# A new test for density-dependent survival - the case of coastal cod populations

Ecology (1999) 80:1278-1288.*Abstract*

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. The power and bias of the new test is investigated 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 errors. The model is applied 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 of 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 do 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.

Key words: Stochastic population dynamics; Gadus morhua; Generalized Additive Model; Time series analysis; Age-structured interactions; Negative binomial, gamma and Poisson variance; Competition; Cannibalism.