Sequential Population Analysis (SPA) is a common model used to estimate the size of fish stocks in Canada and many other countries. SPA is a version of cohort analysis in which commercial catches, other sources of mortality, and the results from fisheries surveys are used. These are longitudinal data measured with error. The objective of this research is to improve the data inputs and the modelling method. A common theme involves the use of random effects models.
We will use generalized linear mixed models (GLMM's) with cluster and length-autocorrelated random effects to estimate the relative fishing efficiency of one survey vessel compared to another. Survey catches are used when estimating an SPA, and if there is a change in survey vessels or sampling protocols (e.g. net) then this has to be accounted for in the estimation. Otherwise we may mistake a change in survey catch rates to indicate a change in stock size when the change in catch rates may simply be due to the change in survey protocols. We will also examine the role length-based processes have in an age-structured model like SPA, and make adjustments for such processes. We will also improve estimates of stock maturities using GLMM's in which some random regression parameters are autocorrelated. Maturities are combined with SPA results to estimate spawning stock biomass (SSB) - an important stock quantity. The problem is that maturity data are updated annually for unfinished (e.g. recent) cohorts and this can result in substantial changes in estimates, and substantial retrospective differences in SSB estimates provided by annual stock assessments.
Tagging data can also be used to refine and improve SPA estimates. A difficult problem when analyzing tag-returns from length-selective fisheries is accounting for fish growth between the time of release and capture. Recently, random-effects models have been used for this purpose, and we wish to adapt these approaches for an extensive data set involving cod tagged off the coast of Newfoundland since 1997.
The final area of research involves developing diagnostics to detect when SPA may be in serious error. Highly parameterized SPA's can mask serious violations in model assumptions, and this can create large biases in stock estimates. We will investigate methods that indicate when an SPA is seriously misspecified, and what the source of the misspecification is.