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Modeling spatiotemporal variability of fish stocks is important for interpreting changes in magnitude and distribution over time. Biomass indices for four stocks with differences in life history, spatial extent, proportion of zero observations, biomass trajectory, and stock status were modeled using the Vector Autoregressive Spatio-Temporal (VAST) model. We iteratively tested model settings following a workflow developed to find the best model for each stock in the context of developing an absolute index of abundance from fisheries independent data. The best model was determined based on AIC, RMSE, cross-validation, and several metrics of deviation from design-based estimates if one is available for comparison. Biomass indices from the best VAST model had good agreement with design-based indices in three of the stocks. Improvements in model fit tended to asymptote at around 1000 knots for all stocks. The generalized gamma error distribution with a logit link was the best model for two of the stocks, and the gamma error distribution with Poisson link was the best model for the other two. Occasionally a model was selected with much larger estimated biomass compared to the design-based estimates, and metrics based on comparisons with design-based estimates helped resolve model selection in these instances. Simulation self-tests were performed from the best model and fitted with several estimation models, and the model selection tools comparing fitted models to design-based indices calculated from the simulated data were found to be robust in recovering the specifications of the original model. Additional visualizations for spatial residuals and clustering were used to aid interpretation of model fit and to highlight latent spatial patterns. These metrics may be useful in identifying important covariates. We added a depth covariate to the best model for each stock to demonstrate how future model building might proceed. [ABSTRACT FROM AUTHOR]

Highlights • Stock, ecosystem, habitat, and climate assessments use different methods and vocabulary. • Population density across space, time, and species is a "common currency". • I provide guidance for 15 major decisions when using Vector Autoregressive Spatio-Temporal (VAST) models. • Three case-studies illustrate decisions in different assessment types. • Economic and survey-optimization assessments are important future research. Abstract Fisheries scientists provide stock, ecosystem, habitat, and climate assessments to support interdisplinary fisheries management in the US and worldwide. These assessment activities have evolved different models, using different review standards, and are communicated using different vocabulary. Recent research shows that spatio-temporal models can estimate population density for multiple locations, times, and species, and that this is a "common currency" for addressing core goals in stock, ecosystem, habitat, and climate assessments. I therefore review the history and "design principles" for one spatio-temporal modelling package, the Vector Autoregressive Spatio-Temporal (VAST) package. I then provide guidance on fifteen major decisions that must be made by users of VAST, including: whether to use a univariate or multivariate model; when to include spatial and/or spatio-temporal variation; how many factors to use within a multivariate model; whether to include density or catchability covariates; and when to include a temporal correlation on model components. I finally demonstrate these decisions using three case studies. The first develops indices of abundance, distribution shift, and range expansion for arrowtooth flounder (Atheresthes stomias) in the Eastern Bering Sea, showing the range expansion for this species. The second involves "species ordination" of eight groundfishes in the Gulf of Alaska bottom trawl survey, which highlights the different spatial distribution of flathead sole (Hippoglossoides elassodon) relative to sablefish (Anoplopoma fimbria) and dover sole (Microstomus pacificus). The third involves a short-term forecast of the proportion of coastwide abundance for five groundfishes within three spatial strata in the US West Coast groundfish bottom trawl survey, and predicts large interannual variability (and high uncertainty) in the distribution of lingcod (Ophiodon elongatus). I conclude by recommending further research exploring the benefits and limitations of a "common currency" approach to stock, ecosystem, habitat, and climate assessments, and discuss extending this approach to optimal survey design and economic assessments. [ABSTRACT FROM AUTHOR]

• Scale of estimated abundance indices varies for different distribution functions using delta models. • Comparison with design-based indices shows similar scale for delta-gamma and Tweedie models. • Epsilon bias-correction mitigates sensitivity to spatial resolution during index standardization. • Simulation experiment confirms that delta-gamma and Tweedie work well even when mis-specified. Delta-models (a.k.a. hurdle models) are widely used to fit biomass samples that include zeros and a skewed response for positive catches, and spatio-temporal extensions of these models are increasingly used to quantify trends in abundance (i.e., estimate abundance indices). Previous research has shown estimated indices are proportional to changes in abundance. However, little research has tested the performance of delta-models for estimating "scale"; that is, whether abundance indices are not just proportional to population changes but also have the correct absolute value. We use data for twenty species in the eastern Bering Sea and Gulf of Alaska as well as a factorial experiment conditioned on data for Gulf of Alaska Pacific cod to support five conclusions related to scale in spatio-temporal delta-models. First, we show that conventional (nonspatial) delta-models are surprisingly sensitive to the a priori choice of probability distribution for positive catches, where gamma and Tweedie models give similar scale estimates but other distributions generally differ. Second, these same distributions also estimate widely different scales when using spatio-temporal delta-models, and the delta-gamma and Tweedie models provide similar scale to design-based indices. Third, model selection using marginal AIC often identifies the lognormal distribution as most parsimonious, despite it resulting in systematically higher abundance than design-based indices for many species. Fourth, scale is sensitive to the spatial resolution (i.e., number of knots) used in fitting the spatio-temporal model when using a naïve "empirical Bayes" estimator, but less sensitive when applying an epsilon bias-correction estimator. Fifth, the factorial simulation experiment suggests that the Tweedie and delta-gamma distributions perform well even when applied to data simulated from an inverse-Gaussian or lognormal distribution, whereas the opposite is not true. We conclude that index scale is sensitive to delta-model specification, and we make five recommendations when using spatio-temporal delta-models for index standardization: (1) apply the epsilon or other bias-correction methods to reduce sensitivity of index scale on spatio-temporal model resolution; either (2) compare the scale of delta-model indices with that of design-based indices when design-based indices are available or (3) use the delta-gamma or Tweedie distribution by default when design-based indices are not available; (4) do not assume that AIC will identify the model specification that results in the most appropriate scale; and (5) consider apparent mismatches in index scale depending upon whether an assessment model specifies or estimates the associated catchability coefficient and whether the design-based index is believed to measure total abundance for a fully-selected age or length-class. [ABSTRACT FROM AUTHOR]

• Calanus , Metridia and Neocalanus copepods were sampled during pollock age-0 year. • Strong correlation between lipid-rich copepods and pollock abundance 3 years later. • Higher correlation to age-3 pollock with model than sample-based copepod indices. • Age-3 pollock indices significantly related to cold pool area (age-0 year). In the southeastern Bering Sea, years with above-average sea ice extent have been associated with elevated abundances of large lipid-rich copepods in both net tows and age-0 walleye pollock (Gaduschalcogrammus) diets, followed by high overwinter pollock survival and stronger recruitment into the fishery three years later. In this study, we directly compare large copepod abundances of taxa important in age-0 pollock diets (Calanus glacialis/marshallae , Metridia pacifica and Neocalanus spp.) to age-3 pollock abundance from stock assessments for year classes 2002–2015 (excluding 2013). Copepod samples from bongo nets were collected on fishery oceanography surveys in late summer during warm (low ice) and cold (high ice) climate stanzas. In addition to mean estimates of large copepods among stations (sample-based), we implemented a spatial delta-generalized linear mixed model using the Vector Autoregressive Spatio-Temporal (VAST) package to account for variations in survey coverage among years. Positive significant linear relationships were found for both of these estimates of large copepods during the age-0 year and the abundance of these pollock at age-3. Correlations were stronger using VAST model-based indices compared with sample-based indices (R 2 = 0.74 versus 0.43, respectively, all copepod taxa combined). A significant relationship was also observed between the bottom cold pool (< 2 °C) area (indicative of sea ice coverage in the prior winter) during the age-0 year and subsequent age-3 pollock abundance (R 2 = 0.56) and recruits per spawner, (ln(age-3 abundance /spawning stock biomass), R 2 = 0.77). Consequently, the large copepod index or cold pool index may be used to predict future recruitment success of pollock three years in advance. Results provide support for the revised oscillating control hypothesis that suggests as the climate warms, reductions in sea ice and consequent reduced availability of ice-associated algae, an early spring food source, could be detrimental to large copepods and recruitment of the pollock stock in the region. [ABSTRACT FROM AUTHOR]

• A CAPAM workshop highlighted five conclusions about spatio-temporal models for index standardization. • These models improve density predictions in areas with little to no data. • They can weight density predictions by area to account for spatial changes in sampling intensity. • They can calculate age/length composition and weight these by fishery catch to inform fishery removals. • They can estimate distribution shifts, and combine data from multiple sources to improve spatial scale for indices. Abstract Spatio-temporal models are increasingly used to develop indices of population abundance from fishery-dependent and –independent data. Developments in spatio-temporal index standardization were discussed at a workshop hosted by The Center for the Advancement of Population Assessment Methodology (CAPAM) titled " Development and application of spatio-temporal models to derive indices of relative abundance " (La Jolla, CA, USA; Feb. 26-March 2, 2018). This special issue includes ten submissions that highlight potential benefits arising from spatio-temporal index standardization including: (1) improved prediction for areas with little-to-no data; (2) capacity to weight densities by area to account for sampling rates that vary spatially; (3) calculation of the composition (e.g. age or length) of the indices and to weight predictions by catch to inform the composition of fishery removals, (4) estimation of distribution shifts and range expansion/contraction; and (5) capacity to combine data sources. The articles in this Special Issue highlight the need for continued development and testing for spatio-temporal index standardization methods, so that the relative strengths and weaknesses of different approaches are fully understood. The articles also identify topics that warrant further research including improved model diagnostics, accounting for biased rates of sampling ("preferential sampling"), and improvements in computational efficiency. Keywords: Index standardization; Spatial analysis; Vector autoregressive spatio-temporal model; VAST; Distribution shift; Stock assessment; Catch-per-unit-effort Spatio-temporal models are increasingly used to develop indices of population abundance from fishery-dependent and –independent data. Developments in spatio-temporal index standardization were discussed at a workshop hosted by The Center for the Advancement of Population Assessment Methodology (CAPAM) titled " Development and application of spatio-temporal models to derive indices of relative abundance " (La Jolla, CA, USA; Feb. 26-March 2, 2018). This special issue includes ten submissions that highlight potential benefits arising from spatio-temporal index standardization including: (1) improved prediction for areas with little-to-no data; (2) capacity to weight densities by area to account for sampling rates that vary spatially; (3) calculation of the composition (e.g. age or length) of the indices and to weight predictions by catch to inform the composition of fishery removals, (4) estimation of distribution shifts and range expansion/contraction; and (5) capacity to combine data sources. The articles in this Special Issue highlight the need for continued development and testing for spatio-temporal index standardization methods, so that the relative strengths and weaknesses of different approaches are fully understood. The articles also identify topics that warrant further research including improved model diagnostics, accounting for biased rates of sampling ("preferential sampling"), and improvements in computational efficiency. [ABSTRACT FROM AUTHOR]

• Distribution modelling and CPUE standardizations showed similar trends. • Trends were inconsistent with biological parameters or integrated population models. • Fisheries catch rates are unlikely to represent biomass. • Distribution modelling standardization could not account for fisher targeting. • Single-area integrated population models outperformed distribution modelling. Most models used for assessing the status of fish stocks and providing quantitative advice for fisheries management are not spatially explicit despite the well-known spatial heterogeneity of fish populations. Statistical spatial distribution modelling, which can derive spatially-resolved biomass from catch rates, is a method increasingly used to infer trends in population biomass, particularly where integrated population models are not available. Although the spatial distribution modelling tool VAST was developed to analyze survey data, such methods have also been used with fisheries-dependent catch and effort data, particularly when survey data are not available. We developed a statistical spatial distribution model for Antarctic toothfish (Dissostichus mawsoni) in the Ross Sea region of the Southern Ocean using the VAST (Vector Autoregressive Spatio-Temporal model) approach. We based the VAST model on catch-rate (catch per unit effort) data from the long-line fishery and compared the biomass time series obtained to that of existing single-area and spatially-explicit integrated population models which have also been developed for this population. The time series obtained from the statistical spatial distribution modelling approach was highly variable between years, inconsistent with constraints imposed on population dynamics by biological parameters, and substantially different from biomass trends obtained from the integrated models. Although it has been used successfully in other analyses, in this instance, the spatial distribution modelling could not overcome fine-scale spatial and vessel-based variability in fishery catch rates to estimate the underlying abundance of toothfish at the scale of the Ross Sea region measurable with the more-informed integrated models. [ABSTRACT FROM AUTHOR]