A Bayesian uncertainty analysis of cetacean demography and bycatch mortality using age-at-death data.

Wildlife ecologists and managers are challenged to make the most of sparse information for understanding demography of many species, especially those that are long lived and difficult to observe. For many odontocete (dolphin, porpoise, toothed whale) populations, only fertility and age-at-death data are feasibly obtainable. We describe a Bayesian approach for using fertilities and two types of age-at-death data (i.e., age structure of deaths from all mortality sources and age structure of anthropogenic mortalities only) to estimate rate of increase, mortality rates, and impacts of anthropogenic mortality on those rates for a population assumed to be in a stable age structure. We used strandings data from 1977 to 1993 (n = 96) and observer bycatch data from 1989 to 1993 (n = 233) for the Gulf of Maine, USA, and Bay of Fundy, Canada, harbor porpoise (Phocoena phocoena) population as a case study. Our method combines mortality risk functions to estimate parameters describing age-specific natural and bycatch mortality rates. Separate functions are simultaneously fit to bycatch and strandings data, the latter of which are described as a mixture of natural and bycatch mortalities. Euler-Lotka equations and an estimate of longevity were used to constrain parameter estimates, and we included a parameter to account for unequal probabilities of natural vs. bycatch deaths occurring in a sample. We fit models under two scenarios intended to correct for possible data bias due to indirect bycatch of calves (i.e., death following bycatch mortality of mothers) being underrepresented in the bycatch sample. Results from the two scenarios were "model averaged" by sampling from both Markov Chain Monte Carlo (MCMC) chains with uniform probability. The median estimate for potential population growth (r(nat)) was 0.046 (90% credible interval [CRI] = 0.004-0.116). The median for actual growth (r) was -0.030 (90% CRI = -0.192 to +0.065). The probability of population decline due to added fisheries mortality, prior to management to reduce bycatch, was 0.690. Our approach takes into account multiple sources of uncertainty in data and process, and it provides posterior distributions for a rich set of demographic rate parameters that are unknown for most cetaceans. This method should be easily adaptable to other taxa for which fertility and age-at-death data are available.