Conservation in the EU and all over the world aims at reducing biodiversity loss which has become a great issue in the last decades. However, despite existing efforts, Earth is assumed to face a sixth mass extinction. One major challenge for conservation is to reconcile the targets with conflicting interests, e.g. for food production in intensively used agricultural landscapes. Agriculture is an example of a coupled human-environment system that is approached in this thesis with the help of mathematical models from two directions. Firstly, the ecological subsystem is considered to find processes relevant for the effect of habitat connectivity on population abundances. Modelling theory predicts that the species-specific growth parameters (intrinsic growth rate and carrying capacity) indicate whether dispersal has a positive or negative effect on the total population size at equilibrium (r-K relationship). We use laboratory experiments in combination with a system of ordinary differential equations and deliver the first empirical evidence for a negative effect of dispersal on the population size in line with this theory. The result is of particular relevance for the design of dispersal corridors or stepping stones which are meant to increase connectivity between habitats. These measures might not be effective for biological conservation. A second population model, consisting of two coupled Ricker maps with a mate-finding Allee effect, is analyzed in order to examine the effect of bistability due to the Allee effect in combination with overcompensation in a spatial system. The interplay can cause complex population dynamics including multiple coexisting attractors, long transients and sudden population collapses. Essential extinction teaches us that not only small populations are prone to extinction but chaotic dynamics can drive a population extinct in a short period of time as well. By a comprehensive model analysis, we find that dispersal can prevent essential extinction of a population. In the context of conservation that is: habitat connectivity can promote rescue effects to save a population that exhibits an Allee effect. The two findings of the first part of this thesis have contrasting implications for conservation which shows that universal recommendations regarding habitat connectivity are impossible without knowledge of the specific system. Secondly, a model for the socio-economic subsystem is presented. Agri-environment schemes (AES) are payments that compensate farmers for forgone profits on the condition that they improve the ecological state of the agricultural system. However, classical economic models that describe the cost-effectiveness of AES often do not take the social network of farmers into account. Numerical simulations of the socio-economic model presented in this thesis suggest that social norms can hinder farmers from scheme participation. Moreover, social norms lead to multistability in farmers’ land-use decision behaviour. Informational campaigns potentially decrease the threshold towards more long-term scheme participation and might be a good tool to complement compensation payments if social norms affect land-use decisions. Finally, a coupled human-environment system is analyzed. An integrated economicecological model is studied to investigate the cost-effectiveness of AES if the species of concern exhibits an Allee effect. A numerical model analysis indicates large trade-offs between agricultural production and persistence probability. Moreover, conservation success strongly depends on the initial population size, meaning that conservation is well advised to start before the species is threatened. Spatial aggregation of habitat can promote rescue effects, suggesting land-sparing solutions for conservation. In that case,agglomeration bonuses may serve to increase the effectiveness of AES. Possible causes for population declines are diverse and can be a combination of human influences, e.g. due to habitat degradation and inherent ecosystem properties. That complicates the task of conservation. The models presented in this thesis simplify complex systems in order to extract processes relevant for biological conservation. The analysis of spatial effects and dynamical model complexity, e.g. due to Allee effects or a nonlinear utility function, allows us improve the understanding of coupled human-environment systems.

Zahlungen für Ökosystemdienstleistungen (Payments for EcosystemServices, PES) sind in den letzten Jahren zum Aushängeschild von Umweltorganisation geworden. Der Gedanke, die Bereitstellung von Ökosystemdienstleistungen durch PES abzusichern, ist in praktischen Diskursen von Vermittlern zu finden, die an potentiell Zahlende gerichtet sind. Praktikern ist bisher jedoch schwer gefallen, zu zeigen, dass PES tatsächlich zu den vorgesehenen Zielen führen können. Forscher haben darauf hingewiesen, dass zahlreiche PES-Schemata, insbesondere diejenigen mit Bezug auf Wasser, auf unsicheren Annahmen beruhen und außerdem gewichtige Kausalzusammenhänge zwischen Eingriffen in die Landnutzung und Ökosystemdienstleistungen vermissen lassen. Diese Unsicherheit in PES-Schemata geht nicht nur aus praktischen Schwierigkeiten hervor, sondern aus der Komplexität von Mensch-Umwelt-Systemen (human-environment systems) und aus der Begrenztheit des Wissens über diese Systeme. Forscher sind zwar in derLage, diese wesentlichen Herausforderungen zu beschreiben und zu diskutieren. In der Fachliteratur mangelt es jedoch an empirischen Studien,die die zusätzliche Wirksamkeitvon PES-Schemata untersuchen, d.h. ob diese Schemata zusätzliche Wirkungen zeigen, die anderen Faktoren nicht zurechenbar sind, bzw. Studien, die die Bedeutung von Nachweisen für ihre Wirksamkeit für die Interessengruppen (stakeholders) untersuchen. Die Dissertation trägt dazu bei, diese empirische Lücke zu schließen: Dazu untersucht sie vier wasserbezogene Zahlungsschemata, hier auch Zahlungen für Wassereinzugsgebietsleistungen genannt, in Kolumbien. Sie vergleicht die vier Fälle hinsichtlich der Bestrebungen, durch Beobachtung (monitoring) und Evaluation Nachweise für die Wirksamkeit zu erbringen, sowie hinsichtlich der damit verbundenen Herausforderungen. Eines der Kapitel enthält auch drei Fallstudien aus Brasilien, die als Vergleich zu den Fällen aus Kolumbien und der Darstellung von Unterschieden und Gemeinsamkeiten dienen. / Payments for Ecosystem Services (PES) have become the flagship of conservation organizations in recent years. The idea of securing ecosystem service (ES) provision through PES has been present in practical discourses of intermediaries directed at potential payers. However, demonstrating that PES can actually achieve the intended goals has been difficult for practitioners. Researchers have pointed out that many PES schemes, particularly water-related ones, are based on unreliable assumptions and lack strong causal links between land use interventions and ecosystem services. This uncertainty in PES schemes arises not only from practical difficulties, but from the complexity of human-environment systems (HES), and the limits of knowledge about them. Researchers have been able to describe and discuss these major challenges. However, the literature is still poor on empirical studies exploring the additionality of PES schemes, that is, if those schemes produce additional effects not attributable to other factors, as well as studies exploring the importance of impact evidence for stakeholders involved. This dissertation contributes to filling this empirical gap by exploring four water-related payments schemes (here also called payments for watershed services, PWS) in Colombia, comparing the cases in terms of their efforts to produce impact evidence through monitoring and evaluation, and their associated challenges. Three cases from Brazil are also included in one of the chapters and compared with the Colombian cases by illustrating differences and similarities.

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.