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

Abstract

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.

References Agresti, A., & Coull, B. A. (1998). Approximate is better than “exact” for interval estimation of binomial proportions. American Statistician, 52, 119–126. Ahrestani, F. S., Hebblewhite, M., & Post, E. (2013). The importance of observation versus process error in analyses of global ungulate populations. Scientific Reports, DOI: 10.1038/srep03125 Andelman, S. J., Groves, C., & Regan, H. M. (2004). A review of protocols for selecting species at risk in the con- text of US Forest Service viability assessments. Acta Oecologica, 26, 75–83. Anderson, L. E., Lee, S. T., & Levin, P. S. (2013). Costs of delaying conservations: Regulations and recreational values of exploited and co-occurring species. Land Economics, 89, 371–385. Beaudreau, A. H., & Whitney, E. J. (2016). Historical patterns and drivers of spatial changes in recreational fishing activity in Puget Sound, Washington. PLoS ONE, 11, e0152190 Beissinger, S. R. (2002). Population viability analysis: Past, present and future. In S. R. Beissinger, & D. R. Mccullough (Eds.), Population viability analysis (pp. 5–17). Chicago, IL: The University of Chicago Press. Buckland, S. T., Newman, K. B., Thomas, L., & Koesters, N. B. (2004). State-space models for the dynamics of wild animal populations. Ecological Modeling, 117, 157–175. doi:0.1016/j.ecolmodel.2003.08.002 Burnham, K. P., & Anderson, D. R. (1998). Model selection and inference: A practical information-theoretic approach. New York, NY: Springer-Verlag. Butchart, S. H. M., & Bird, J. P. (2010). Data deficient birds on the IUCN Red List: What don't we know and why does it matter? Biological Conservation, 143, 239–247. doi:10.1016/j.biocon.2009.10.008 Dennis, B., Munholland, P. L., & Scott, J. M. (1991). Estimation of growth and extinction parameters for endangered species. Ecological Monographs, 61, 115–143. Dennis, B., Ponciano, J. M., Lele, S. R., Taper, M. L., & Staples, D. F. (2006). Estimating density dependence, process noise, and observation error. Ecological Monographs, 76, 323–341. doi:10.1890/0012-9615(2006)76[323:eddpna]2.0.co;2 Dennis, B., Ponciano, J. M., & Taper, M. L. (2010). Replicated sampling increases efficiency in monitoring biological populations. Ecology, 91, 610–620. Drake, J.S., Berntson, E. A., Cope, J. M., Gustafson, R. G., Holmes, E. E., Levin, P.S., Tolimieri, N., Waples, R.S., Sog- ard, S.M., and Williams, G.D. (2010). Status review of ve rock sh species in Puget Sound, Washington: bocaccio (Sebastes pau- cispinis), canary rock sh (S. pinniger), yelloweye rock sh (S. ruberrimus), greenstriped rock sh (S. elongatus), and redstripe rock sh (S. proriger) U.S. Dept. Commer., NOAA Tech. Memo. NMFS-NWFSC-108, 234 p. Hampton, S. E., Holmes, E. E., Scheef, P., Scheuerell, M. D., Katz, S., Pendleton, D. E., & Ward, E. J. (2013). Quantifying effects of abiotic and biotic drivers on community dynamics with multivariate autoregressive models. Ecology, 94, 2663–2669. Harvey, A. C. (1990). Forecasting, structural time series models and the Kalman filter (p. 572). Cambridge: Cambridge University Press. Hilborn, R., Quinn, T. P., Schindler, D. E., & Rogers, D. E. (2003). Biocomplexity and fisheries sustainability. Proceedings of the National Academy of Sciences of the United States of America, 100, 6564–6568. Hinrichsen, R. A., & Holmes, E. E. (2009). Using multivariate state-space models to study spatial structure and dynamics. In: R. S. Cantrell, C. Cosner & S. Ruan (Eds.) Spatial ecology (pp. 145–166). Boca Raton, FL: CRC/Chapman Hall. Holmes, E. E. (2001). Estimating risks in declining populations with poor data. Proceedings of the National Academy of Sciences of the United States of America, 98, 5072–5077. Holmes, E. E. (2004). Beyond theory to application and evaluation: Diffusion approximations for population viability analysis. Ecological Applications, 14, 1272–1293. Holmes, E. E., Sabo, J. L., Viscido, S. V., & Fagan, W. F. (2007). A statistical approach to quasi-extinction forecasting. Ecology Letters, 10, 1182–1198. Holmes, E. E., & Semmens, B. (2004). Population viability analysis for metapopulations: A diffusion approximation approach. In: I. Hanski & O. E. Gaggiotti (Eds.), Ecology, genetics, and evolution of metapopulations (pp. 565–598). Elsevier Press, San Diego, California: Elsevier Press. Holmes, E. E., Ward, E. J., & Scheuerell, M. D. (2014). Analysis of multivariate time-series using the MARSS package (pp. 238). Seattle, WA: NOAA Fisheries, Northwest Fisheries Science Center. Holmes, E. E., Ward, E. J., & Wills, K. (2012). Marss: Multivariate autoregressive state-space models for analyzing time-series data. The R Journal, 4, 11–19. Humbert, J.-Y., Mills, L. S., Horne, J. S., & Dennis, B. (2009). A better way to estimate population trends. Oikos, 118, 1940–1946. doi:10.1111/j.1600-0706.2009.17839.x Ives, A. R., Dennis, B., Cottingham, K. L., & Carpenter, S. R. (2003). Estimating community stability and ecological interactions from time series data. Ecological Monographs, 73, 301–330. Knape, J. (2008). Estimability of density dependence in models of time series data. Ecology, 89, 2994–3000. Knape, J., Besbeas, P., & De Valpine, P. (2013). Using uncertainty estimates in analyses of population time series. Ecology, 94, 2097–2107. Linden, A., & Knape, J. (2009). Estimating environmental effects on population dynamics: Consequences of observation error. Oikos, 118, 675–680. Love, M. S., Yoklavich, M., & Thorsteinson, L. (2002). The rockfishes of the Northeast Pacific (p. 404). Berkley and Los Angeles: University of California Press. Morais, A. R., Siqueira, M. N., Lemes, P., Maciel, N. M., De Marco, P. Jr., & Brito, D. (2013). Unraveling the conservation status of data deficient species. Biological Conservation, 166, 98–102. doi:10.1016/j.biocon.2013.06.010 Morris, W. E., & Doak, D. F. (2002). Quantitative conservation biology: Theory and practice of population viability analysis (p. 480). Sunderland, MA: Sinauer Associates. Pietsch, T. W., & Orr, J. W. (2015). Fishes of the Salish Sea: a compilation and distributional analysis. NOAA Professional Paper, NMFS, 18, 106, doi:10.7755/PZRP.18 R Core Team. 2014. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. REEF. 2014. Reef Environmental Education Foundation. World Wide Web electronic publication. www.reef.org, Accessed 11 October 2014. Rueda-Cediel, P., Anderson, K. E., Regan, T. J., Franklin, J., Regan, H. M. (2015). Combined Influences of Model Choice, Data Quality, and Data Quantity When Estimating Population Trends. PLoS ONE, 10(7), e0132255. doi:10.1371/journal.pone.0132255 Schindler, D. E., Armstrong, J. B., & Reed, T. E. (2015). The portfolio concept in ecology and evolution. Frontiers in Ecology and the Environment, 15, 257–263. doi:10.1890/140275 Shumway, R. H., & Stoffer, D. S. (2010). Time series analysis and its applications: With R examples (p. 596). New York, NY: Springer-Verlag. Smith, D., Punt, A., Dowling, N., Smith, A., Tuck, G., & Knuckey, I. (2009). Reconciling approaches to the assessment and management of data-poor species and fisheries with Australia's harvest strategy policy. Marine and Coastal Fisheries: Dynamics, Management, and Ecosystem Science, 1(1), 244–254. doi:10.1577/C08-041.1 Thibaut, L. M., Connolly, S. R., & Sweatman, H. P. A. (2012). Diversity and stability of herbivorous fishes on coral reefs. Ecology, 93, 891–901. Tonnes, D., Bhuthimethee, M., Sawchuck, J., Tolimieri, N., Andrews, K., & Nichols, K. (2016). Yelloweye rockfish (Sebastes ruberrimus), canary rockfish (Sebastes pinniger), and bocaccio (Sebastes paucispinis) of the Puget Sound/Georgia Basin: 5-Year Review: Summary and Evaluation. Seattle WA, USA: NOAA's National Marine Fisheries Service, Office of Protected Resources. Ward, E. J., Chirakkal, H., González-Suárez, M., Aurioles-Gamboa, D., Holmes, E. E., & Gerber, L. (2010). Inferring spatial structure from time-series data: Using multivariate state-space models to detect metapopulation structure of California sea lions in the Gulf of California, Mexico. Journal of Applied Ecology, 47, 47–56. doi:10.1111/j.1365-2664.2009.01745.x Williams, G. D., Levin, P. S., & Palsson, W. A. (2010). Rockfish in Puget sound: An ecological history of exploitation. Marine Policy, 34, 1010–1020. doi:10.1016/j.marpol.2010.02.008 Zuur, A. F., Tuck, I. D., & Bailey, N. (2003). Dynamic factor analysis to estimate common trends in fisheries time series. Canadian Journal of Fisheries and Aquatic Sciences, 60, 542–552.