There are no data available on the absolute global population size of Greenland Shark. Population trend data are available from three sources (1) local abundance estimates, (2) an estimate of maximum population growth rate, which combined with catch data was used to (3) reconstruct population trajectory from 1600 to 2020.

First, in unfished areas local densities can be high in summer ranging from 0.4–15.5 individuals km^-2 in the eastern Canadian Arctic Archipelago. These density estimates are comparable to estimates of Grey Reef Shark (Carcharhinus amblyrhynchos) in the relatively pristine Palmyra atoll. These comprise mainly juvenile size classes with an average length of 2.48 m and a notable absence of adults (Devine et al. 2018). However, in areas where there have been large historic fisheries Greenland Shark are now less common. However, this could be an artefact of using fishing gear that is not strong enough to land the larger individuals (N.E. Hussey pers. comm. 26/08/2020). Annual demersal trawl surveys throughout west, south, and east Greenland suggest Greenland Shark are patchily distributed and uncommon. For example, only 106 individuals were captured from 9,744 hauls between 1988–2011 by the Greenland Institute of Natural Resources (GNIR) survey (Nielsen et al. 2014) and catch rates in Canadian Research surveys are low (Simpson et al. 2018). However, large catches can be made in certain places and at times of year, e.g. catches of 5–15 sharks on 50 hooks in a 12-hour period (N.E. Hussey pers. comm. 26/08/2020). Trawl swept area estimates are highly uncertain yet suggest high biomass and abundance of 70,000 t and 100,000 individuals in West Greenland Shelf, from south Greenland to Upernavik (Hedeholm et al. 2018). However, this estimate depends highly on catchability and little is known of catchability in trawls, but it is likely lower than the catchability of this species in longlines (D.W. Kulka unpubl. data 2020).

Second, while patchily abundant throughout Arctic and boreal regions of the Atlantic, this species is thought to have the world's longest generation length (GL) of 274 years, however, this age has not been validated and is more likely that the generation length is much lower (S.E. Campana pers. comm. 24/08/2020) and here we assume a more conservative value of 150 years. The median maximum intrinsic rate of population increase, r_max, of Greenland Shark is 0.032 year⁻¹ (95th percentile = 0.025–0.044; Supplementary Information). This is nearly half the lowest r_max previously calculated for any shark or ray. For comparison, the lowest shark r_max is 0.054 for the Leafscale Gulper Shark (Centrophorus squamosus) and the lowest ray r_maxis 0.067 for the Manta Ray (Mobula birostris) (Pardo et al. 2016). The median maximum intrinsic rate of population increase, r_max, is the limit of fishing mortality that can be withstood without the population declining to extinction, F_extincthence 100*(exp(r_max)-1) yields the percentage mortality each year that would drive this species to extinction which is 3.3% (95th percentile = 2.5–4.5%). Assuming the breeding population size (N_b) was 130,945 (calculated estimated assuming a GL of 150) (Walter et al. 2017) then killing only around 4,300 adults (95th percentile = 3,321–5,832) would be sufficient to cause a decline. The current estimated bycatch of around 3,500 individuals may be sufficient to cause a decline (see Supplementary Information). We caution that this bycatch level assumes 100% post-release mortality and this species may have moderate discard survival. Hence, this species is least likely to be able to sustain even light levels of fishing mortality.

Third, the population trajectory was reconstructed over the 420 years 1600–2020 (approximately 2.5 generation lengths, assuming a 150 GL) based on a Schaeffer-Logistic population model and reconstructed catches, assuming a carrying capacity of 3.2 million individuals and a population growth rate r_max = 0.032 year⁻¹ (95th percentile = 0.025–0.044; Supplementary Information). These carrying capacity estimates are arbitrary but smaller numbers resulted in the catch reconstruction tending toward extinction. It is likely that the Greenland Shark has been declining since the early 1600s with steepest declines beginning in the early 1800s through to the 1940s whereupon most target fisheries were ended. Since then the population is most likely to have increased despite continued low levels of bycatch mortality that most recently are in the region of 3,500 individuals captured annually (Supplementary Information). These broad patterns are highly sensitive to generation length, r_max, and carrying capacity assumptions. Slightly lower generation length, r_max, and carrying capacity assumptions led to extinction and slightly higher values led to complete recovery. Any values capturing the likely decline due to target fishing also suggest there has been recovery since the cessation of target fisheries. Specifically, the population reconstruction reveals that the Greenland Shark has declined by 57% in the 420 years since the 1600 (range 9–100% depending on r_max and carrying capacity assumptions). In the past century 1920–2020 Greenland Shark has increased slightly 3% (range: 57% increase to 100% decline). The global estimated population reduction is 59.3% (range 9.8–100%) over the equivalent of three generation lengths (450 years) (Supplementary Information, Figure 6b middle panel). Assuming a much more modest generation length of 50–75 years, then the estimated population reduction is 11.7% (range 1%–99.9%) over three generation lengths (Supplementary Information, Figure 6a middle panel). Assuming a longer generation length of 274 years, then the estimated population reduction is 72.9% (range 22.9%–100%) over three generation lengths (Supplementary Information, Figure 6c middle panel).

Fourth, the population reduction analysis does not consider the likely reduction in carrying capacity of Greenland Shark from anthropogenic climate change, which is affecting the quantity, dynamics, and distribution of Arctic sea ice (Edwards et al. 2019). With few exceptions, Greenland shark is primarily found in the seas around the Arctic polar icecap and in continental and insular fjord ecosystems (Walter et al. 2017). While poorly understood, the rate of projected loss of sea ice will have and will continue to negatively influence the abundance, distribution and availability of prey (Edwards et al. 2019). Overall, the Greenland Shark has undergone an inferred population reduction of 30–49% over the past three generations lengths (450 years), but this value could range from 11.7–72.9% depending on whether the generation length is shorter (50–75 years) or longer (274 years).