Exploring resilience with agent-based models: State of the art,knowledge gaps and recommendations for coping with multidimensionality

Anthropogenic pressures increasingly alter natural systems. Therefore, understanding the resilience of agent-based complex systems such as ecosystems, i.e. their ability to absorb these pressures and sustain their functioning and services, is a major challenge. However, the mechanisms underlying resilience are still poorly understood. A main reason for this is the multidimensionality of both resilience, embracing the three fundamental stability properties recovery, resistance and persistence, and of the specific situations for which stability properties can be assessed. Agent-based models (ABM) complement empirical research which is, for logistic reasons, limited in coping with these multiple dimensions. Besides their ability to integrate multidimensionality through extensive manipulation in a fully controlled system, ABMs can capture the emergence of system resilience from individual interactions and feedbacks across different levels of organization. To assess the extent to which this potential of ABMs has already been exploited, we reviewed the state of the art in exploring resilience and its multidimensionality in ecological and socio-ecological systems with ABMs. We found that the potential of ABMs is not utilized in most models, as they typically focus on a single dimension of resilience by using variability as a proxy for persistence, and are limited to one reference state, disturbance type and scale. Moreover, only few studies explicitly test the ability of different mechanisms to support resilience. To overcome these limitations, we recommend to simultaneously assess multiple stability properties for different situations and under consideration of the mechanisms that are hypothesised to render a system resilient. This will help us to better exploit the potential of ABMs to understand and quantify resilience mechanisms, and hence support solving real-world problems related to the resilience of agent-based complex systems.     

Sensitivity Analysis of an ENteric Immunity SImulator (ENISI)-Based Model of Immune Responses to Helicobacter pylori Infection

Agent-based models (ABM) are widely used to study immune systems, providing a procedural and interactive view of the underlying system. The interaction of components and the behavior of individual objects is described procedurally as a function of the internal states and the local interactions, which are often stochastic in nature. Such models typically have complex structures and consist of a large number of modeling parameters. Determining the key modeling parameters which govern the outcomes of the system is very challenging. Sensitivity analysis plays a vital role in quantifying the impact of modeling parameters in massively interacting systems, including large complex ABM. The high computational cost of executing simulations impedes running experiments with exhaustive parameter settings. Existing techniques of analyzing such a complex system typically focus on local sensitivity analysis, i.e. one parameter at a time, or a close “neighborhood” of particular parameter settings. However, such methods are not adequate to measure the uncertainty and sensitivity of parameters accurately because they overlook the global impacts of parameters on the system. In this article, we develop novel experimental design and analysis techniques to perform both global and local sensitivity analysis of large-scale ABMs. The proposed method can efficiently identify the most significant parameters and quantify their contributions to outcomes of the system. We demonstrate the proposed methodology for ENteric Immune SImulator (ENISI), a large-scale ABM environment, using a computational model of immune responses to Helicobacter pylori colonization of the gastric mucosa.     

Using Uncertainty and Sensitivity Analyses in Socioecological Agent-Based Models to Improve Their Analytical Performance and Policy Relevance

Agent-based models (ABMs) have been widely used to study socioecological systems. They are useful for studying such systems because of their ability to incorporate micro-level behaviors among interacting agents, and to understand emergent phenomena due to these interactions. However, ABMs are inherently stochastic and require proper handling of uncertainty. We propose a simulation framework based on quantitative uncertainty and sensitivity analyses to build parsimonious ABMs that serve two purposes: exploration of the outcome space to simulate low-probability but high-consequence events that may have significant policy implications, and explanation of model behavior to describe the system with higher accuracy. The proposed framework is applied to the problem of modeling farmland conservation resulting in land use change. We employ output variance decomposition based on quasi-random sampling of the input space and perform three computational experiments. First, we perform uncertainty analysis to improve model legitimacy, where the distribution of results informs us about the expected value that can be validated against independent data, and provides information on the variance around this mean as well as the extreme results. In our last two computational experiments, we employ sensitivity analysis to produce two simpler versions of the ABM. First, input space is reduced only to inputs that produced the variance of the initial ABM, resulting in a model with output distribution similar to the initial model. Second, we refine the value of the most influential input, producing a model that maintains the mean of the output of initial ABM but with less spread. These simplifications can be used to 1) efficiently explore model outcomes, including outliers that may be important considerations in the design of robust policies, and 2) conduct explanatory analysis that exposes the smallest number of inputs influencing the steady state of the modeled system.     

Testing,tracing and isolation in compartmental models

Existing compartmental mathematical modelling methods for epidemics, such as SEIR models, cannot accurately represent effects of contact tracing. This makes them inappropriate for evaluating testing and contact tracing strategies to contain an outbreak. An alternative used in practice is the application of agent- or individual-based models (ABM). However ABMs are complex, less well-understood and much more computationally expensive. This paper presents a new method for accurately including the effects of Testing, contact-Tracing and Isolation (TTI) strategies in standard compartmental models. We derive our method using a careful probabilistic argument to show how contact tracing at the individual level is reflected in aggregate on the population level. We show that the resultant SEIR-TTI model accurately approximates the behaviour of a mechanistic agent-based model at far less computational cost. The computational efficiency is such that it can be easily and cheaply used for exploratory modelling to quantify the required levels of testing and tracing, alone and with other interventions, to assist adaptive planning for managing disease outbreaks.     

基于智能体模型的土地利用动态模拟研究进展

土地利用动态变化是全球变化和可持续发展研究的基础,对区域水循环、大气循环、环境质量、气候变化及陆地生态系统生产力等具有重要影响,也是造成生物多样性衰减的最主要原因.目前,建立于复杂性科学基础上的的智能体模型(ABM)成为土地利用动态模拟的重要方法.智能体模型能模拟个体或群体的行为及决策模式,从而能将政府、城市规划、房地产开发商、住户等社会群体及个人对土地利用产生的影响进行模拟,同时能对不同社会经济政策对土地动态影响进行模拟.智能体模型在元胞自动机基础上,加入了人为因素的智能体概念,从而能更好地模拟土地动态.在分析总结了智能体模型的相关概念和组织结构,并分析了其在土地利用动态、城市动态模拟及生态过程模拟等方面的应用与元胞自动机的关系,比较了常用的智能体模型的主要软件,最后概括了智能体模型优点、发展趋势及存在的主要问题.     

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques

ABSTRACT: BACKGROUND: Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations. This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. RESULTS: Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. CONCLUSIONS: In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.     

A patient-specific in silico model of inflammation and healing tested in acute vocal fold injury

The development of personalized medicine is a primary objective of the medical community and increasingly also of funding and registration agencies. Modeling is generally perceived as a key enabling tool to target this goal. Agent-Based Models (ABMs) have previously been used to simulate inflammation at various scales up to the whole-organism level. We extended this approach to the case of a novel, patient-specific ABM that we generated for vocal fold inflammation, with the ultimate goal of identifying individually optimized treatments. ABM simulations reproduced trajectories of inflammatory mediators in laryngeal secretions of individuals subjected to experimental phonotrauma up to 4 hrs post-injury, and predicted the levels of inflammatory mediators 24 hrs post-injury. Subject-specific simulations also predicted different outcomes from behavioral treatment regimens to which subjects had not been exposed. We propose that this translational application of computational modeling could be used to design patient-specific therapies for the larynx, and will serve as a paradigm for future extension to other clinical domains.     

A network-patch methodology for adapting agent-based models for directly transmitted disease to mosquito-borne disease

Mosquito-borne diseases cause significant public health burden and are widely re-emerging or emerging. Understanding, predicting, and mitigating the spread of mosquito-borne disease in diverse populations and geographies are ongoing modelling challenges. We propose a hybrid network-patch model for the spread of mosquito-borne pathogens that accounts for individual movement through mosquito habitats, extending the capabilities of existing agent-based models (ABMs) to include vector-borne diseases. The ABM are coupled with differential equations representing ‘clouds’ of mosquitoes in patches accounting for mosquito ecology. We adapted an ABM for humans using this method and investigated the importance of heterogeneity in pathogen spread, motivating the utility of models of individual behaviour. We observed that the final epidemic size is greater in patch models with a high risk patch frequently visited than in a homogeneous model. Our hybrid model quantifies the importance of the heterogeneity in the spread of mosquito-borne pathogens, guiding mitigation strategies.     

From theory to practice in pattern-oriented modelling: identifying and using empirical patterns in predictive models

To robustly predict the effects of disturbance and ecosystem changes on species, it is necessary to produce structurally realistic models with high predictive power and flexibility. To ensure that these models reflect the natural conditions necessary for reliable prediction, models must be informed and tested using relevant empirical observations. Pattern-oriented modelling (POM) offers a systematic framework for employing empirical patterns throughout the modelling process and has been coupled with complex systems modelling, such as in agent-based models (ABMs). However, while the production of ABMs has been rising rapidly, the explicit use of POM has not increased. Challenges with identifying patterns and an absence of specific guidelines on how to implement empirical observations may limit the accessibility of POM and lead to the production of models which lack a systematic consideration of reality. This review serves to provide guidance on how to identify and apply patterns following a POM approach in ABMs (POM-ABMs), specifically addressing: where in the ecological hierarchy can we find patterns; what kinds of patterns are useful; how should simulations and observations be compared; and when in the modelling cycle are patterns used? The guidance and examples provided herein are intended to encourage the application of POM and inspire efficient identification and implementation of patterns for both new and experienced modellers alike. Additionally, by generalising patterns found especially useful for POM-ABM development, these guidelines provide practical help for the identification of data gaps and guide the collection of observations useful for the development and verification of predictive models. Improving the accessibility and explicitness of POM could facilitate the production of robust and structurally realistic models in the ecological community, contributing to the advancement of predictive ecology at large.     

Introduction of an agent-based multi-scale modular architecture for dynamic knowledge representation of acute inflammation

Background  

One of the greatest challenges facing biomedical research is the integration and sharing of vast amounts of information, not only for individual researchers, but also for the community at large. Agent Based Modeling (ABM) can provide a means of addressing this challenge via a unifying translational architecture for dynamic knowledge representation. This paper presents a series of linked ABMs representing multiple levels of biological organization. They are intended to translate the knowledge derived from in vitro models of acute inflammation to clinically relevant phenomenon such as multiple organ failure.     

Optimizing agent-based transmission models for infectious diseases

Background

Infectious disease modeling and computational power have evolved such that large-scale agent-based models (ABMs) have become feasible. However, the increasing hardware complexity requires adapted software designs to achieve the full potential of current high-performance workstations.

Results

We have found large performance differences with a discrete-time ABM for close-contact disease transmission due to data locality. Sorting the population according to the social contact clusters reduced simulation time by a factor of two. Data locality and model performance can also be improved by storing person attributes separately instead of using person objects. Next, decreasing the number of operations by sorting people by health status before processing disease transmission has also a large impact on model performance. Depending of the clinical attack rate, target population and computer hardware, the introduction of the sort phase decreased the run time from 26 % up to more than 70 %. We have investigated the application of parallel programming techniques and found that the speedup is significant but it drops quickly with the number of cores. We observed that the effect of scheduling and workload chunk size is model specific and can make a large difference.

Conclusions

Investment in performance optimization of ABM simulator code can lead to significant run time reductions. The key steps are straightforward: the data structure for the population and sorting people on health status before effecting disease propagation. We believe these conclusions to be valid for a wide range of infectious disease ABMs. We recommend that future studies evaluate the impact of data management, algorithmic procedures and parallelization on model performance.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0612-2) contains supplementary material, which is available to authorized users.     

Parameter inference for an individual based model of chytridiomycosis in frogs

Individual based models (IBMs) and Agent based models (ABMs) have become widely used tools to understand complex biological systems. However, general methods of parameter inference for IBMs are not available. In this paper we show that it is possible to address this problem with a traditional likelihood-based approach, using an example of an IBM developed to describe the spread of chytridiomycosis in a population of frogs as a case study. We show that if the IBM satisfies certain criteria we can find the likelihood (or posterior) analytically, and use standard computational techniques, such as MCMC, for parameter inference.     

Bayesian calibration of a stochastic,multiscale agent-based model for predicting in vitro tumor growth

Hybrid multiscale agent-based models (ABMs) are unique in their ability to simulate individual cell interactions and microenvironmental dynamics. Unfortunately, the high computational cost of modeling individual cells, the inherent stochasticity of cell dynamics, and numerous model parameters are fundamental limitations of applying such models to predict tumor dynamics. To overcome these challenges, we have developed a coarse-grained two-scale ABM (cgABM) with a reduced parameter space that allows for an accurate and efficient calibration using a set of time-resolved microscopy measurements of cancer cells grown with different initial conditions. The multiscale model consists of a reaction-diffusion type model capturing the spatio-temporal evolution of glucose and growth factors in the tumor microenvironment (at tissue scale), coupled with a lattice-free ABM to simulate individual cell dynamics (at cellular scale). The experimental data consists of BT474 human breast carcinoma cells initialized with different glucose concentrations and tumor cell confluences. The confluence of live and dead cells was measured every three hours over four days. Given this model, we perform a time-dependent global sensitivity analysis to identify the relative importance of the model parameters. The subsequent cgABM is calibrated within a Bayesian framework to the experimental data to estimate model parameters, which are then used to predict the temporal evolution of the living and dead cell populations. To this end, a moment-based Bayesian inference is proposed to account for the stochasticity of the cgABM while quantifying uncertainties due to limited temporal observational data. The cgABM reduces the computational time of ABM simulations by 93% to 97% while staying within a 3% difference in prediction compared to ABM. Additionally, the cgABM can reliably predict the temporal evolution of breast cancer cells observed by the microscopy data with an average error and standard deviation for live and dead cells being 7.61±2.01 and 5.78±1.13, respectively.     

A hybrid multi-compartment model of granuloma formation and T cell priming in tuberculosis

Tuberculosis is a worldwide health problem with 2 billion people infected with Mycobacterium tuberculosis (Mtb, the bacteria causing TB). The hallmark of infection is the emergence of organized structures of immune cells forming primarily in the lung in response to infection. Granulomas physically contain and immunologically restrain bacteria that cannot be cleared. We have developed several models that spatially characterize the dynamics of the host-mycobacterial interaction, and identified mechanisms that control granuloma formation and development. In particular, we published several agent-based models (ABMs) of granuloma formation in TB that include many subtypes of T cell populations, macrophages as well as key cytokine and chemokine effector molecules. These ABM studies emphasize the important role of T-cell related mechanisms in infection progression, such as magnitude and timing of T cell recruitment, and macrophage activation. In these models, the priming and recruitment of T cells from the lung draining lymph node (LN) was captured phenomenologically. In addition to these ABM studies, we have also developed several multi-organ models using ODEs to examine trafficking of cells between, for example, the lung and LN. While we can predict temporal dynamic behaviors, those models are not coupled to the spatial aspects of granuloma. To this end, we have developed a multi-organ model that is hybrid: an ABM for the lung compartment and a non-linear system of ODE representing the lymph node compartment. This hybrid multi-organ approach to study TB granuloma formation in the lung and immune priming in the LN allows us to dissect protective mechanisms that cannot be achieved using the single compartment or multi-compartment ODE system. The main finding of this work is that trafficking of important cells known as antigen presenting cells from the lung to the lymph node is a key control mechanism for protective immunity: the entire spectrum of infection outcomes can be regulated by key immune cell migration rates. Our hybrid multi-organ implementation suggests that effector CD4+ T cells can rescue the system from a persistent infection and lead to clearance once a granuloma is fully formed. This could be effective as an immunotherapy strategy for latently infected individuals.     

Agent-based models to investigate sound impact on marine animals: bridging the gap between effects on individual behaviour and population level consequences

Marine ambient sound levels have risen due to noisy human activities, such as shipping, fishing, seismic surveys and piling for windfarms. Marine mammals and fishes are two prominent taxonomic groups that are exposed to this noise pollution, which may experience detrimental effects at the population level. Acoustic effects on individual behaviour such as deterrence, disturbance, distraction and masking of biologically relevant sounds, can be translated energetically to changes in vital rates (growth, maturation, reproduction and survival) in a population consequences of acoustic disturbance (PCAD) approach. However, we typically neglect spatial variation in species distributions and noise pollution, while abiotic factors like temperature, bathymetry and currents, as well as habitat quality in terms of feeding or hiding opportunities, will also have a geographically variable impact on potential consequences. We here address the conceptual integration of agent based models (ABM) into the PCAD framework, as a suitable theoretical tool with high potential for the exploration of these spatial factors and their modifying role in noise impact assessment studies. We review five ABM case studies, including investigations into: 1) effects of movement strategy on the impact of explosions in harbour porpoise; 2) effects of disturbance sensitivity on pile driving impact on migrating cod; 3) impact of seismic survey sounds on Atlantic mackerel distribution and movement; 4) population-level impact of mitigation of harbour porpoise bycatch with pingers; and 5) population effects of alternative windfarm construction scenarios in harbour porpoise. We discuss similarities and differences among these studies in sound and species mapping approaches and we evaluate model realism and pattern validation. We believe that ABMs are a valuable tool for integrating spatial information into ecological impact studies that investigate acoustic disturbance, for any type of sound source, and for both marine mammals and fish.     

基于智能体模型的青岛市林地生态格局评价与优化

设计并在GIS平台上开发了基于智能体的生态格局评价模型,以青岛市及周边地区林地为研究对象,分析不同林地空间格局及生态网络保护框架对于物种生存与扩散的影响.结果表明,与现状相比,不同等级的生态网络框架对物种种群数量与物种迁移都有明显提升,且等级越高的生态网络框架提升作用越明显.然而仅仅依靠生态网络框架不足以使研究区域林地系统形成功能上的相互连通,因此,在分析研究区域现状土地利用格局基础上,提出与湿地系统结合,在胶州湾周围及大沽河干流地区增加林地的空间布局.通过模型模拟分析,发现优化后的林地空间格局结合生态网络框架能有效提升林地之间的物种扩散.基于模拟结果,为研究区林地生态格局构建提出如下建议:(1)保证现有的规模较大的林地不被破坏;(2)青岛市中部湿地系统可以作为新增林地的理想区域;(3)生态网络框架可作为青岛市建立城市组团间生态间隔的空间参考.     

An immune response directed to proteinase and adhesin functional epitopes protects against Porphyromonas gingivalis-induced periodontal bone loss

Porphyromonas gingivalis, a pathogen associated with periodontitis, bound to fibrinogen, fibronectin, hemoglobin, and collagen type V with a similar profile to that of its major virulence factor, the cell surface RgpA-Kgp proteinase-adhesin complex. Using peptide-specific, purified Abs in competitive inhibition ELISAs and epitope mapping assays, we have identified potential adhesin binding motifs (ABMs) of the RgpA-Kgp complex responsible for binding to host proteins. The RgpA-Kgp complex and synthetic ABM and proteinase active site peptides conjugated to diphtheria toxoid, when used as vaccines, protected against P. gingivalis-induced periodontal bone loss in the murine periodontitis model. The most efficacious peptide and protein vaccines were found to induce a high-titer IgG1 Ab response. Furthermore, mice protected in the lesion and periodontitis models had a predominant P. gingivalis-specific IL-4 response, whereas mice with disease had a predominant IFN-gamma response. The peptide-specific Abs directed to the ABM2 sequence (EGLATATTFEEDGVA) protected against periodontal bone loss and inhibited binding of the RgpA-Kgp complex to fibrinogen, fibronectin, and collagen type V. Furthermore, the peptide-specific Abs directed to the ABM3 sequence (GTPNPNPNPNPNPNPGT) protected against periodontal bone loss and inhibited binding to hemoglobin. However, the most protective Abs were those directed to the active sites of the RgpA and Kgp proteinases. The results suggest that when the RgpA-Kgp complex, or functional binding motif or active site peptides are used as a vaccine, they induce a Th2 response that blocks function of the RgpA-Kgp complex and protects against periodontal bone loss.     

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks

Background

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging.

Results

To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions.

Conclusions

The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-256) contains supplementary material, which is available to authorized users.     

Dimension reduction of multivariate outputs of socio-environmental agent-based models

Often, socio-environmental agent-based models (ABMs) are driven by a host of parameters, and their outputs are similarly multidimensional or vastly high-dimensional. While this complex data and its inter-relationships may be rendered tractable, the task is far from trivial. In this paper, we study the multidimensional outcome space of the socio-environmental, land-use RHEA ABM (Risks and Hedonics in an Empirical Agent-based Land Market), specifically the inter-distances among the outcome measures, and their reducibility using several well-known dimension reduction techniques, variants of multidimensional scalings. In testing the efficacy of several reduction algorithms, we temporally characterize the model’s reducibility while exposing changes in behavior across a wide parameter space that can signal sudden or gradual shifts and possible critical transitions. Our findings reveal that the ABM’s signature reducibility trends exhibit idiosyncrasies and unexpected non-linearity as well as discontinuities. These non-linearities and discontinuities are indicative of both gradual and sudden shifts, signaling potential propensity to internal perturbations induced by parameter settings. Additionally, we related the outcome space via their inter-distances to the multidimensional input parameter space, effectively assessing outcome “reducibility to model controls”. This analysis reveals that the model’s sensitivity to parameters is not only temporally dependent, but also can be partitioned by them, some of which suppress variability in this reduction to model controls, raising questions regarding the extent and structure of endogeneity that yields the distinct temporal trends in the relationship between inputs and outputs and their connections to outcome reducibility.