Population assessment using multivariate time-series analysis: A case study of rockfishes in Puget Sound

Estimating a population's growth rate and year-to-year variance is a key component of population viability analysis (PVA). However, standard PVA methods require time series of counts obtained using consistent survey methods over many years. In addition, it can be difficult to separate observation and process variance, which is critical for PVA. Time-series analysis performed with multivariate autoregressive state-space (MARSS) models is a flexible statistical framework that allows one to address many of these limitations. MARSS models allow one to combine surveys with different gears and across different sites for estimation of PVA parameters, and to implement replication, which reduces the variance-separation problem and maximizes informational input for mean trend estimation. Even data that are fragmented with unknown error levels can be accommodated. We present a practical case study that illustrates MARSS analysis steps: data choice, model set-up, model selection, and parameter estimation. Our case study is an analysis of the long-term trends of rockfish in Puget Sound, Washington, based on citizen science scuba surveys, a fishery-independent trawl survey, and recreational fishery surveys affected by bag-limit reductions. The best-supported models indicated that the recreational and trawl surveys tracked different, temporally independent assemblages that declined at similar rates (an average of -3.8% to -3.9% per year). The scuba survey tracked a separate increasing and temporally independent assemblage (an average of 4.1% per year). Three rockfishes (bocaccio, canary, and yelloweye) are listed in Puget Sound under the US Endangered Species Act (ESA). These species are associated with deep water, which the recreational and trawl surveys sample better than the scuba survey. All three ESA-listed rockfishes declined as a proportion of recreational catch between the 1970s and 2010s, suggesting that they experienced similar or more severe reductions in abundance than the 3.8-3.9% per year declines that were estimated for rockfish populations sampled by the recreational and trawl surveys.