Mathematical models of social-ecological systems: Coupling human behavioural and environmental dynamics

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Title: Mathematical models of social-ecological systems: Coupling human behavioural and environmental dynamics
Authors: Sun, Tithnara Anthony
ORCID of the author: https://orcid.org/0000-0002-5277-7861
Thesis advisor: Prof. Dr. Frank Hilker
Thesis referee: Prof. Dr. Karin Frank
Prof. Dr. Yoh Iwasa
Abstract: There is an increasing concern for the impact of humans on the environment. Traditionally, ecological models consider human influence as a constant or linearly varying parameter, whereas socioeconomic models and frameworks tend to oversimplify the ecological system. But tackling complex environmental challenges faced by our societies requires interdisciplinary approaches due to the intricate feedbacks between the socioeconomic and ecological systems involved. Thus, models of social-ecological systems couple an ecological system with a socioeconomic system to investigate their interaction in the integrated dynamical system. We define this coupling formally and apply the social-ecological approach to three ecological cases. Indeed, we focus on eutrophication in shallow freshwater lakes, which is a well-known system showing bistability between a clear water state and a turbid polluted state. We also study a model accounting for an aquifer (water stock) and a model accounting for a biotic population exhibiting bistability through an Allee effect. The socioeconomic dynamics is driven by the incentive that agents feel to act in a desirable or undesirable way. This incentive can be represented by a difference in utility, or in payoff, between two strategies that each agent can adopt: agents can cooperate and act in an environment-friendly way, or they can defect and act in an ecologically undesirable way. The agents' motivation includes such factors as the economic cost of their choice, the concern they feel for the environment and conformism to the collective attitude of the human group. Thus, the incentive to cooperate responds to the state of the ecological system and to the agents' collective opinion, and this response can be linear, nonlinear and monotonic, or non-monotonic. When investigating the mathematical form of this response, we find that monotonic non-linear responses may result in additional equilibria, cycles and basins of attraction compared to the linear case. Non-monotonic responses, such as resignation effects, may produce much more complicated nullclines such as a closed nullcline and weaken our ability to anticipate the dynamics of a social-ecological system. Regarding the modelling of the socioeconomic subsystem, the replicator dynamics and the logit best-response dynamics are widely used mathematical formulations from evolutionary game theory. There seems to be little awareness about the impact of choosing one or the other. The replicator dynamics assumes that the socioeconomic subsystem is stationary when all agents adopt the same behaviour, whereas the best-response dynamics assumes that this situation is not stationary. The replicator dynamics has formal game theoretical foundations, whereas best-response dynamics comes from psychology. Recent experiments found that the best-response dynamics explains empirical data better. We find that the two dynamics can produce a different number of equilibria as well as differences in their stability. The replicator dynamics is a limit case of the logit best-response dynamics when agents have an infinite rationality. We show that even generic social-ecological models can show multistability. In many cases, multistability allows for counterintuitive equilibria to emerge, where ecological desirability and socioeconomic desirability are not correlated. This makes generic management recommendations difficult to find and several policies with and without socioeconomic impact should be considered. Even in cases where there is a unique equilibrium, it can lose stability and give rise to sustained oscillations. We can interpret these oscillations in a way similar to the cycles found in classical predator-prey systems. In the lake pollution social-ecological model for instance, the agents' defection increases the lake pollution, which makes agents feel concerned and convince the majority to cooperate. Then, the ecological concern decreases because the lake is not polluted and the incentive to cooperate plummets, so that it becomes more advantageous for the agents to defect again. We show that the oscillations obtained when using the replicator dynamics tend to produce a make-or-break dynamics, where a random perturbation could shift the system to either full cooperation or full defection depending on its timing along the cycle. Management measures may shift the location of the social-ecological system at equilibrium, but also make attractors appear or disappear in the phase plane or change the resilience of stable steady states. The resilience of equilibria relates to basins of attraction and is especially important in the face of potential regime shifts. Sources of uncertainty that should be taken into account for the management of social-ecological systems include multistability and the possibility of counterintuitive equilibria, the wide range of possible policy measures with or without socioeconomic interventions, and the behaviour of human collectives involved, which may be described by different dynamics. Yet, uncertainty coming from the collective behaviour of agents is mitigated if they do not give up or rely on the other agents' efforts, which allows modelling to better inform decision makers.
URL: https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-202003312720
Subject Keywords: social-ecological system; social-ecological model; mathematical model; lake eutrophication; coupled human-environment system; modelling of human behaviour; multistability; oscillations; best-response; replicator; best-reply; evolutionary game theory; theoretical ecology
Issue Date: 31-Mar-2020
License name: Attribution 3.0 Unported
License url: http://creativecommons.org/licenses/by/3.0/
Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB06 - E-Dissertationen

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