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. Delay-difference model. It is assumed that weight-at-age follows the equation.
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.
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
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
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)
Lt: Estimated number of recruited scallops in year t
K=B1: K~LN(8.006,1/1.57754), (10-90%)=(600,15000)
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%.