Bay of Fundy scallops SPA 4

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Bay of Fundy scallops SPA 4
Case study

• Smith et al. 2005
• Delay-difference model
• Data from 1983 to 2005 (23 years)
• Multiple data sequences
• Prediction under various future exploitation
  rates.

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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.
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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
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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
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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
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Some priors

• KB1 KLN(8.006,1/1.57754), (10-90)(600,15000)
  
• SUnif(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.