Although all models are simplified approximations of reality, they remain useful tools for understanding, predicting, and managing populations and ecosystems. However, a model's utility is contingent on its suitability for a given task. Here, we examine two model types: single-species fishery stock assessment and multispecies marine ecosystem models. Both are efforts to predict trajectories of populations and ecosystems to inform fisheries management and conceptual understanding. However, many of these ecosystems exhibit nonlinear dynamics, which may not be represented in the models. As a result, model outputs may underestimate variability and overestimate stability. Using nonlinear forecasting methods, we compare predictability and nonlinearity of model outputs against model inputs using data and models for the California Current System. Compared with model inputs, time series of model-processed outputs show more predictability but a higher prevalence of linearity, suggesting that the models misrepresent the actual predictability of the modeled systems. Thus, caution is warranted: using such models for management or scenario exploration may produce unforeseen consequences, especially in the context of unknown future impacts.