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

2Chapter 9 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.  and  assumed to be known constants.

3Chapter 9 Population equation N t : Number of fully recruited scallops in year t B t : Biomass of fully recruited scallops in year t R t : Number of scallops recruiting in year t s t : Survival rate in year t k : Age of recruitment which lead to

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

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

6Chapter 9 Some priors K=B 1 : K ~LN(8.006,1/ ), (10-90%)=(600,15000) S ~Unif(0.10,0.99) For lognormal error terms LN(0  2 ), say, inverse gamma prior on  2 chosen so that mean(  2 )=sd(  2 ), with mean(  2 ) corresponding to a CV of either 50% or 75%.