An Integrated Framework to Study Ecological Tipping Points in Social-Ecological Systems

Sudden regime shifts or tipping points pose a major threat to various ecosystems and people\u27s livelihoods worldwide. However, tipping points are still hard to predict and often occur without warning. To avoid dramatic social-ecological consequences, it is crucial to understand tipping point behaviour and to identify early warning indicators. Previous studies have hardly implemented an integrated social-ecological approach, which has led to a fragmented understanding and oversimplification of tipping point phenomena. Against this background, we present a systemic research framework that harmonizes ecological and social perspectives to gain a mechanistic understanding of tipping point behaviour. We utilize a social-ecological systems (SES) approach to identify drivers, consequences, and feasible preventive strategies. Our proposed framework consists of a retrospective, a comparative and a prospective perspective; each of them utilizes interdisciplinary studies in both sub systems at multiple scales. The research framework was developed by the members of NamTip, an inter- and transdisciplinary research project aiming to understand and manage desertification tipping points in Namibia’s semi-arid rangelands. The NamTip project represents a practical implementation of the research framework, that uses an integrated, social-ecological study design combining the threefold approach with dynamic modelling. This includes analyses of time-series and archival data, experimental and observational studies, as well as scenario development and exploration of decision-making with local farmers. After the initial practical implementation and with our ongoing evaluation, we are convinced that such an ambitious and complex framework will guide the way to a profound understanding of tipping point phenomena and feasible management options

Approximation Algorithms for Max-Min Share Allocations of Indivisible Chores and Goods

We consider Max-min Share (MmS) allocations of items both in the case whereitems are goods (positive utility) and when they are chores (negative utility).We show that fair allocations of goods and chores have some fundamentalconnections but differences as well. We prove that like in the case for goods,an MmS allocation does not need to exist for chores and computing an MmSallocation - if it exists - is strongly NP-hard. In view of these non-existenceand complexity results, we present a polynomial-time 2-approximation algorithmfor MmS fairness for chores. We then introduce a new fairness concept calledoptimal MmS that represents the best possible allocation in terms of MmS thatis guaranteed to exist. For both goods and chores, we use connections toparallel machine scheduling to give (1) an exponential-time exact algorithm and(2) a polynomial-time approximation scheme for computing an optimal MmSallocation when the number of agents is fixed