{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T16:39:22Z","timestamp":1792427962043,"version":"4.5.0"},"reference-count":38,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T00:00:00Z","timestamp":1790553600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009193","name":"Marsden Fund","doi-asserted-by":"publisher","award":["23-UOC-003"],"award-info":[{"award-number":["23-UOC-003"]}],"id":[{"id":"10.13039\/501100009193","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"NSERC","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The loss of biodiversity due to the likely widespread extinction of species in the near future is a focus of current concern in conservation biology. One approach to measure the impact of this extinction is based on the predicted loss of phylogenetic diversity. These predictions have become a focus of the Zoological Society of London\u2019s \u2018EDGE2\u2019 program for quantifying biodiversity loss and involves considering the HED (heightened evolutionary distinctiveness) and HEDGE (heightened evolutionary distinctiveness and globally endangered) indices which are based on phylogenetic diversity on a tree. Here, we show how to generalise the HED(GE) indices by expanding their application to more general settings (to phylogenetic networks, to feature diversity on discrete traits, and to arbitrary biodiversity measures). We provide a simple and explicit description of the mean and, importantly, the variance of such measures, and illustrate our results by an application to the phylogeny and a small set of features for all 27 extant Crocodilians.<\/jats:p>","DOI":"10.1093\/sysbio\/syag075","type":"journal-article","created":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T12:23:45Z","timestamp":1790425425000},"source":"Crossref","is-referenced-by-count":0,"title":["Properties of Biodiversity Indices that Incorporate Future Extinction Risk"],"prefix":"10.1093","author":[{"given":"Mike","family":"Steel","sequence":"first","affiliation":[{"name":"Biomathematics Research Centre, University of Canterbury , Christchurch, 8041 ,","place":["New Zealand"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4275-5546","authenticated-orcid":false,"given":"Kristina","family":"Wicke","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, New Jersey Institute of Technology , Newark, NJ 07102 ,","place":["USA"]},{"name":"National Institute for Theory and Mathematics in Biology, Northwestern University and The University of Chicago , Chicago, IL 60611 ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arne","family":"Mooers","sequence":"additional","affiliation":[{"name":"Department of Biological Sciences, Simon Fraser University , Vancouver, BC V5A 1S6 ,","place":["Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,9,28]]},"reference":[{"key":"2026101911413946800_bib1","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.tcs.2022.03.012","article-title":"On the complexity of optimising variants of phylogenetic diversity on phylogenetic networks","volume":"917","author":"Bordewich","year":"2022","journal-title":"Theoretical Computer Science"},{"issue":"40","key":"2026101911413946800_bib2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00285-024-02059-y","article-title":"Quantifying the difference between phylogenetic diversity and diversity indices","volume":"88","author":"Bordewich","year":"2024","journal-title":"Journal of Mathematical Biology"},{"issue":"6","key":"2026101911413946800_bib3","doi-asserted-by":"publisher","first-page":"3172","DOI":"10.1016\/j.aim.2012.08.008","article-title":"Hyperconvexity and tight-span theory for diversities","volume":"231","author":"Bryant","year":"2012","journal-title":"Advances in Mathematics"},{"issue":"81","key":"2026101911413946800_bib4","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1186\/s12862-020-01642-3","article-title":"Phylogenetic and spatial distribution of evolutionary diversification, isolation, and threat in turtles and crocodilians (non-avian archosauromorphs)","volume":"20","author":"Colston","year":"2020","journal-title":"BMC Evolutionary Biology"},{"key":"2026101911413946800_bib5","first-page":"77","volume-title":"The Fair Proportion Is a Shapley Value on Phylogenetic Networks Too","author":"Coronado","year":"2018"},{"issue":"48","key":"2026101911413946800_bib6","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s00285-024-02142-4","article-title":"An interchange property for the rooted phylogenetic subnet diversity on phylogenetic networks","volume":"89","author":"Coronado","year":"2024","journal-title":"Journal of Mathematical Biology"},{"issue":"6515","key":"2026101911413946800_bib7","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1126\/science.abe1530","article-title":"Set ambitious goals for biodiversity and sustainability","volume":"370","author":"D\u00edaz","year":"2020","journal-title":"Science"},{"issue":"1","key":"2026101911413946800_bib8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0006-3207(92)91201-3","article-title":"Conservation evaluation and phylogenetic diversity","volume":"61","author":"Faith","year":"1992","journal-title":"Biological Conservation"},{"issue":"6","key":"2026101911413946800_bib9","doi-asserted-by":"publisher","first-page":"1461","DOI":"10.1111\/j.1523-1739.2008.01068.x","article-title":"Threatened species and the potential loss of phylogenetic diversity: Conservation scenarios based on estimated extinction probabilities and phylogenetic risk analysis","volume":"22","author":"Faith","year":"2008","journal-title":"Conservation Biology"},{"key":"2026101911413946800_bib10","doi-asserted-by":"publisher","first-page":"20140011","DOI":"10.1111\/j.1523-1739.2008.01068.x","article-title":"Phylogenetic diversity, functional trait diversity and extinction: avoiding tipping points and worst-case losses","volume":"370","author":"Faith","year":"2015","journal-title":"Phil. 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