Long-term time series of sardine and anchovy landings often suggest negative dependence between these species, and an array of mechanisms have been proposed as explanations. We reduce these propositions to four basic hypotheses of (1) independence, (2) correlated process noise, (3) interspecific interactions, and (4) correlated observational error. We use a Bayesian approach to develop priors for parsimonious state space models with both process noise and observation error that represent each of these hypotheses, and apply this approach to five long-term time series of landings collected from the Pacific and Atlantic Oceans. Model comparison criteria suggest that the hypothesis of correlated process noise has the broadest support, where the temporal dependence of anchovy and sardines may be caused in part by either direct environmental influence on their physiology, or indirect bottom-up effects on their prey. However, all hypotheses find some degree of support within the five time series, and in general, the sardine and anchovy landings suggest weak intraspecific density dependence and susceptibility to both environmental and anthropogenic perturbation. Results additionally suggest that the best fitting hypothesis depends on the choice of geographic scale, temporal scale, and stock definition of the recorded landings.