A conceptual framework for the dynamic modeling of time-resolved phenotypes for sets of genotype-environment-management combinations: a model library.

Introduction: Dynamic crop growth models are an important tool to predict complex traits, like crop yield, for modern and future genotypes in their current and evolving environments, as those occurring under climate change. Phenotypic traits are the result of interactions between genetic, environmental, and management factors, and dynamic models are designed to generate the interactions producing phenotypic changes over the growing season. Crop phenotype data are becoming increasingly available at various levels of granularity, both spatially (landscape) and temporally (longitudinal, time-series) from proximal and remote sensing technologies. Methods: Here we propose four phenomenological process models of limited complexity based on differential equations for a coarse description of focal crop traits and environmental conditions during the growing season. Each of these models defines interactions between environmental drivers and crop growth (logistic growth, with implicit growth restriction, or explicit restriction by irradiance, temperature, or water availability) as a minimal set of constraints without resorting to strongly mechanistic interpretations of the parameters. Differences between individual genotypes are conceptualized as differences in crop growth parameter values. Results: We demonstrate the utility of such low-complexity models with few parameters by fitting them to longitudinal datasets from the simulation platform APSIM-Wheat involving in silico biomass development of 199 genotypes and data of environmental variables over the course of the growing season at four Australian locations over 31 years. While each of the four models fits well to particular combinations of genotype and trial, none of them provides the best fit across the full set of genotypes by trials because different environmental drivers will limit crop growth in different trials and genotypes in any specific trial will not necessarily experience the same environmental limitation. Discussion: A combination of low-complexity phenomenological models covering a small set of major limiting environmental factors may be a useful forecasting tool for crop growth under genotypic and environmental variation.

Four Aspects Affecting Health Economic Decision Models and Their Validation.

Health care decision makers in many jurisdictions use cost-effectiveness analysis based on health economic decision models for policy decisions regarding coverage and price negotiation for medicines and medical devices. While validation of health economic decision models has always been considered important, many reviews of model-based cost-effectiveness studies report limitations regarding their validation. The current opinion paper discusses four aspects of current health economic decision modeling with relevance for future directions in model validation: increased use of complex models, international cooperation, open-source modeling, and stakeholder involvement. First, new, more complex clinical study designs and treatment strategies may require relatively complex model structures and/or input data analyses. Simultaneously, more widespread technical knowledge along with wider data availability have led to a broader range of model types. This puts extra requirements on model validation and transparency. Second, increased international cooperation of policy makers and, in particular, health technology assessment (HTA) authorities in performing model assessments is discussed in relation to the repeated use of health economic models (multi-use disease models). We argue such coordinated efforts may benefit model validity. Third, open-source modeling is discussed as one possible answer to increased transparency requirements. Finally, involvement of all relevant stakeholders throughout the whole decision process is an ongoing development that necessarily also includes health economic modeling. We argue this implies that model validity should be considered in a broader perspective, with more focus on conceptual modeling, model transparency, accuracy requirements, and choice of relevant model outcomes than previously.

Emerging forest-peatland bistability and resilience of European peatland carbon stores.

Northern peatlands store large amounts of carbon. Observations indicate that forests and peatlands in northern biomes can be alternative stable states for a range of landscape settings. Climatic and hydrological changes may reduce the resilience of peatlands and forests, induce persistent shifts between these states, and release the carbon stored in peatlands. Here, we present a dynamic simulation model constrained and validated by a wide set of observations to quantify how feedbacks in water and carbon cycling control resilience of both peatlands and forests in northern landscapes. Our results show that 34% of Europe (area) has a climate that can currently sustain existing rainwater-fed peatlands (raised bogs). However, raised bog initiation and restoration by water conservation measures after the original peat soil has disappeared is only possible in 10% of Europe where the climate allows raised bogs to initiate and outcompete forests. Moreover, in another 10% of Europe, existing raised bogs (concerning ∼20% of the European raised bogs) are already affected by ongoing climate change. Here, forests may overgrow peatlands, which could potentially release in the order of 4% (∼24 Pg carbon) of the European soil organic carbon pool. Our study demonstrates quantitatively that preserving and restoring peatlands requires looking beyond peatland-specific processes and taking into account wider landscape-scale feedbacks with forest ecosystems.

An agent based model representation to assess resilience and efficiency of food supply chains.

Trying to meet the Sustainable Development Goals is challenging. Food supply chains may have to become more efficient to meet the increasing food requirement of 10 Billion people by 2050. At the same time, food and nutrition security are at risk from increasingly likely shocks like extreme climate events, market shocks, pandemics, changing consumer preferences, and price volatility. Here we consider some possibilities and limitations regarding the improvement of resilience (the capacity to deal with shocks) and efficiency (here interpreted as the share of produced food delivered to consumers) of food supply chains. We employ an Agent Based Model of a generic food chain network consisting of stylized individuals representing producers, traders, and consumers. We do this: 1/ to describe the dynamically changing disaggregated flows of crop items between these agents, and 2/ to be able to explicitly consider agent behaviour. The agents have implicit personal objectives for trading. We quantify resilience and efficiency by linking these to the fraction of fulfilment of the overall explicit objective to have all consumers meet their food requirement. We consider different types of network structures in combination with different agent interaction types under different types of stylized shocks. We find that generally the network structures with higher efficiency are also more sensitive to shocks, while less efficient network types display more resilience. At first glance these results seem to confirm the existence of a system-level trade-off between resilience and efficiency similar to what is reported in business management and ecology literature. However, the results are modified by the trading interactions and the type of shock. In our simulations resilience and efficiency are affected by 'soft' boundaries caused by the preference and trust of agents (i.e., social aspects) in trading. The ability of agents to switch between trading partners represents an important aspect of resilience, namely a capacity to reorganize. These insights may be relevant when considering the reorganization of real-life food chains to increase their resilience to meet future food and nutrition security goals.

Spatial early warning signals for impending regime shifts: A practical framework for application in real-world landscapes.

Prediction of ecosystem response to global environmental change is a pressing scientific challenge of major societal relevance. Many ecosystems display nonlinear responses to environmental change, and may even undergo practically irreversible 'regime shifts' that initiate ecosystem collapse. Recently, early warning signals based on spatiotemporal metrics have been proposed for the identification of impending regime shifts. The rapidly increasing availability of remotely sensed data provides excellent opportunities to apply such model-based spatial early warning signals in the real world, to assess ecosystem resilience and identify impending regime shifts induced by global change. Such information would allow land-managers and policy makers to interfere and avoid catastrophic shifts, but also to induce regime shifts that move ecosystems to a desired state. Here, we show that the application of spatial early warning signals in real-world landscapes presents unique and unexpected challenges, and may result in misleading conclusions when employed without careful consideration of the spatial data and processes at hand. We identify key practical and theoretical issues and provide guidelines for applying spatial early warning signals in heterogeneous, real-world landscapes based on literature review and examples from real-world data. Major identified issues include (1) spatial heterogeneity in real-world landscapes may enhance reversibility of regime shifts and boost landscape-level resilience to environmental change (2) ecosystem states are often difficult to define, while these definitions have great impact on spatial early warning signals and (3) spatial environmental variability and socio-economic factors may affect spatial patterns, spatial early warning signals and associated regime shift predictions. We propose a novel framework, shifting from an ecosystem perspective towards a landscape approach. The framework can be used to identify conditions under which resilience assessment with spatial remotely sensed data may be successful, to support well-informed application of spatial early warning signals, and to improve predictions of ecosystem responses to global environmental change.

A New Statistical Method to Determine the Degree of Validity of Health Economic Model Outcomes against Empirical Data.

BACKGROUND: The validation of health economic (HE) model outcomes against empirical data is of key importance. Although statistical testing seems applicable, guidelines for the validation of HE models lack guidance on statistical validation, and actual validation efforts often present subjective judgment of graphs and point estimates. OBJECTIVES: To discuss the applicability of existing validation techniques and to present a new method for quantifying the degrees of validity statistically, which is useful for decision makers. METHODS: A new Bayesian method is proposed to determine how well HE model outcomes compare with empirical data. Validity is based on a pre-established accuracy interval in which the model outcomes should fall. The method uses the outcomes of a probabilistic sensitivity analysis and results in a posterior distribution around the probability that HE model outcomes can be regarded as valid. RESULTS: We use a published diabetes model (Modelling Integrated Care for Diabetes based on Observational data) to validate the outcome "number of patients who are on dialysis or with end-stage renal disease." Results indicate that a high probability of a valid outcome is associated with relatively wide accuracy intervals. In particular, 25% deviation from the observed outcome implied approximately 60% expected validity. CONCLUSIONS: Current practice in HE model validation can be improved by using an alternative method based on assessing whether the model outcomes fit to empirical data at a predefined level of accuracy. This method has the advantage of assessing both model bias and parameter uncertainty and resulting in a quantitative measure of the degree of validity that penalizes models predicting the mean of an outcome correctly but with overly wide credible intervals.

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.

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.

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.

Ecological consequences of global bifurcations in some food chain models.

Food chain models of ordinary differential equations (ode's) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the changes in long-term (asymptotic) behaviour under parameter variation. For the detection of local bifurcations there exists standardised software, but until quite recently most software did not include any capabilities for the detection and continuation of global bifurcations. We focus here on the occurrence of global bifurcations in four food chain models, and discuss the implications of their occurrence. In two stoichiometric models (one piecewise continuous, one smooth) there exists a homoclinic bifurcation, that results in the disappearance of a limit cycle attractor. Instead, a stable positive equilibrium becomes the global attractor. The models are also capable of bistability. In two three-dimensional models a Shil'nikov homoclinic bifurcation functions as the organising centre of chaos, while tangencies of homoclinic cycle-to-cycle connections 'cut' the chaotic attractors, which is associated with boundary crises. In one model this leads to extinction of the top predator, while in the other model hysteresis occurs. The types of ecological events occurring because of a global bifurcation will be categorized. Global bifurcations are always catastrophic, leading to the disappearance or merging of attractors. However, there is no 1-on-1 coupling between global bifurcation type and the possible ecological consequences. This only emphasizes the importance of including global bifurcations in the analysis of food chain models.

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.

Exploring the impact of target cell heterogeneity on HIV loads in a within-host model.

HIV can be transmitted from blood plasma or semen of an infected male. Viral loads in blood plasma are routinely measured, but the same is not true of semen. Even before drug treatment, viral loads have been shown to be different in the two body compartments (blood and genital tract), and this heterogeneity may be exacerbated by treatments using those antiretroviral drugs which have different efficacies in the two compartments. In addition to this heterogeneity, and despite highly effective drugs (in the blood) low-level viral replication is commonly reported for HIV patients as are differences in drug resistant mutation patterns in the two compartments. In this paper we investigate the effect of target cell heterogeneity between compartments on HIV viral loads using a within-host model that includes wildtype and drug resistant strains of HIV. We find that modelling target cell heterogeneity in the blood and male genital tract gives different viral loads in the two compartments prior to treatment and allows low-level viral loads to persist during therapy even if drug penetration is good. The model also allows coexistence of the two viral strains (in the absence of a mutation mechanism) with different dominance patterns in each body compartment. Our results suggest that monitoring of blood plasma viral strains may not give an accurate picture of the strains of HIV being transmitted between individuals and that continued research into the nature of HIV target cells in the male genital tract would be beneficial.

Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect.

Species establishment in a model system in a homogeneous environment can be dependent not only on the parameter setting, but also on the initial conditions of the system. For instance, predator invasion into an established prey population can fail and lead to system collapse, an event referred to as overexploitation. This phenomenon occurs in models with bistability properties, such as strong Allee effects. The Allee effect then prevents easy re-establishment of the prey species. In this paper, we deal with the bifurcation analyses of two previously published predator-prey models with strong Allee effects. We expand the analyses to include not only local, but also global bifurcations. We show the existence of a point-to-point heteroclinic cycle in these models, and discuss numerical techniques for continuation in parameter space. The continuation of such a cycle in two-parameter space forms the boundary of a region in parameter space where the system collapses after predator invasion, i.e. where overexploitation occurs. We argue that the detection and continuation of global bifurcations in these models are of vital importance for the understanding of the model dynamics.