1. The relative importance of density-dependent and -independent factors on interannual variation in over-winter survival was investigated in the fluctuating population of Soay sheep on St Kilda, Scotland, over the period 1985–96.
2. Population density had a negative effect on survival in lambs and adult males while adult female survival showed no evidence of density dependence over the observed range of population densities.
3. Climatic fluctuations associated with the winter North Atlantic oscillation index (NAO) also affected survival, which decreased in winters that were relatively warm, wet and windy. The effect was most pronounced in lambs.
4. Survival was modelled using logistic regression analysis with and without year fitted as a random effect. The former incorporated stochastic year to year variation in survival. Results from the two modelling approaches were similar in terms of the regression coefficients estimated. However, the standard errors of the year-dependent covariates, population size and NAO, were underestimated when the random year effect was ignored, leading to incorrect inferences about the relative significance of terms being made.
5. Using both modelling approaches, density dependence was found to have a greater influence on survival than the effect of NAO in lambs and adult males, whereas in adult females NAO was the more important.
6. Once random between-year effects were taken into account, the individually varying terms such as body weight and faecal egg count were the most significant factors explaining differences in survival.