Correlations between time series of the abundance of predator and prey fish species in heavily exploited western North Atlantic marine fisheries vary temporally but are generally positive in southern, warmer waters and negative in northern, colder ones. The correlations provide an index of trophic structure and dynamics. We construct a framework to quantify critical thresholds between states in which the predator–prey correlations are positive or negative. We do so by developing a quantitative model of the distribution of the correlations between predator (15 species) and prey (8 species) functional groups based on the annual predator depletion rates and bottom temperatures (or alternatively species richness). The model accounts for 58% of the variance of the correlations with a root mean square error of 0.3. This index of trophic structure indicates that warmer, species-rich, southern fish populations resist transformation from positive to negative predator–prey correlations at exploitation rates that can be double those in the colder, relatively species-poor, northern areas. The model can be used to set limits for exploitation rates that preserve the functional relationships between predator–prey groups in emerging fisheries, and to assess the potential for and measures required to achieve recovery of degraded fish communities.