Incorporating uncertainty into estimation of natural mortality for two species of Rajidae fished in Chile

Methods to estimate annual mortality rate (MM) are usually based on life history traits and their application provide a deterministic estimate for MM. However, there are two sources of uncertainty coming from equations that describe these methods: (i) error in the life history traits estimates (hereafter ‘trait-error’) and (ii) variability of the equations coefficients (hereafter ‘coefficient-error’). Thus, we use these two sources of uncertainty to incorporate error on MM estimates for yellownose skate (Dipturus chilensis) and roughskin skate (Dipturus trachyderma  ) off the Chilean coast. Based on the quality of the life history parameters available for these species, five methods to estimate MM were selected which required the analysis of lifespan amaxamax, age at maturity a50%a50%, and von Bertalanfy growth parameters (l∞l∞, t0t0, and k  ). For Pauly’s methods, the error on the habitat temperature was also assessed. Incorporating only uncertainty from trait errors produced estimates of median MM for D. chilensis ranging from 0.12 to 0.15 year−1 for females and 0.14 to 0.18 year−1 for males. For D. trachyderma, this same estimate was 0.09–0.15 year−1 for both sexes combined. Incorporating all sources of uncertainty (trait and coefficient-error) increased the coefficients of variation (CV) of MM nine-fold for D. chilensis (females) and seven-fold for D. trachyderma   and increased estimates of MM by up to 35% in comparison with median values. We think Pauly’s method is the most appropriate for both analysed species in terms of trade-off between parameter needed and CV of MM estimates incorporating all sources of uncertainty. Most of the empirical methods used herein were proposed, in principle, for teleost fishes within a deterministic framework. We discuss the applicability of these methods to elasmobranchs and how the incorporation of uncertainty may improve population modelling for these species.