Integrating spatial synchrony/asynchrony of population distribution into stock assessment models: a spatial hierarchical Bayesian statistical catch-at-age approach

ICES Journal of Marine Science ICES Journal of Marine Science (2016), 73(7), 1725– 1738. doi:10.1093/icesjms/fsw036 Editor ’s Choice Integrating spatial synchrony/asynchrony of population distribution into stock assessment models: a spatial hierarchical Bayesian statistical catch-at-age approach 1 Department of Fish and Wildlife Conservation, Virginia Polytechnic Institute and State University, 100 Cheatham Hall, Blacksburg, VA 24061-0321, USA Virginia Marine Resources Commission, 2600 Washington Avenue, Newport News, VA 23607, USA 3 Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0321, USA 2 *Corresponding author: tel: +1 540 231 5749; fax: +1 540 231 7580; e-mail: Jiao, Y., O’Reilly, R., Smith, E., and Orth, D. Integrating spatial synchrony/asynchrony of population distribution into stock assessment models: a spatial hierarchical Bayesian statistical catch-at-age approach. – ICES Journal of Marine Science, 73: 1725– 1738. Received 20 May 2015; revised 7 February 2016; accepted 21 February 2016. In many marine fisheries assessments, population abundance indices from surveys collected by different states and agencies do not always agree with each other. This phenomenon is often due to the spatial synchrony/asynchrony. Those indices that are asynchronous may result in discrepancies in the assessment of temporal trends. In addition, commonly employed stock assessment models, such as the statistical catch-at-age (SCA) models, do not account for spatial synchrony/asynchrony associated with spatial autocorrelation, dispersal, and environmental noise. This limits the value of statistical inference on key parameters associated with population dynamics and management reference points. To address this problem, a set of geospatial analyses of relative abundance indices is proposed to model the indices from different surveys using spatial hierarchical Bayesian models. This approach allows better integration of different surveys with spatial synchrony and asynchrony. We used Atlantic weakfish (Cynoscion regalis) as an example for which there are state-wide surveys and expansive coastal surveys. We further compared the performance of the proposed spatially structured hierarchical Bayesian SCA models with a commonly used Bayesian SCA model that assumes relative abundance indices are spatially independent. Three spatial models developed to mimic different potential spatial patterns were compared. The random effect spatially structured hierarchical Bayesian model was found to be better than the commonly used SCA model and the other two spatial models. A simulation study was conducted to evaluate the uncertainty resulting from model selection and the robustness of the recommended model. The spatially structured hierarchical Bayesian model was shown to be able to integrate different survey indices with/without spatial synchrony. It is suggested as a useful tool when there are surveys with different spatial characteristics that need to be combined in a fisheries stock assessment. Keywords: Atlantic weakfish, spatial hierarchical Bayesian model, spatial synchrony/asynchrony, statistical catch-at-age. Introduction Many marine fisheries assessments require the modeller to combine survey population abundance indices from different states and agencies. A potentially important problem is that the indices do not always agree with each other and the use of different indices may lead to different decisions (NEFSC, 2008; NDPSWG, 2009). The discrepancy among different survey indices can be attributed to the spatial and temporal aggregation of fish distributions, nonrandom search behaviour of fishers, fishing power changes, gear selectivity, gear saturation, and other factors (Pope and Garrod, 1975; MacCall, 1976; Rose and Leggett, 1991). Spatial heterogeneity refers to the uneven distribution of observations of interest, such as a trait, event, fish abundance, density, or relationship across a region (Anselin, 2010). Even for well-designed surveys, the indices of abundance can suggest different trends at different locations because of temporal changes in the densities of the population in different locations, shown as spatial asynchronous patterns (Buonaccorsi et al., 2001; Liebhold et al., 2004). Spatial heterogeneity among locations # International Council for the Exploration of the Sea 2016. All rights reserved. For Permissions, please email: Yan Jiao 1 *, Rob O’Reilly 2, Eric Smith 3, and Don Orth 1 1726 may not change over time but if it does change it would show as spatial asynchrony. Reasons for spatial synchrony/asynchrony include extrinsic environmental stochasticity (Moran effect; Moran, 1953), non-linear density-dependency, and dispersal and species interactions (Heino et al., 1997; Hudson and Cattadori, 1999; Buonaccorsi et al., 2001; Cheal et al., 2007; Vasseur, 2007; Haynes et al., 2009; Massie et al., 2015). Atlantic weakfish (Cynoscion regalis) is used as an example stock in our study. It is very representative of the species along the western Y. Jiao et al. coast of the Atlantic Ocean because the surveys available for Atlantic weakfish are also available for most other species distributed in this area. Each state along the North Atlantic has its own localized surveys, and there are also two expansive coastal surveys for this species (Supplementary Table S1; Figure 1). The discrepancy among different survey indices is considerable (NEFSC, 2009). A preliminary analysis based on cross correlation among relative abundance indices that are not standardized, but were reported by each state and agency (NEFSC, 2009), indicated that most of the Figure 1. Map of western Atlantic with states that handle Atlantic weakfish surveys indicated. This figure is available in black and white in print and in colour at ICES Journal of Marine Science online. 1727 A spatial hierarchical Bayesian statistical catch-at-age approach Data and methods The Atlantic weakfish population was selected as an example and its most recent stock assessment information was used. Data used were from the Atlantic States Marine Fisheries Commission Weakfish Technical Committee (NEFSC, 2009). Detailed information on the catch-at-age matrix and relative abundance surveys are available from the same report. Following the recommendation from the weakfish technical committee, catch data from 1982 to 2007 were used (Supplementary Figure S1). There were 15 relative abundance indices available for this fishery (Supplementary Figure S2). Among them, six provided age-structured relative abundance indices (Supplementary Figure S2a), and eight of them provided age 1 relative abundance that were used in the assessment to calibrate recruitment dynamics (Supplementary Figure S2b and Table S1). Detailed description on the relative abundance indices is given in Supplementary data, Table S1. A series of stochastic age-structured models was constructed to represent the dyna (...truncated)