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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.

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Bay of fundy scallops spa 4 l.jpg

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


Delay difference model l.jpg
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


Population equation l.jpg
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


Simplified population equation l.jpg
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


The data l.jpg
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


Some priors l.jpg
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


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