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Background. Global sustainability is an enmeshed system of complex socio-economic, climato-logical and ecological interactions. The numerous objectives of the United Nations’ Sustainable Development Goals (SDGs) and the Paris Agreement have various levels of interdependence, making it difficult to ascertain the influence of changes in particular indicators across the whole system. Methods. We present a method to find interlinkages amongst the 17 SDGs and climate change, including non-linear and non-monotonic dependences, by using 400 indicators that track their temporal changes. The method detects statistically significant dependencies amongst the time evolution of the objectives by using partial distance correlations, a non-linear measure of conditional dependence that also discounts spurious correlations originating from lurking variables. We then employ a network representation to identify the most important objectives (using network centrality) and to obtain nexuses of objectives (defined as highly interconnected clusters in the network). Findings. Using temporal data from 181 countries spanning 20 years, we analyse dependencies amongst SDGs and climate for 35 country groupings based on region, development and income 2 level. Our results show that the significant interlinkages, central objectives, and nexuses identified vary greatly across country groupings, yet partnerships for the goals (SDG 17) and climate change rank as highly important across many country groupings.Temperature rise is strongly linked to urbanisation, air pollution, and slum expansion (SDG 11), especially in country groupings likely to be worst affectedby climate breakdown such as Africa. In several groupings encompassing the developing countries, a consistent nexus of strongly interconnected objectives is formed by poverty reduction (SDG 1), education (SDG 4), and economic growth (SDG 8), sometimes incorporating gender equality (SDG 5), and peace and justice (SDG 16). Interpretation. The differences across groupings emphasise the need to define goals in accordance with local circumstances and priorities. Our analysis highlights global partnerships (SDG 17) as a pivot in global sustainability efforts, which have been strongly linked to economic growth (SDG 8). Yet, if economic growth and trade expansion were repositioned as means instead of ends of development, our analysis shows that education (SDG 4) and poverty reduction (SDG 1) become more central, thus suggesting these could be prioritised in global partnerships. Urban livelihoods (SDG 11) are also flagged as important to avoid replicating unsustainable patterns of the past. Funding. This work has been primarily supported by the EPSRC under Grant EP/N014529/1 funding the Centre for Mathematics of Precision Healthcare at Imperial College London, and partly by the UKRI’s Trade, Development and the Environment Hub (Trade Hub) project, ES/S008160/1 |