A new test for density-dependent survival: The case of coastal cod populations

A new test based on the generalized additive model is proposed to investigate density-dependent mortality in the juvenile cohorts of cod. Density dependence implies that the function linking the count of a cohort in one year to the count in the succeeding year is convex. The method estimates (without functional assumptions) the function linking the two counts and provides a level of significance for any convexity. We investigate the power and bias of the new test on the basis of simulated data. The power compares well with a test of unit slope in a log-log plot (although it is usually somewhat lower). However, in contrast to the latter method, the test for convexity is much more resistant to measurement error. We applied the model to long-term survey data from two areas of the Norwegian Skagerrak coast. In both cases, the variance is intermediate between the Gamma (variance proportional to the squared mean) and the Poisson (variance proportional to the mean) distributions. A negative binomial (with k ≃ 3.5) describes the variance well. The variance is interpreted as resulting from sampling errors, spatial heterogeneity, and environmental stochasticity. Incorporating this error structure, the optimal models linking the two main juvenile stages are, for each area, nonlinear and significantly convex (P < 0.05). The full models are highly significant (P < 0.001), and the examination of the residuals does not reveal any remaining structure. We conclude that the survival of juvenile cod along the Norwegian Skagerrak coast is density dependent, probably because of cannibalism, competition for habitat, and food limitation. The functional form of density-dependence in the per capita survival rate is estimated to be approximately log-linear.