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Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, regularity, complexity, or higher-order stochastic properties such as multi-stability. In recent years, several classes of methods have been put forward to study these critical transitions in time series data that are based on concepts from nonlinear dynamics, complex systems science, information theory, and stochastic analysis. These include approaches such as phase space-based recurrence plots and recurrence networks, visibility graphs, order pattern-based entropies, and stochastic modelling. Here, we review and compare in detail several prominent methods from these fields by applying them to the same set of marine palaeoclimate proxy records of African climate variations during the past 5 million years. Applying these methods, we observe notable nonlinear transitions in palaeoclimate dynamics in these marine proxy records and discuss them in the context of important climate events and regimes such as phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation and the mid-Pleistocene transition. We find that the studied approaches complement each other by allowing us to point out distinct aspects of dynamical regime shifts in palaeoclimate time series. We also detect significant correlations of these nonlinear regime shift indicators with variations of Earth's orbit, suggesting the latter as potential triggers of nonlinear transitions in palaeoclimate. Overall, the presented study underlines the potentials of nonlinear time series analysis approaches to provide complementary information on dynamical regime shifts in palaeoclimate and their driving processes that cannot be revealed by linear statistics or eyeball inspection of the data alone. [ABSTRACT FROM AUTHOR]

• First integrated, multi-method study on climate-related disasters and conflict. • Disaster do not enhance conflict risks per se, but only in certain contexts. • Relevant context factors: large population, ethnic exclusion, low development. • Improved opportunity structures are the main explanatory mechanism. Climate-related disasters are among the most societally disruptive impacts of anthropogenic climate change. Their potential impact on the risk of armed conflict is heavily debated in the context of the security implications of climate change. Yet, evidence for such climate-conflict-disaster links remains limited and contested. One reason for this is that existing studies do not triangulate insights from different methods and pay little attention to relevant context factors and especially causal pathways. By combining statistical approaches with systematic evidence from QCA and qualitative case studies in an innovative multi-method research design, we show that climate-related disasters increase the risk of armed conflict onset. This link is highly context-dependent and we find that countries with large populations, political exclusion of ethnic groups, and a low level of human development are particularly vulnerable. For such countries, almost one third of all conflict onsets over the 1980-2016 period have been preceded by a disaster within 7 days. The robustness of the effect is reduced for longer time spans. Case study evidence points to improved opportunity structures for armed groups rather than aggravated grievances as the main mechanism connecting disasters and conflict onset. [ABSTRACT FROM AUTHOR]