Clustering future scenarios based on extremal properties of ecological outcomes

Abstract:

In order to make future predictions in ecology, often multiple scenarios are proposed. This is due to the difficulty of prediction, a plethora of alternative models are used, consistent with ecological knowledge. However, various unknown factors such as differing human policy responses and climate models can drastically change outcomes. We are interested in the analysis of comparing the outputs of these various predictions. A central aim of our study is to answer the question, how should one measure the similarity between prediction X and prediction Y? In order to answer such a question, we analyze the predicted distributions of 1700 mammals across 34 scenarios, differing along dimensions of CMIP6 climate models: GCMs (global climate models), possible future representative concentration(RCP) pathways, and time period. The key aspect of these predictions is the extremes of the outcomes. Two outcomes should be considered similar if they make similar predictions about the extreme events that will occur. Thus we propose a similarity measure based on the similarity of extremes in the predictions. To accomplish this we use a novel conditioned copula approach, allowing us to focus on tail dependence of the extremes instead of say, correlation, which does not emphasize the extreme behavior and rather focuses on central tendencies. Clustering using this tail dependence similarity will reveal which predictions are similar/redundant, while differentiating scenarios that may look at first similar (say with similar means) but have differing extreme predictions. One interesting application of the proposed similarity measure is to quantify the time difference between (for example) an RCP of 8.5 scenario versus an RCP of 2.6.