Bay of Fundy scallops SPA 4

1. Case study Bay of Fundy scallops SPA 4 • Smith et al. 2005 • Delay-difference model • Data from 1983 to 2005 (23 years) • Multiple data sequences • Prediction under various future exploitation rates. Chapter 9

2. Delay-difference model It is assumed that weight-at-age follows the equation (which equivalent to assuming a von-Bertalanffy curve for weight as a function of age. a and r assumed to be known constants. Chapter 9

3. Population equation Nt: Number of fully recruited scallops in year t Bt: Biomass of fully recruited scallops in year t Rt: Number of scallops recruiting in year t st: Survival rate in year t k: Age of recruitment which lead to Chapter 9

4. Simplified population equation If the average weight of recruited scallops, wk+, is assumed known, then the popn equation can be simplified to and separating natural and fishing mortality, we get Chapter 9

5. The data Terms contributing to the likelihood are given by: It: Estimated biomass of recruited scallops in year t R't: Biomass of scallops recruiting in year t Zt: Number of clappers in year t (used to provide information about natural mortality) Also? Lt: Estimated number of recruited scallops in year t Chapter 9

6. Some priors K=B1: K~LN(8.006,1/1.57754), (10-90%)=(600,15000) S~Unif(0.10,0.99) For lognormal error terms LN(0,s2), say, inverse gamma prior on s2 chosen so that mean(s2)=sd(s2), with mean(s2) corresponding to a CV of either 50% or 75%. Chapter 9