Jiao, Y., Hayes, C., and Cortés, E. 2009. Hierarchical Bayesian approach for population dynamics modelling of fish complexes without species-specific data. – ICES Journal of Marine Science, 66: 367–377.Modelling the population dynamics of fish complexes is challenging, and many species have been assessed and managed as a complex that was treated as a single species. Two Bayesian state-space surplus production models with multilevel priors (hierarchical models) were developed to simulate variability in population growth rates of species in a complex, using the hammerhead shark complex (Sphyrna spp.) of the Atlantic and Gulf of Mexico coasts of the US as an example. The complex consists of three species: scalloped (Sphyrna lewini), great (Sphyrna mokarran), and smooth hammerhead (Sphyrna zygaena). Bayesian state-space surplus production models with multilevel priors fitted the hammerhead data better than a model based on single-level priors. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that do not include variability among species, and highly parameterized models that assign an estimate of parameters to each species. By ignoring the variability among species, confidence intervals of the estimates of stock status indicators can be unrealistically narrow, possibly leading to high-risk management strategies being adopted. Use of multilevel priors in a hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modelling fish complexes lacking species-specific data.

Jiao, Y., Smith, E. P., O'Reilly, R., and Orth, D. J. 2012. Modelling non-stationary natural mortality in catch-at-age models. – ICES Journal of Marine Science, 69: 105–118. Non-stationarity in the natural mortality of many species has been discussed among research scientists, but no generally applicable models/methods have been developed where a statistical catch-at-age (SCA) model framework is used. Using the Atlantic weakfish (Cynoscion regalis) fishery as an example, several SCA models are developed to assess the population dynamics, then compared. Models used included (i) an SCA with constant natural mortality, (ii) an SCA with unknown natural mortality, but with a hierarchical prior distribution from a mixture of distributions based on life-history information, (iii) an SCA with age-specific unknown natural mortality, (iv) an SCA with time-varying natural mortality, following a random-walk process, and (v) an SCA with age-specific time-varying natural mortality. The last two models imply that the population dynamics are not stationary. A Bayesian approach was used to estimate parameters, and performance of the models was compared through goodness-of-fit and the retrospective patterns of the models. A simulation study was then conducted to test the uncertainty resulting from model selection, the efficiency of using the best model selected based on deviance information criterion, and whether changes in natural mortality could be detected. An SCA with time-varying natural mortality, following a random-walk process, is proposed for the example fishery here. The estimated non-stationary temporal patterns in natural mortality were linked further to climate–ocean oscillation indices, to diagnose possible mechanisms/linkages to these temporal variations in natural mortality.

Appropriate inference for stocks or species with low‐quality data (poor data) or limited data (data poor) is extremely important. Hierarchical Bayesian methods are especially applicable to small‐area, small‐sample‐size estimation problems because they allow poor‐data species to borrow strength from species with good‐quality data. We used a hammerhead shark complex as an example to investigate the advantages of using hierarchical Bayesian models in assessing the status of poor‐data and data‐poor exploited species. The hammerhead shark complex (Sphyrna spp.) along the Atlantic and Gulf of Mexico coasts of the United States is composed of three species: the scalloped hammerhead (S. lewini), the great hammerhead (S. mokarran), and the smooth hammerhead (S. zygaena) sharks. The scalloped hammerhead comprises 70–80% of the catch and has catch and relative abundance data of good quality, whereas great and smooth hammerheads have relative abundance indices that are both limited and of low quality presumably because of low stock density and limited sampling. Four hierarchical Bayesian state‐space surplus production models were developed to simulate variability in population growth rates, carrying capacity, and catchability of the species. The results from the hierarchical Bayesian models were considerably more robust than those of the nonhierarchical models. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that assume different population parameters for each species and those that assume all species share identical parameters. Use of the hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modeling fish complexes with species‐specific data, because the poor‐data species can borrow strength from the species with good data, making the estimation more stable and robust.

Many marine species exhibit temporal variation in individual growth. Yearly variation in growth has been identified for red abalone ( Haliotis rufescens ) in southern California, USA, but has not been previously incorporated into growth models. In this study, Bayesian hierarchical models were developed to describe variability in growth rates for the Johnsons Lee red abalone population. Although the Bayesian hierarchical modeling estimates are close to estimates of the nonhierarchical highly parameterized model that assigns an estimate of parameters to each data period when the sample sizes are high, the hyperparameters in the hierarchical model are more useful in incorporating the temporal variability into the stock assessment. By ignoring temporal variability, confidence intervals of the estimates of growth can be unrealistically narrow, possibly leading to bias when these models are used for developing biological reference points such as F_0.1, F_max, or F_x%. The use of a Bayesian hierarchical approach is generally suggested for future growth modeling and for per-recruitment models that include growth when determining precautionary management decisions.

Appropriate inference of population status for endangered species is extremely important. Using a single model for estimating population growth rates is typically inadequate for assessing endangered species because inferences based on only one “best” model ignore model uncertainty. In this study, the endangered dromedary pearlymussel ( Dromus dromas ) in the Clinch and Powell rivers of eastern Tennessee, USA, was used as an example to demonstrate the importance of multiple models, with consideration of environmental noises for evaluating population growth. Our results showed that more than one model deserves consideration in making inferences of population growth rate. A Bayesian model averaging approach was used to make inferences by weighting each model using the deviance information criterion. To test the uncertainty resulting from model selection and the efficiency of the Bayesian averaging approach, a simulation study was conducted on the dromedary pearlymussel populations, which showed that model selection uncertainty is very high. The results of these tests lead us to recommend using Bayesian model averaging to assess population growth status for endangered species, by balancing goodness-of-fit and selection uncertainty among alternate models.