Selectivity and two biomass measures in an age-based assessment of Antarctic krill (Euphausia superba)

An integrated, age-structured model was fitted to different combinations of survey data using two forms of selectivity (logistic or double-logistic) with time-constant or annually varying selectivity to investigate the population dynamics of Antarctic krill (Euphausia superba) near the Antarctic Peninsula. The data were from surveys conducted by the U.S. Antarctic Marine Living Resources Program around the South Shetland Islands from 1992 to 2011. Two indices of krill biomass based on (1) trawl-net samples and (2) hydroacoustic sampling were combined with length-compositions from the nets. Sixteen model configurations using different combinations of the two biomass surveys with the various options for modeling selectivities were examined. Parameters were estimated in phases with the sequential order of the phases randomized until an invertible Hessian matrix was obtained. Model consistency for the estimates of derived quantities was tested using simulated data. Annual trends in the estimates of total biomass, spawning biomass, and recruitment were similar among different configurations assuming time-constant selectivity, but the absolute scaling ranged widely depending on which biomass indices were used. All configurations with time-constant selectivities were able to reproduce the derived quantities of the operating model when fitted to simulated data. Annually varying selectivities produced more variable estimates of the trends in population biomass, but less variable estimates of scale, compared to time-constant configurations fitted to the same data. The models with annually varying selectivities did not produce invertible Hessian matrices, and four of these configurations could not reproduce the derived parameters of their operating model when fitted to simulated data. Using AIC, the model with logistic, time-constant selectivities was selected as the best configuration to fit both sources of biomass data. The two-stage approach of first randomizing the phase order until an invertible Hessian matrix is achieved and then verifying the reproducibility of the estimates of derived quantities using simulated data could be employed in any integrated stock assessment with parameters estimated in phases.