:00 PM

GROUP DISCUSSION OF MOST PRESSING ISSUES IN Dealing with complex systems; picking of issues to discuss Wednesday afternoon

12:00 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Yoh Iwasa - Modeling socio-economic aspects of ecosystem management and biodiversity conservation

For successful ecosystem management and biodiversity conservation, in addition to ecological and evolutionary processes, we need to consider social and economic influences on the management target. Here, we introduce several theoretical models that address economic and social aspects of human society that are closely related to ecosystem management.

The first model analyzes coupled socio-economical and ecological dynamics for lake water pollution. Players choose between cooperative (but costly) option and economical option, and their decision is affected by the fraction of cooperators in the community and by the importance of water pollution problem. When an opportunity for choice arrives, players take the option with the higher utility. This social dynamics is coupled with the dynamics of lake water pollution. First, oscillation of large amplitude is generated if social change occurs faster than ecosystem responses. Second, the model can show "paradox of nutrient removal". If phosphorus is removed more effectively either from the inflow or from the lake water, the pollution level may increase (rather than decrease) due to the decline in people's willingness to cooperate.

The second model discusses how activities that promote social concern about biodiversity help to maintain public support for biodiversity conservation. We study the optimal investment in the trade-off between activities that increase social concern and those that maintain and improve the conservation target.

The third model analyzes punishment as a mechanism to maintain cooperative behavior in a social group. We discuss the efficiency of a graduated punishment system, in which the severity of the punishment applied to deviators increases with the amount of harm caused by the selfish action, which field research has shown to be essential for successful resource management. We conclude that graduated punishment is the most efficient way to ensure cooperation when evaluation errors are unavoidable and when the social group is heterogeneous with respect to the sensitivity of its members to utility difference.

03:00 PM
04:00 PM

GROUP DISCUSSION

04:00 PM
05:30 PM

Reception and Poster session in MBI Lounge

05:45 PM

Shuttle pick-up from MBI

Tuesday, September 17, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Volker Grimm - Individual-based Ecology: Theories, Predictions, Simplifications

Individual-based Ecology: Theories, Predictions, Simplifications

10:00 AM
10:30 AM

Break

10:30 AM
11:30 AM
Sergei Petrovskii - Sustainability of agroecosystems: insights from the multiscale insect pest monitoring

Sustainability of agroecosystems: insights from the multiscale insect pest monitoring

11:30 AM
12:00 PM

Discussion

12:00 PM
02:00 PM

Lunch - Pizza provided by MBI

02:00 PM
03:00 PM
Mac Hyman - A network-patch modeling framework for the transmission of vector-borne infections

We have developed a network-patch model for the spread of mosquito-borne pathogens, including chikungunya, dengue, and West Nile virus. The model accounts for the movement of individual people through mosquito habitats that respond to environmental factors, such as rainfall and temperature. Our approach extends the capabilities of existing agent-based models for human movement developed to predict the spread of directly transmitted pathogens in human populations. These agent-based models are combined with differential equations representing clouds of mosquitoes in geographic patches that account for heterogeneity in mosquito density, mosquito emergence rates, and the extrinsic incubation period of the pathogen. I will illustrate the importance of heterogeneity in both human and mosquito populations on disease spread. The new hybrid agent-based/differential equation model can help quantify the importance of heterogeneity in predicting the spread and invasion of mosquito-borne pathogens and extend the capabilities of existing agent-based models to include vector-borne diseases. This research is in collaboration with Carrie Manore, Kyle Hickmann, Ivo Foppa, Dawn Wesson, Chris Mores, and Sara Del Valle.

03:00 PM
03:30 PM

Break

03:30 PM
04:30 PM
Priyanga Amarasekare - A trait-based perspective of complex systems

Populations and communities are complex systems whose properties result from the interplay between non-linear feedbacks that are intrinsic to the system (e.g., biotic interactions that lead to density- and frequency-dependence) and external inputs (e.g., abiotic factors) that are outside the feedback structure of the system. Understanding this interplay requires that we understand the mechanisms by which the effects of external inputs on lower levels of the system (e.g., traits of organisms) influence properties at higher levels (e.g., population viability, species diversity). Using temperature as the axis of abiotic variation, I develop a mechanistic theoretical framework for elucidating how abiotic effects on traits translate into population dynamics and species interactions, and how these ecological dynamics in turn feedback into the trait response, causing trait evolution. I test model predictions with data on insects. The integration of theory and data paves the way for making testable predictions about the effects of climate warming on population viability, biodiversity and the control of invasive species.

04:45 PM

Shuttle pick-up from MBI

Wednesday, September 18, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Karen Abbott - Stochasticity in complex systems

Stochasticity in complex systems

10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM
Sebastian Wieczorek - Rate-induced Tipping Points: Critical Rates, Non-obvious Thresholds and Failure to Adapt to Changing External Conditions

Complex systems subject to changing external conditions can undergo unexpected rapid transitions from one stable state to another, a phenomenon known as "tipping". The well established tipping mechanism is a traditional bifurcation, where the stable state disappears or destabilises at some critical level of external conditions. I will describe a different tipping mechanism termed the "rate-induced tipping". Here, the stable state exists continuously for all fixed levels of external conditions and never bifurcates. When external conditions vary in time, the position of the stable state changes and the system tries to keep pace with the changes. However, some systems fail to adapt to the changing stable state and tip if the external conditions are changed too fast.


Scientists often find rate-induced tipping counter-intuitive because there is no obvious loss of stability and no obvious tipping threshold. On the other hand, these non-autonomous instabilities cannot be captured by classical bifurcation theory and remain fairly unexplored. I will present an approach based on geometrical singular perturbation theory to study critical rates of change and non-obvious tipping thresholds. I will also discuss repercussions for climate change policy making which currently focuses on critical levels of the atmospheric temperature whereas the critical factor may be the rate of warming rather than the temperature itself.

11:00 AM
12:30 PM

Discussion

12:30 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Chris Cosner - Challenges in Modeling Biological Invasions and Population Distributions in a Changing Climate

Classical models for dispersal and invasion typically assume that the underlying environment is fixed in size, shape, and location. They also typically focus on a single species or a pair of interacting species, with fixed attributes and interactions. In the presence of climate change and other anthropogenic changes to the environment those assumptions often will not be valid. In a changing climate the structure and properties of the underlying environment will change with time, which by itself poses modeling challenges. Climate change could shift the timing of events such as flowering, migration, or emergence from hibernation in different ways for different species, thus changing the interactions experienced by any particular focal species. To account for that models would have to explicitly include parameters describing the timing of events. Climate change could also shift the ranges of species in space, which could also change species interactions and could cause niches to open up because the species occupying a particular niche has shifted its range and left that niche empty in some locations. To account for that, models would have to include multiple species. Finally, both climate change and the invasion process itself may impose novel selection pressures, so the attributes of a species invading a new region while the climate is changing are not likely to remain fixed. To address that would seem to require building some evolutionary processes into invasion models. This talk will discuss those issues and suggest some modeling approaches and ideas that might be relevant to addressing them.

03:00 PM
03:30 PM

Break

03:30 PM
05:00 PM

Breakout groups to dicsuss isues raised on Monday; followed by report outs

05:15 PM

Shuttle pick-up from MBI

Thursday, September 19, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Alan Hastings - Role of time scales in sustainability of complex systems

Role of time scales in sustainability of complex systems

10:00 AM
10:45 AM

Break

10:45 AM
11:45 AM
Yannis Kevrekidis - No Equations, No Variables: An approach to complex/multiscale systems Modeling and Computation

In current modeling practice for complex systems, including agent-based and network-based simulations, the best available descriptions of a system often come at a fine level (atomistic, stochastic, individual-based) while the questions asked and the tasks required by the modeler (parametric analysis, optimization, control) are at a much coarser, averaged, macroscopic level. Traditional modeling approaches start by deriving macroscopic evolution equations from the microscopic models. I will review a mathematically inspired, systems-based computational enabling technology that allows the modeler to perform macroscopic tasks acting on the microscopic models directly in an input-output mode. This €œequation-free€? approach circumvents the step of obtaining accurate macroscopic descriptions. I will discuss applications of this approach and its linking with recent developments in data mining algorithms, exploring large complex data sets to find good "reduction coordinates".

12:00 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Carl Simon - Computing Tipping Points in Contagion and Ecology Models

There are three kinds of tipping points (or thresholds) in dynamic models: points that separate one basin of attraction from another in a single system, parameter points at which the parametrized system changes its behavior, and (a simple case of the latter) functions of the parameters which determine whether or not zero is a stable equilibrium (e.g., basic reproduction numbers). We will illustrate a simple procedure for computing such basic reproduction numbers for general contagion models vis Lyapunov functions without computing the eigenvalues of a matrix.

03:00 PM
03:30 PM

Break

03:30 PM
05:00 PM

Breakout groups to dicsuss isues raised on Monday; followed by report outs

05:15 PM

Shuttle pick-up from MBI

06:30 PM
07:00 PM

Cash Bar

07:00 PM
09:00 PM

Banquet in the Fusion Room @ Crowne Plaza Hotel

Friday, September 20, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
08:45 AM

Breakfast

08:45 AM
09:45 AM
Damaris Zurell - Beyond the proof of concept: virtual ecologists in complex dynamic systems

The virtual ecologist is an intuitive and widely used approach which includes simulating artificial species or ecosystem data, an observer that collects data according to a specific sampling protocol, the statistical analysis or modelling of the collected data and subsequent evaluation of the results against known (virtual) truth. In my talk, I will briefly review the concept and existing examples. For example, in global change research this approach holds great potential for rigorous testing of different modelling methods under controlled and changing conditions and with controlled sampling bias. Specifically, I want to emphasize the merit of using complex dynamic simulation models for simulating data and observers. This ingredient takes the virtual ecologist approach beyond simple proof of concept making it a truly integrative and rigorous framework not only for testing sampling protocols or modelling and analysis tools but for theory development and testing more generally.

09:45 AM
10:00 AM

Break

10:00 AM
11:00 AM
Otso Ovaskainen - Models and data: from individuals to populations to communities

Most observational data sets in ecological research have a spatial component, but analysis of spatial data is challenging. Observations that are made in nearby locations are often similar and consequently the data points are not independent of each other. The presence of spatial autocorrelation can be considered as trouble, as simple statistical tests assuming independence are not valid, or as an opportunity of learning about the biological processes creating a given level of autocorrelation. One point in case is research on animal movement. Consecutive locations in an animal track are necessarily correlated, invalidating e.g. the assumption of independence in models of habitat use. I discuss how this problem can be avoided by analyzing animal movement data either with state-space models or with randomization tests. I also discuss how the level of autocorrelation (or persistence in direction) as well as long-term movement behavior can be summarized for a wide family a models with two parameters only: the characteristic spatial and temporal scales of movement. I then move to species distribution modeling, which I extend to community-level models in two different ways. First, I describe a multivariate regression model that can be used to ask if some species combinations occur more or less often together than by expected by random. This approach is suited for cases where there are much data on few species. Second, for the opposite case of few data on many species, I describe how statistical inference can be improved by gluing the species-specific models together with a higher-level community model.

11:00 AM
12:00 PM

Summary Discussion

12:00 PM

Shuttle pick-up from MBI (One to hotel, One to Airport)

Name Email Affiliation
Abbott, Karen kcabbott@case.edu Biology, Case Western Reserve University
Afassinou, Komi komia@aims.ac.za School of Mathematics, Statistic and Computer Science, University of KwaZulu-Natal
Altenberg, Lee altenber@santafe.edu Editorial Board, BioSystems, Elsevier Journal
Amarasekare, Priyanga amarasek@eeb.ucla.edu Ecology and Evolutionary Biology, University of California Los Angeles
Anand, Madhur manand@uoguelph.ca School of Environmental Sciences, University of Guelph
Armi, Zina armi.zina@yahoo.fr Laboratoire du Milieu Marin, Institut National des Sciences et Technologies de la Mer
Artzy-Randrup, Yael YArtzy@umich.edu Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam
Baetens, Jan Jan.baetens@ugent.be Mathematical Modelling, Statistics and Bioinformatics, Ghent University
Bakshi, Bhavik bakshi.2@osu.edu Chemical and Biomolecular Engineering, The Ohio State University
Berkel, Derek vanberkel.3@osu.edu Geography, Ohio State University
Bogra, Shelly shbogr@gmail.com William G. Lowrie Department of Chemical and Biomolecular Engineering, Ohio State University
Collins, Obiora obioracollins1@gmail.com School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal
Cosner, Chris gcc@math.miami.edu Mathematics, University of Miami
Cutler, Emma ecutler@bowdoin.edu Mathematics, Bowdoin College
Daly, Aisling Aisling.Daly@UGent.be Mathematical Modelling, Statistics and Bioinformatics, Universiteit Gent
Giske, Jarl Jarl.Giske@bio.uib.no Biology, University of Bergen
Grimm, Volker volker.grimm@ufz.de Ecological Modelling, Helmholtz Zentrum München (German Research Center for Enviromental Health)
Gutierrez, Juan jgutierr@uga.edu Mathematics, Institute of Bioinformatics, University of Georgia
Hartig, Florian florian.hartig@biom.uni-freiburg.de Biometry and Environmental System Analysis, University of Freiburg
Hastings, Alan amhastings@ucdavis.edu Department of Environmental Science and Policy, University of California, Davis
Hyman, James mhyman@tulane.edu Department of Mathematics, Tulane University
Iwasa, Yoh yohiwasa@kyushu-u.org Biology, Kyushu University
Kaper, Hans kaper@mcs.anl.gov n/a, Mathematics and Climate Research Network
Kazanci, Caner caner@uga.edu Department of Mathematics, University of Georgia
Kevrekidis, Yannis yannis@arnold.princeton.edu Chemical and Biological Engineering, Princeton University
Kim, Hyeyoung kim.3594@osu.edu Geography,
Kimba Phongi, Eddy kimbaphongi@ukzn.ac.za School of Mathematics, Computer science and Statistic, University of KwaZulu-Natal
Koka, Nithya koka.4@osu.edu Chemical Engineering, Ohio State University
Krishnadas, Meghna krishnadas.1@osu.edu Evolution, Ecology, and Organismal Biology, The Ohio State University
Landsbergen, Kim landsbergen.2@osu.edu EEOB, The Ohio State University
Langebrake Inman, Jessica jessica.langebrake@gmail.com Biology, University of Florida
Lee, Jiyoung lee.3598@osu.edu Environmental Health Sciences, Ohio State University
Lewis, Mark mark.lewis@ualberta.ca Canada Research Chair in Mathematical Biology, University of Alberta
Li, Bai-Lian Larry bai-lian.li@ucr.edu Botany & Plant Sciences, University of California, Riverside
Lutscher, Frithjof flutsche@uottawa.ca Mathematics and Statistics, University of Ottawa
Massey, David massey.89@osu.edu Geography, The Ohio State University
McCarthy, Maeve mmccarthy@murraystate.edu Mathematics & Statistics, Murray State University
Merugula, Laura merugula.1@osu.edu Chemical and Biomolecular Engineering, The Ohio State University
Moritz, Mark moritz.42@osu.edu Anthropology, The Ohio State University
Morozov, Andrew am379@leicester.ac.uk Mathematics, University of Leicester
Munroe, Darla munroe.9@osu.edu Geography, The Ohio State University
Ovaskainen, Otso otso.ovaskainen@helsinki.fi Biological and Environmental Sciences, University of Helsinki
Petrovskii, Sergei sp237@le.ac.uk Mathematics, University of Leicester
Poggiale, Jean-Christophe jean-christophe.poggiale@univ-amu.fr Institut Pytheas (OSU), Aix-Marseille University
Railsback, Steven Steve@LangRailsback.com Mathematics, Humboldt State University
Reineking, Bjoern bjoern.reineking@uni-bayreuth.de Research Unit Mountain Ecosystems, Irstea
Robertson, Suzanne srobertson@mbi.osu.edu Department of Mathematics and Applied Mathematics, Virginia Commonwealth University
Sieber, Jan j.sieber@exeter.ac.uk College of Engineering, Mathematics and Physical Sciences, University of Exeter
Simon, Carl cpsimon@umich.edu Ford School of Public Policy, University of Michigan
Vasudevan, Ritvik vasudevan.26@osu.edu Engineering, The Ohio State University
Vidal, Guillermo guillermo.vidal@ugent.be Mathematical Modeling, Statistics and BioInformatics, Ghent University
Wieczorek, Sebastian S.M.Wieczorek@exeter.ac.uk Mathematics, University of Exeter
Wilson, James jwilson@maine.edu School of Marine Sciences, University of Maine
Zeeman, Mary Lou mlzeeman@bowdoin.edu Department of Mathematics, Bowdoin College
Zurell, Damaris dzurell@uni-potsdam.de Institute for Biochemistry and Biology, University of Potsdam
Stochasticity in complex systems

Stochasticity in complex systems

A trait-based perspective of complex systems

Populations and communities are complex systems whose properties result from the interplay between non-linear feedbacks that are intrinsic to the system (e.g., biotic interactions that lead to density- and frequency-dependence) and external inputs (e.g., abiotic factors) that are outside the feedback structure of the system. Understanding this interplay requires that we understand the mechanisms by which the effects of external inputs on lower levels of the system (e.g., traits of organisms) influence properties at higher levels (e.g., population viability, species diversity). Using temperature as the axis of abiotic variation, I develop a mechanistic theoretical framework for elucidating how abiotic effects on traits translate into population dynamics and species interactions, and how these ecological dynamics in turn feedback into the trait response, causing trait evolution. I test model predictions with data on insects. The integration of theory and data paves the way for making testable predictions about the effects of climate warming on population viability, biodiversity and the control of invasive species.

Challenges in Modeling Biological Invasions and Population Distributions in a Changing Climate

Classical models for dispersal and invasion typically assume that the underlying environment is fixed in size, shape, and location. They also typically focus on a single species or a pair of interacting species, with fixed attributes and interactions. In the presence of climate change and other anthropogenic changes to the environment those assumptions often will not be valid. In a changing climate the structure and properties of the underlying environment will change with time, which by itself poses modeling challenges. Climate change could shift the timing of events such as flowering, migration, or emergence from hibernation in different ways for different species, thus changing the interactions experienced by any particular focal species. To account for that models would have to explicitly include parameters describing the timing of events. Climate change could also shift the ranges of species in space, which could also change species interactions and could cause niches to open up because the species occupying a particular niche has shifted its range and left that niche empty in some locations. To account for that, models would have to include multiple species. Finally, both climate change and the invasion process itself may impose novel selection pressures, so the attributes of a species invading a new region while the climate is changing are not likely to remain fixed. To address that would seem to require building some evolutionary processes into invasion models. This talk will discuss those issues and suggest some modeling approaches and ideas that might be relevant to addressing them.

Individual-based Ecology: Theories, Predictions, Simplifications

Individual-based Ecology: Theories, Predictions, Simplifications

The ODD protocol: a standard format for describing individual-based and agent-based models

The ODD protocol: a standard format for describing individual-based and agent-based models.

When do we want to develop an individual-based model instead of a more aggregated one?

When do we want to develop an individual-based model instead of a more aggregated one?

Role of time scales in sustainability of complex systems

Role of time scales in sustainability of complex systems

Ricker models and complexity in ecology

Ricker models and complexity in ecology

A network-patch modeling framework for the transmission of vector-borne infections

We have developed a network-patch model for the spread of mosquito-borne pathogens, including chikungunya, dengue, and West Nile virus. The model accounts for the movement of individual people through mosquito habitats that respond to environmental factors, such as rainfall and temperature. Our approach extends the capabilities of existing agent-based models for human movement developed to predict the spread of directly transmitted pathogens in human populations. These agent-based models are combined with differential equations representing clouds of mosquitoes in geographic patches that account for heterogeneity in mosquito density, mosquito emergence rates, and the extrinsic incubation period of the pathogen. I will illustrate the importance of heterogeneity in both human and mosquito populations on disease spread. The new hybrid agent-based/differential equation model can help quantify the importance of heterogeneity in predicting the spread and invasion of mosquito-borne pathogens and extend the capabilities of existing agent-based models to include vector-borne diseases. This research is in collaboration with Carrie Manore, Kyle Hickmann, Ivo Foppa, Dawn Wesson, Chris Mores, and Sara Del Valle.

Modeling socio-economic aspects of ecosystem management and biodiversity conservation

For successful ecosystem management and biodiversity conservation, in addition to ecological and evolutionary processes, we need to consider social and economic influences on the management target. Here, we introduce several theoretical models that address economic and social aspects of human society that are closely related to ecosystem management.

The first model analyzes coupled socio-economical and ecological dynamics for lake water pollution. Players choose between cooperative (but costly) option and economical option, and their decision is affected by the fraction of cooperators in the community and by the importance of water pollution problem. When an opportunity for choice arrives, players take the option with the higher utility. This social dynamics is coupled with the dynamics of lake water pollution. First, oscillation of large amplitude is generated if social change occurs faster than ecosystem responses. Second, the model can show "paradox of nutrient removal". If phosphorus is removed more effectively either from the inflow or from the lake water, the pollution level may increase (rather than decrease) due to the decline in people's willingness to cooperate.

The second model discusses how activities that promote social concern about biodiversity help to maintain public support for biodiversity conservation. We study the optimal investment in the trade-off between activities that increase social concern and those that maintain and improve the conservation target.

The third model analyzes punishment as a mechanism to maintain cooperative behavior in a social group. We discuss the efficiency of a graduated punishment system, in which the severity of the punishment applied to deviators increases with the amount of harm caused by the selfish action, which field research has shown to be essential for successful resource management. We conclude that graduated punishment is the most efficient way to ensure cooperation when evaluation errors are unavoidable and when the social group is heterogeneous with respect to the sensitivity of its members to utility difference.

No Equations, No Variables: An approach to complex/multiscale systems Modeling and Computation

In current modeling practice for complex systems, including agent-based and network-based simulations, the best available descriptions of a system often come at a fine level (atomistic, stochastic, individual-based) while the questions asked and the tasks required by the modeler (parametric analysis, optimization, control) are at a much coarser, averaged, macroscopic level. Traditional modeling approaches start by deriving macroscopic evolution equations from the microscopic models. I will review a mathematically inspired, systems-based computational enabling technology that allows the modeler to perform macroscopic tasks acting on the microscopic models directly in an input-output mode. This “equation-free� approach circumvents the step of obtaining accurate macroscopic descriptions. I will discuss applications of this approach and its linking with recent developments in data mining algorithms, exploring large complex data sets to find good "reduction coordinates".

Aquaculture and Sustainability of Coastal Ecosystem

Aquaculture and Sustainability of Coastal Ecosystem

Models and data: from individuals to populations to communities

Most observational data sets in ecological research have a spatial component, but analysis of spatial data is challenging. Observations that are made in nearby locations are often similar and consequently the data points are not independent of each other. The presence of spatial autocorrelation can be considered as trouble, as simple statistical tests assuming independence are not valid, or as an opportunity of learning about the biological processes creating a given level of autocorrelation. One point in case is research on animal movement. Consecutive locations in an animal track are necessarily correlated, invalidating e.g. the assumption of independence in models of habitat use. I discuss how this problem can be avoided by analyzing animal movement data either with state-space models or with randomization tests. I also discuss how the level of autocorrelation (or persistence in direction) as well as long-term movement behavior can be summarized for a wide family a models with two parameters only: the characteristic spatial and temporal scales of movement. I then move to species distribution modeling, which I extend to community-level models in two different ways. First, I describe a multivariate regression model that can be used to ask if some species combinations occur more or less often together than by expected by random. This approach is suited for cases where there are much data on few species. Second, for the opposite case of few data on many species, I describe how statistical inference can be improved by gluing the species-specific models together with a higher-level community model.

Sustainability of agroecosystems: insights from the multiscale insect pest monitoring

Sustainability of agroecosystems: insights from the multiscale insect pest monitoring

Computing Tipping Points in Contagion and Ecology Models

There are three kinds of tipping points (or thresholds) in dynamic models: points that separate one basin of attraction from another in a single system, parameter points at which the parametrized system changes its behavior, and (a simple case of the latter) functions of the parameters which determine whether or not zero is a stable equilibrium (e.g., basic reproduction numbers). We will illustrate a simple procedure for computing such basic reproduction numbers for general contagion models vis Lyapunov functions without computing the eigenvalues of a matrix.

Rate-induced Tipping Points: Critical Rates, Non-obvious Thresholds and Failure to Adapt to Changing External Conditions

Complex systems subject to changing external conditions can undergo unexpected rapid transitions from one stable state to another, a phenomenon known as "tipping". The well established tipping mechanism is a traditional bifurcation, where the stable state disappears or destabilises at some critical level of external conditions. I will describe a different tipping mechanism termed the "rate-induced tipping". Here, the stable state exists continuously for all fixed levels of external conditions and never bifurcates. When external conditions vary in time, the position of the stable state changes and the system tries to keep pace with the changes. However, some systems fail to adapt to the changing stable state and tip if the external conditions are changed too fast.


Scientists often find rate-induced tipping counter-intuitive because there is no obvious loss of stability and no obvious tipping threshold. On the other hand, these non-autonomous instabilities cannot be captured by classical bifurcation theory and remain fairly unexplored. I will present an approach based on geometrical singular perturbation theory to study critical rates of change and non-obvious tipping thresholds. I will also discuss repercussions for climate change policy making which currently focuses on critical levels of the atmospheric temperature whereas the critical factor may be the rate of warming rather than the temperature itself.

Beyond the proof of concept: virtual ecologists in complex dynamic systems

The virtual ecologist is an intuitive and widely used approach which includes simulating artificial species or ecosystem data, an observer that collects data according to a specific sampling protocol, the statistical analysis or modelling of the collected data and subsequent evaluation of the results against known (virtual) truth. In my talk, I will briefly review the concept and existing examples. For example, in global change research this approach holds great potential for rigorous testing of different modelling methods under controlled and changing conditions and with controlled sampling bias. Specifically, I want to emphasize the merit of using complex dynamic simulation models for simulating data and observers. This ingredient takes the virtual ecologist approach beyond simple proof of concept making it a truly integrative and rigorous framework not only for testing sampling protocols or modelling and analysis tools but for theory development and testing more generally.

The ODD protocol: a standard format for describing individual-based and agent-based models
When do we want to develop an individual-based model instead of a more aggregated one?
Ricker models and complexity in ecology
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Ricker models and complexity in ecology
Alan Hastings

Ricker models and complexity in ecology

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When do we want to develop an individual-based model instead of a more aggregated one?
Volker Grimm

When do we want to develop an individual-based model instead of a more aggregated one?

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The ODD protocol: a standard format for describing individual-based and agent-based models
Volker Grimm

The ODD protocol: a standard format for describing individual-based and agent-based models.

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A network-patch modeling framework for the transmission of vector-borne infections
James Hyman

We have developed a network-patch model for the spread of mosquito-borne pathogens, including chikungunya, dengue, and West Nile virus. The model accounts for the movement of individual people through mosquito habitats that respond to enviro

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Sustainability of agroecosystems: insights from the multiscale insect pest monitoring
Sergei Petrovskii

Sustainability of agroecosystems: insights from the multiscale insect pest monitoring

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Individual-based Ecology: Theories, Predictions, Simplifications
Volker Grimm

Individual-based Ecology: Theories, Predictions, Simplifications

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No Equations, No Variables: An approach to complex/multiscale systems Modeling and Computation
Yannis Kevrekidis

In current modeling practice for complex systems, including agent-based and network-based simulations, the best available descriptions of a system often come at a fine level (atomistic, stochastic, individual-based) while the questions asked

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Role of time scales in sustainability of complex systems
Alan Hastings

Role of time scales in sustainability of complex systems

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Beyond the proof of concept: virtual ecologists in complex dynamic systems
Damaris Zurell

The virtual ecologist is an intuitive and widely used approach which includes simulating artificial species or ecosystem data, an observer that collects data according to a specific sampling protocol, the statistical analysis or modelling of

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Aquaculture and Sustainability of Coastal Ecosystem
Mark Lewis

Aquaculture and Sustainability of Coastal Ecosystem