Background. The directed harvest and global trade in the gill plates of mantas, and devil rays, has led to increased fishing pressure and steep population declines in some locations. The slow life history, particularly of the manta rays, is cited as a key reason why such species have little capacity to withstand directed fisheries. Here, we place their life history and demography within the context of other sharks and rays.Methods. Despite the limited availability of data, we use life history theory and comparative analysis to estimate the intrinsic risk of extinction (as indexed by the maximum intrinsic rate of population increase rmax) for a typical generic manta ray using a variant of the classic Euler–Lotka demographic model. This model requires only three traits to calculate the maximum intrinsic population growth rate rmax: von Bertalanffy growth rate, annual pup production and age at maturity. To account for the uncertainty in life history parameters, we created plausible parameter ranges and propagate these uncertainties through the model to calculate a distribution of the plausible range of rmax values.Results. The maximum population growth rate rmax of manta ray is most sensitive to the length of the reproductive cycle, and the median rmax of 0.116 year−1 95th percentile [0.089–0.139] is one of the lowest known of the 106 sharks and rays for which we have comparable demographic information.Discussion. In common with other unprotected, unmanaged, high-value large-bodied sharks and rays the combination of very low population growth rates of manta rays, combined with the high value of their gill rakers and the international nature of trade, is highly likely to lead to rapid depletion and potential local extinction unless a rapid conservation management response occurs worldwide. Furthermore, we show that it is possible to derive important insights into the demography extinction risk of data-poor species using well-established life history theory.

Summary1. Somatic growth is a fundamental property of living organisms, and is of particular importance for species with indeterminate growth that can change in size continuously throughout their life. For example, fishes can increase in size by 2-6 orders of magnitude during their lifetime, resulting in changes in production, consumption and function at the ecosystem scale. Within species, growth rates are traded off against other life-history parameters, hence an accurate description of growth is essential to understand the comparative demography, productivity, fisheries yield and extinction risk of populations and species. 2. The growth trajectory of indeterminate growing sharks and rays (elasmobranchs) and bony fishes (teleosts) is usually modelled using a three-parameter logarithmic function, the von Bertalanffy growth function (VBGF), to describe the total length of the average individual at any given age. Recently, however, a two-parameter form has gained popularity. Rather than being estimated in the model fitting process, the third y-intercept parameter (L 0 ) of the VBGF has been interpreted as being biologically equivalent to, and thus fixed as, the empirically estimated size at birth. 3. We tested the equivalence assumption that L 0 is the same or similar to size at birth by comparing empirical estimates of size at birth available from the literature with estimates of L 0 from published data from elasmobranchs, and found that even though there is an overlap of values, there is a high degree of variability between them. 4. We calculate the bias in the growth coefficient (k) of the VBGF by comparison between the two-and threeparameter estimation methods. We show that slight deviations in fixed L 0 can cause considerable bias in growth estimates in the two-parameter VBGF while providing no benefit even when L 0 matches the true value. We show that the effect of this biased growth estimate has profound consequences for fisheries stock status. 5. We strongly recommend the use of the three-parameter VBGF and discourage use of the two-parameter VBGF because it results in substantially biased growth estimates even with slight variations in the value of fixed L 0 .

Fish gill surface area varies across species and with respect to ecological lifestyles. The majority of previous studies only qualitatively describe gill surface area in relation to ecology and focus primarily on teleosts. Here, we quantitatively examined the relationship of gill surface area with respect to specific ecological lifestyle traits in elasmobranchs, which offer an independent evaluation of observed patterns in teleosts. As gill surface area increases ontogenetically with body mass, examination of how gill surface area varies with ecological lifestyle traits must be assessed in the context of its allometry (scaling). Thus, we examined how the relationship of gill surface area and body mass across 11 shark species from the literature and one species for which we made measurements, the Gray Smoothhound Mustelus californicus, varied with three ecological lifestyle traits: activity level, habitat, and maximum body size. Relative gill surface area (gill surface area at a specified body mass; here we used 5,000g, termed the 'standardized intercept') ranged from 4,724.98 to 35,694.39 cm 2 (mean and standard error: 17,796.65 AE 2,948.61 cm 2 ) and varied across species and the ecological lifestyle traits examined. Specifically, larger-bodied, active, oceanic species had greater relative gill surface area than smaller-bodied, less active, coastal species. In contrast, the rate at which gill surface area scaled with body mass (slope) was generally consistent across species (0.85 AE 0.02) and did not differ statistically with activity level, habitat, or maximum body size. Our results suggest that ecology may influence relative gill surface area, rather than the rate at which gill surface area scales with body mass. Future comparisons of gill surface area and ecological lifestyle traits using the quantitative techniques applied in this study can provide further insight into patterns dictating the relationship between gill surface area, metabolism, and ecological lifestyle traits. K E Y W O R D Sallometry, ecomorphology, gill surface area, metabolism, scaling

Devil rays (Mobula spp.) face intensifying fishing pressure to meet the ongoing international demand for gill plates. The paucity of information on growth, mortality, and fishing effort for devil rays make quantifying population growth rates and extinction risk challenging. Furthermore, unlike manta rays (Manta spp.), devil rays have not been listed on CITES. Here, we use a published size-at-age dataset for the Spinetail Devil Ray (Mobula japanica), to estimate somatic growth rates, age at maturity, maximum age, and natural and fishing mortality. We then estimate a plausible distribution of the maximum intrinsic population growth rate (rmax) and compare it to 95 other chondrichthyans. We find evidence that larger devil ray species have low somatic growth rate, low annual reproductive output, and low maximum population growth rates, suggesting they have low productivity. Fishing rates of a small-scale artisanal Mexican fishery were comparable to our estimate of rmax, and therefore probably unsustainable. Devil ray rmax is very similar to that of manta rays, indicating devil rays can potentially be driven to local extinction at low levels of fishing mortality and that a similar degree of protection for both groups is warranted.