Modelling the growth, mortality, and predation interactions of cod juveniles and capelin larvae in the Barents Sea using a novel proto-moment population dynamics model

Abstract

Abstract Hallfredsson, E. H., and Pope, J. G. 2007. Modelling the growth, mortality, and predation interactions of cod juveniles and capelin larvae in the Barents Sea using a novel proto-moment population dynamics model. – ICES Journal of Marine Science, 64: 1313–1323. Proto-moments of a fish population, the sums of products of powers of length with numbers at length, relate both to the traditional statistical measures, the mean, the variance, the skewness, and the kurtosis of their size distribution, and to the biologically important measures of the abundance and the biomass of the population. Population models based on this approach are constructed as matrix delay-difference equations. They model moments of the length distributions rather than the age distributions, and express population dynamic problems in an analytically tractable form. Here, a modification of this approach is explored for a case involving a predator–prey relationship among young-of-the-year fish. The modelled species are juvenile cod (the predator) and capelin larvae (the prey) in the Barents Sea. Their population dynamics are modelled by the proto-moment method, but using two different approaches for the derivation of the predation mortality term. The first approach, a published matrix-based formulation, is formed purely in terms of the proto-moments. The second approach, developed here, converts the proto-moments back to consistent size distributions to calculate the rates of predation mortality on each proto-moment. The latter model produces a realistic development in time for the predator and prey length distributions, density in numbers, and biomass for their first summer. It also provides estimates of growth for both species along with estimates of the predation mortality that cod generate on capelin in this time period. The estimates permitted the accuracy of the matrix-based approach to be investigated, better understood, and improved.