Planning for the protection of species often involves difficult choices about which species to prioritize, given constrained resources. One way of prioritizing species is to consider their “evolutionary distinctiveness”, i.e. their relative evolutionary isolation on a phylogenetic tree. Several evolutionary isolation metrics or phylogenetic diversity indices have been introduced in the literature, among them the so-called Fair Proportion index (also known as the “evolutionary distinctiveness” score). This index apportions the total diversity of a tree among all leaves, thereby providing a simple prioritization criterion for conservation. Here, we focus on the prioritization order obtained from the Fair Proportion index and analyze the effects of species extinction on this ranking. More precisely, we analyze the extent to which the ranking order may change when some species go extinct and the Fair Proportion index is re-computed for the remaining taxa. We show that for each phylogenetic tree, there are edge lengths such that the extinction of one leaf per cherry completely reverses the ranking. Moreover, we show that even if only the lowest ranked species goes extinct, the ranking order may drastically change. We end by analyzing the effects of these two extinction scenarios (extinction of the lowest ranked species and extinction of one leaf per cherry) for a collection of empirical and simulated trees. In both cases, we can observe significant changes in the prioritization orders, highlighting the empirical relevance of our theoretical findings.

中文翻译：

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面临灭绝的系统发育多样性排名：公平比例指数的稳健性

鉴于资源有限，物种保护规划常常涉及到优先考虑哪些物种的困难选择。对物种进行优先排序的一种方法是考虑它们的“进化独特性”，即它们在系统发育树上的相对进化隔离性。文献中引入了几种进化隔离指标或系统发育多样性指数，其中包括所谓的公平比例指数（也称为“进化独特性”分数）。该指数将树的总多样性分配给所有叶子，从而为保护提供了简单的优先级标准。在这里，我们重点关注从公平比例指数得出的优先顺序，并分析物种灭绝对该排名的影响。更确切地说，我们分析了当某些物种灭绝并重新计算剩余类群的公平比例指数时排名顺序可能发生变化的程度。我们表明，对于每个系统发育树，都有边长度，使得每个樱桃一片叶子的灭绝完全颠倒了排名。此外，我们表明，即使只有排名最低的物种灭绝，排名顺序也可能会发生巨大变化。最后，我们分析了这两种灭绝情景（排名最低的物种灭绝和每个樱桃一片叶子的灭绝）对一组经验和模拟树木的影响。在这两种情况下，我们都可以观察到优先顺序的显着变化，突出了我们的理论发现的经验相关性。