Model And Calibration

  • 3 species: Cod, Sprat, Herring

3 species : Cod, Sprat, Herring

The Age-structured Model

this model  takes into account the predator-prey relationship between cod and the two other species and is discrete-time, discrete-aged structured.

xi0t=s=1Sγiswisxistxi1,t+1=φi(xi0t)xi,s+1,t+1=αis(xisthist)for s=1,,S2xi,S,t+1=αi,S1(xi,S1,thi,S1,t)+αiS(xiSthiSt).

where xist denotes  the number of fish of species i∈{C,S,H}, where C stands for cod, S for sprat, and H for herring, in age group s=1,…,S and at the beginning of period t=0,1,…t.
αis>0 denotes age-specific survival rates,
γis>0 denotes age-specific proportions of mature individuals,
ωis to denote the mean weights (in kilograms). For cod, all of these parameters are assumed to be constant . For sprat and herring, we assume that proportions of mature individuals and weights are constant, but the survival rates depend on cod spawning stock biomass. 
The recruitment function for species i is denoted by φi(⋅) and the spawning biomass by xi0t, hist denotes the number of fish harvested from cohort s of species i in period t.

The modeling of profits of the cod fishery, is based on the specification from Quaas et al. (2012) with age-specific prices and a cost function of the Spence type .
Thus, profits of the cod fishery in year t are:

where pCs are prices for cod in age group s, instantaneous fishing mortality FCt equals instantaneous effort, and cC is the unit effort cost for the cod fishery.
Sprat and herring are modeled as schooling fisheries , where the market price pi is assumed to be independent of age.
 The profits in the sprat and herring fisheries thus are:

For the harvesting benefits Π(h,x) it is assumed that the fishery manager has some aversion against income inequality across fisheries, thus:

We assume that the aim is to maximize the present value of benefits, i.e., the sum of net benefits from harvest plus biodiversity value:


,with harvesting benefits Π(h,x) and taking a biodiversity value into account. Here, we use two versions of the biodiversity index:
In one version, we use the spawning stock numbers:

in the other one, we use the spawning stock biomasses, xi0t

Updated on 14/09/2016