in the economic model. The total catch

feeds then back into the biological model affecting the stock dynamics. The two sub-models have been specifically estimated and calibrated for the NEA cod fishery using data from the time period 1978–2007 (Table 1). The biological sub-model is based on a previously published model [31], which is parameterized for NEA cod. The biological model is individual-based, age- and length-structured, and describes an individual’s life-cycle from birth to death through annual processes of maturation, growth, reproduction, and mortality [31] and [32]. This model includes stock-specific estimated relationships for maturation tendency, density-dependent growth, stock–recruitment, and energy allocation. Individuals LY2109761 research buy vary in age, body size, and maturation status, which are tracked on an annual basis. Unlike some previous

models [31], [32], [33] and [34], this model reduces complexity by keeping life-history traits monomorphic and by not considering their evolutionary dynamics. The included life-history traits describe an individual’s maturation tendency, growth, and reproductive investment. All model parameters are based on empirical data (Table 1). Each year, the tendency that an immature individual will mature depends on a probabilistic maturation reaction norm [35], [36] and [37], which describes maturation probability pm(a,l) as a function of age a and body length l. This probability equals 50% at the length Metformin cost at age lP50(a)=i+sa, and is given by equation(1) pm(a,l)=1/(1+exp(−(l(a)−lP50(a))/c))pm(a,l)=1/(1+exp(−(l(a)−lP50(a))/c)) selleck screening library The probabilistic maturation reaction norm thus has intercept i   and slope s  . Its width w  , spanning from the 25% to the 75% percentile of maturation probability [31] and [32], is determined by the parameter c   where c=w/[logit(pu)−logit(pl)]c=w/[logit(pu)−logit(pl)],

and pu and pl are the probabilities for the upper and lower bounds of the PMRN. The growth rate of individuals depends on the total biomass of the population, to account for reductions in growth expected when population density is high and resource availability consequently is low. Data from 1978–2009 on annual growth increments g  D,t in year t  , together with data on total stock biomass B  t of individuals aged 3 years or older in year t  , were used to estimate the two parameters g   and x   of an exponential relationship for density-dependent growth, equation(2) gD,t=gexp(−xBt),gD,t=gexp(−xBt),where g   is the maximum growth increment (realized at B  t=0) and x   determines the strength of density dependence in growth ( Table 1). For immature individuals, denoted by a superscript I, body length in year t   is determined by their length in the previous year enhanced by the corresponding growth increment, ltI=lt−1I+gD,t−1.