Multispecies Catch at Age Model (MSCAGEAN): incorporating predation interactions and statistical assumptions for a predator ‑ prey system in the eastern Bering Sea Jesus Jurado-Molina University of Washington Patricia A. Livingston Alaska Fisheries Science Center

Fisheries models Age Structured Models Statistical Assumptions Statistical Catch at Age Models Assumption: Population Isolated Constant Natural Mortality

Fisheries models Virtual Population Analysis Predation Equations M=M1+M2 Multispecies Virtual Population Analysis (MSVPA) No statistical assumptions on error structure included

Multispecies Catch at age Analysis? Predation interactions Age structured model Statistical assumptions on error structure Multispecies Catch at age Analysis

Objectives: To add the predation equations to a CAGEAN model (MSCAGEAN): Comparison of the MSCAGEAN results to the ones estimated with the multispecies VPA, the Multispecies Forecasting Model (MSFOR) and the single species CAGEAN.

Input and outputs of MSVPA-MSFOR

Statistical models Error assumption Prior information Data Model equations

Predation equations S - suitability coefficient of prey p for predator i BS - suitable prey biomass R - annual ration of the predator i W - weight at age of prey p M2 - predation mortality

Multispecies CAGEAN Error assumption Prior information Data Model equations Predation equations

Equations:

Advantages: Multispecies approach We can use the tools used in single species stock assessments Likelihood profile Bayesian statistics (probability distributions) Model selection (Akaike’s information criterion,likelihood ratio )

Assumptions Stomach content measured without error Suitabilities constant (estimated as the average of the annual suitabilities) Recruitment for the simulation is log-normal distributed Recruitment of age-0 individuals for the simulation takes place in the third quarter

Walleye pollock and Pacific cod interactions Walleye pollockPacific cod Fishery

Methods Initial run of the MSVPA updated to Run of Multispecies forecasting (F 40%). Spawning Biomass in 2015 as indicator of performance. Multispecies Catch at Age Analysis updated to 1998 Single species CAGEAN updated to 1998

MSVPA and MSCAGEAN results: Age-0 walleye pollock Natural mortality (1990) MSCAGEANMSVPA 1.55 M2 = 1.70 ± 57

MSVPA and MSCAGEAN results: suitability coefficients MSCAGEANMSVPA ± 0.140

MSVPA AND MSCAGEAN results: Spawning biomass in 2015 MSCAGEANMSFOR SSB = 5.52E6 ± 2.36E6 SSB = 1.33E7 ± 5.25E6 SUM=SUM+1 SUM=SUM+L

MSCAGEAN and CAGEAN results: Spawning biomass in 2015 CAGEANMSCAGEAN SSB = 1.19E07 ± 5.06E06 SSB = 1.33E07 ± 5.25E06

Future tasks To implement the predation equations in the stock assessments methods used in the AFSC assessments