Sensitivity analysis methodologies for analysing emergence using agent-based models

Many human and natural systems are highly complex, because they consist of many interacting parts. Such systems are known as complex adaptive systems (CAS). Understanding CAS is possible only by studying the interactions between constituent parts, rather than focussing only on the properties of the parts in isolation. Often, the possibilities for systematically studying these interactions in real-life systems are limited. Simulation models can then be an important tool for testing what properties may emerge, given various assumptions on the interactions in the system. Agent-based models (ABMs) are particularly useful for studying CAS, because ABMs explicitly model interactions between autonomous agents and their environment. Currently, the utility of ABMs is limited by a lack of available methodologies for analysing their results. The main tool for analysing CAS models is sensitivity analysis. Yet, standard methods of sensitivity analysis are not well-suited to deal with the complexity of ABMs. Thus, there is a need for sensitivity analysis methodologies that are specifically developed for analysing ABMs. The objective of this thesis is to contribute such methodologies. Specifically, we propose methodologies for (1) detecting tipping points, (2) analysing the effects of agent adaptation, and (3) analysing resilience of ABMs. Chapter 2 introduces traditional methods of sensitivity analysis. These methods are demonstrated by applying them to rank the most influential parameters of an ODE model of predator-prey interaction. Furthermore, the role of sensitivity analysis in model validation is discussed. In Chapter 3 we investigate the use of sensitivity analysis for detecting tipping points. Whereas bifurcation analysis methods are available for detecting tipping points in ODE models, these methods are not applicable to ABMs. Therefore, we use an ODE model to verify the results from sensitivity analysis against those of bifurcation analysis. We conclude that one-factor-at-a-time sensitivity analysis (OFAT) is a helpful method for detecting tipping points. However, OFAT is a local method that considers only changes in individual parameters. It is therefore recommended to supplement OFAT with a global method to investigate interaction effects. For this purpose, we recommend all-but-one-at-a-time sensitivity analysis (ABOS) as a graphical sensitivity analysis method that takes into account parameter interactions and can help with the detection of tipping points. In Chapter 4 we introduce a basic ABM model of agents competing in a spatial environment for a renewable resource. This basic model will be extended in the subsequent chapters, and will serve as a testing case for various sensitivity analysis methods. In Chapter 4, it is used to assess the utility of existing sensitivity analysis methods for ABMs. The results show that traditional methods of sensitivity are not sufficient to analyse the ABM, due to the presence of tipping points and other strong non-linearities in the model output. In contrast, OFAT is found to be helpful for detecting tipping points, as was suggested in Chapter 3. Based on these outcomes, OFAT is recommended as a starting point for sensitivity analysis of ABMs, preferably supplemented by a global method to investigate interaction effects. In Chapter 5 we extend the ABM of Chapter 4 by adding agent adaptation in the form of a mechanism of natural selection. On short time-scales, the model behaviour appears to be similar to the non-adaptive model version. On longer time-scales, the agent adaptation causes the state of the model to gradually change as agents continue to adapt to their surroundings. We propose a sensitivity analysis method to measure the effects of this adaptation. This method is based on a quantification of the difference between probability density functions of model version with and without adaptation. Using this method, we show that this adaptation increases the resilience of the system by giving it the flexibility needed to respond to pressures. In Chapter 6 we further extend the test-case by giving agents the option to harvest either cooperatively or individually. Cooperation increases the potential yields, but introduces the risk of defection of the interaction partner. It is shown that ecological factors, which are usually not considered in models on cooperation, strongly affect the level of cooperation in the system. For example, low levels of cooperation lead to a decreased population size, and causes the formation of small groups of agents with a higher level of cooperation. As a result, cooperation persists even without any mechanisms to promote it. Nevertheless, the inclusion of such mechanisms in the form of indirect reciprocity does further increase the level of cooperation. Furthermore, we show that the resulting high levels of cooperation, depending on the circumstances, can increase the resilience of the agent population against shocks. To conclude, in this thesis several methodologies have been proposed to help with ABM analysis. Specifically, OFAT and ABOS are recommended for detecting tipping points in ABMs, and in Chapter 5 a protocol is introduced for quantifying the effects of adaptation. By suggesting these methodologies, this thesis aims to contribute to the utility of ABMs, especially for studying CAS.