In this model, reproductive investment is measured by the gonado-somatic index G, defined as the ratio between an individual’s gonadic and somatic mass. A conversion factor γ accounts for the higher energy content of gonadic tissue relative to somatic tissue [38] and [39]. Consequently, the length of a mature individual is given by equation(3) ltM=3(lt−1M+gD,t−1)/(3+γG) An individual’s fecundity f depends on its body length l, equation(4) f=kjlGD,f=kljGD,where D is the weight-specific packing density

of oocytes [40], and k and j are allometric constants relating body length to somatic body mass. Sex is assigned randomly at birth based on a 1:1 primary sex ratio. The density-dependent newborn mortality is determined by an estimated Beverton–Holt stock–recruitment relationship for 3-year-olds [32], depending on SSB and climate. The climatic variable, the sea-surface buy INK 128 temperature from the Kola meridian transect (33°50′ E, 70°50′ N to 72°50′ N) has been shown to be an important selleck screening library factor for recruitment [41], [42], [43] and [44]. This annual climatic data is used as input to the modelled stock–recruitment relationship (prior to 1990, the mean value from 1980–1989, while from 2004 onwards, the mean value from 1990–2007). Back-calculating from the predicted number of 3-year-olds, the number of 1-year-olds

is determined by setting instantaneous natural mortality rate to 0.2 yr−1, as conventionally done for that stock [11]. Individuals die from natural mortality or fishing mortality. Natural mortality is parsimoniously held constant and set equal to an instantaneous rate of 0.2 yr−1, as routinely assumed

in the stock assessment of NEA cod [11]. In terms of fishing mortality, immature fish can only get captured on the feeding grounds, while mature fish may also experience fishing mortality on the spawning grounds (Fig. 2a). Fishing mortality rates F   from the stock-assessment model [3] are translated into harvest probabilities 1−exp(−ηF)1−exp(−ηF) in the feeding grounds and 1−exp(−κF)1−exp(−κF) in the spawning grounds, where the parameters η and κ convert the total fishing mortality rate into those in the feeding grounds and spawning grounds, respectively. Also taken into account is that only mature fish migrate out of the Barents Sea for about ¼ of the year, and therefore reduced their harvest probabilities thereto. A selectivity cAMP curve accounting for the lower catchability of smaller-sized fish, estimated for the commercial trawling gear used in the NEA cod fishery [45] was also implemented. Initially, fishing mortality is held constant in the model at the 1932–1989 average, in order to allow the population to reach demographic equilibrium (in terms of stable total biomass, SSB, individual growth, and age and length at maturation). After that equilibration, the stock’s observed annual fishing mortality rates for each year between 1990 and 2003 were implemented, resulting in very good matches between model-predicted and observed SSB values.