This paper reports an investigation of stock-recruitment relations for Atlantic salmon (Salmo salar). We regard these relations as stochastic functions characterized by an expected stock-recruitment relation and deviations from this expectation driven by observational error and uncharacterised environmental variability. We estimate model parameters by standard Bayesian methods. Analysis of the input-output characteristics of segments of the salmon life cycle in the Girnock Burn (Northeast Scotland) reveals two independent regulatory processes, one between ova and fry and the other between fry and smolts. Comparison of stock-recruitment relations for Atlantic salmon in Scotland, Ireland, and Canada, reinforced by an extended series of simulation studies, shows that even when comparatively long time series of high quality data are available, it is frequently difficult to exclude the possibility of low stock depensation - an effect whose implication of enhanced extinction risk implies that precautionary management policy would pay special attention to the posssibility of its occurence. A particular feature of our simulation results is their demonstration that inappropriate combination of distinct subpopulations both increases process noise and distorts the expected stock-recruitment relation, thereby greatly reducing the accuracy of any system identification process.