George A. K. van Voorn

Which Sensitivity Analysis Method Should I Use for My Agent-Based Model?

Existing methodologies of sensitivity analysis may be insufficient for a proper analysis of Agent-based Models (ABMs). Most ABMs consist of multiple levels, contain various nonlinear interactions, and display emergent behaviour. This limits the information content that follows from the classical sensitivity analysis methodologies that link model output to model input. In this paper we evaluate the performance of three well-known methodologies for sensitivity analysis. The three methodologies are extended OAT (one-at-a-time), and proportional assigning of output variance by means of model fitting and by means of Sobol’ decomposition. The methodologies are applied to a case study of limited complexity consisting of free-roaming and procreating agents that make harvest decisions with regard to a diffusing renewable resource. We find that each methodology has its own merits and exposes useful information, yet none of them provide a complete picture of model behaviour. We recommend extended OAT as the starting point for sensitivity analysis of an ABM, for its use in uncovering the mechanisms and patterns that the ABM produces.

Food Quality in Producer-Grazer Models: A Generalized Analysis

Stoichiometric constraints play a role in the dynamics of natural populations but are not explicitly considered in most mathematical models. Recent theoretical works suggest that these constraints can have a significant impact and should not be neglected. However, it is not yet resolved how stoichiometry should be integrated in population dynamical models, as different modeling approaches are found to yield qualitatively different results. Here we investigate a unifying framework that reveals the differences and commonalities between previously proposed models for producer‐grazer systems. Our analysis reveals that stoichiometric constraints affect the dynamics mainly by increasing the intraspecific competition between producers and by introducing a variable biomass conversion efficiency. The intraspecific competition has a strongly stabilizing effect on the system, whereas the variable conversion efficiency resulting from a variable food quality is the main determinant for the nature of the instability once destabilization occurs. Only if the food quality is high can an oscillatory instability, as in the classical paradox of enrichment, occur. While the generalized model reveals that the generic insights remain valid in a large class of models, we show that other details such as the specific sequence of bifurcations encountered in enrichment scenarios can depend sensitively on assumptions made in modeling stoichiometric constraints.

Efficient estimation of the robustness region of biological models with oscillatory behavior.

Robustness is an essential feature of biological systems, and any mathematical model that describes such a system should reflect this feature. Especially, persistence of oscillatory behavior is an important issue. A benchmark model for this phenomenon is the Laub-Loomis model, a nonlinear model for cAMP oscillations in Dictyostelium discoideum. This model captures the most important features of biomolecular networks oscillating at constant frequencies. Nevertheless, the robustness of its oscillatory behavior is not yet fully understood. Given a system that exhibits oscillating behavior for some set of parameters, the central question of robustness is how far the parameters may be changed, such that the qualitative behavior does not change. The determination of such a “robustness region” in parameter space is an intricate task. If the number of parameters is high, it may be also time consuming. In the literature, several methods are proposed that partially tackle this problem. For example, some methods only detect particular bifurcations, or only find a relatively small box-shaped estimate for an irregularly shaped robustness region. Here, we present an approach that is much more general, and is especially designed to be efficient for systems with a large number of parameters. As an illustration, we apply the method first to a well understood low-dimensional system, the Rosenzweig-MacArthur model. This is a predator-prey model featuring satiation of the predator. It has only two parameters and its bifurcation diagram is available in the literature. We find a good agreement with the existing knowledge about this model. When we apply the new method to the high dimensional Laub-Loomis model, we obtain a much larger robustness region than reported earlier in the literature. This clearly demonstrates the power of our method. From the results, we conclude that the biological system underlying is much more robust than was realized until now.

The Missing Stakeholder Group: Why Patients Should be Involved in Health Economic Modelling

Evaluations of healthcare interventions, e.g. new drugs or other new treatment strategies, commonly include a cost-effectiveness analysis (CEA) that is based on the application of health economic (HE) models. As end users, patients are important stakeholders regarding the outcomes of CEAs, yet their knowledge of HE model development and application, or their involvement therein, is absent. This paper considers possible benefits and risks of patient involvement in HE model development and application for modellers and patients. An exploratory review of the literature has been performed on stakeholder-involved modelling in various disciplines. In addition, Dutch patient experts have been interviewed about their experience in, and opinion about, the application of HE models. Patients have little to no knowledge of HE models and are seldom involved in HE model development and application. Benefits of becoming involved would include a greater understanding and possible acceptance by patients of HE model application, improved model validation, and a more direct infusion of patient expertise. Risks would include patient bias and increased costs of modelling. Patient involvement in HE modelling seems to carry several benefits as well as risks. We claim that the benefits may outweigh the risks and that patients should become involved.

Resilience through adaptation

Adaptation of agents through learning or evolution is an important component of the resilience of Complex Adaptive Systems (CAS). Without adaptation, the flexibility of such systems to cope with outside pressures would be much lower. To study the capabilities of CAS to adapt, social simulations with agent-based models (ABMs) provide a helpful tool. However, the value of ABMs for studying adaptation depends on the availability of methodologies for sensitivity analysis that can quantify resilience and adaptation in ABMs. In this paper we propose a sensitivity analysis methodology that is based on comparing time-dependent probability density functions of output of ABMs with and without agent adaptation. The differences between the probability density functions are quantified by the so-called earth-mover’s distance. We use this sensitivity analysis methodology to quantify the probability of occurrence of critical transitions and other long-term effects of agent adaptation. To test the potential of this new approach, it is used to analyse the resilience of an ABM of adaptive agents competing for a common-pool resource. Adaptation is shown to contribute positively to the resilience of this ABM. If adaptation proceeds sufficiently fast, it may delay or avert the collapse of this system.