Highlights d More than one-third of chondrichthyan fish species are threatened by overfishing d Disproportionate threat in tropics risk loss of ecosystem functions and services d Three species not seen in >80 years are Critically Endangered (Possibly Extinct)d The depletion of these species has been driven by continuing demand for human food

Overfishing is the primary cause of marine defaunation, yet individual species' declines and rising extinction risk are difficult to measure, particularly for the largest predators found in the high seas 1-3 . We calculate two well-established indicators to track progress towards Aichi Biodiversity Targets and Sustainable Development Goals 4,5 : the Living Planet Index (a measure of changes in abundance aggregating 57 abundance time-series for 18 oceanic shark and ray species), and the Red List Index (a measure of change in extinction risk calculated for all 31 oceanic species). We find that, since 1970, the global abundance of oceanic sharks and rays has declined by 71% due to an 18-fold increase in Relative Fishing Pressure. This depletion elevated global extinction risk to the point where three-quarters of this functionally important assemblage are threatened with extinction. Strict prohibitions and precautionary science-based catch limits are urgently needed to avert population collapse 6,7 , avoid disruption of ecological function, and promote species recovery 8,9 .Over the United Nations 'Decade of Biodiversity' from 2011-2020, governments committed to improve human well-being and food security by safeguarding ecosystem services and halting biodiversity loss 10 . The Sustainable Development Goals, adopted by all United Nations Member States, and the 20 Aichi Biodiversity Targets of the Convention on Biological Diversity, provide a framework to track progress towards the 2020 deadline 4,5,10 . Seafood sustainability is an integral part of these commitments, and wild capture fisheries are essential nutritional and economic resources for millions of people globally 11,12 . Yet beneath the ocean surface, it is difficult to assess changes in the state of biodiversity and ecosystem structure, function, and services 13 .

The International Union for Conservation of Nature's (IUCN) Red List is the global standard for quantifying extinction risk but assessing population reduction (criterion A) of wide-ranging, long-lived marine taxa remains difficult and controversial. We show how Bayesian state-space models (BSSM), coupled with expert knowledge at IUCN Red List workshops, can combine regional abundance data into indices of global population change. To illustrate our approach, we provide examples of the process to assess four circumglobal sharks with differing temporal and spatial datadeficiency: Blue Shark (Prionace glauca), Shortfin Mako (Isurus oxyrinchus), Dusky Shark (Carcharhinus obscurus), and Great Hammerhead (Sphyrna mokarran). For each species, the BSSM provided global population change estimates over three generation lengths bounded by uncertainty levels in intuitive outputs, enabling informed decisions on the status of each species. Integrating similar analyses into future workshops would help conservation practitioners ensure robust, consistent, and transparent Red List assessments for other long-lived, wide-ranging species. K E Y W O R D SBayesian state-space model, biodiversity conservation, demography, elasmobranch, extinction risk, population decline, threatened speciesThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Fishing activity is closely monitored to an increasing degree, but its effects on biodiversity have not received such attention. Using iconic and well-studied fish species such as tunas, billfishes, and sharks, we calculate a continuous Red List Index of yearly changes in extinction risk over 70 years to track progress toward global sustainability and biodiversity targets. We show that this well-established biodiversity indicator is highly sensitive and responsive to fishing mortality. After ~58 years of increasing risk of extinction, effective fisheries management has shifted the biodiversity loss curve for tunas and billfishes, whereas the curve continues to worsen for sharks, which are highly undermanaged. While populations of highly valuable commercial species are being rebuilt, the next management challenge is to halt and reverse the harm afflicted by these same fisheries to broad oceanic biodiversity.

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