Recent work in the undeveloped Rio Murta Basin, located in Chilean Patagonia, identified an evolutionary trend in the fluvial system as it progresses toward and away from dynamic equilibrium. A location-for-time-substitution model employed over the longitudinal extent of a 16 km study site assessed the performance of extremal hypotheses in identifying dynamic equilibrium conditions. Numerous extremal hypotheses were successful in identifying the spatial trend, but no means were available to discern differences between them. Thus, this study uses field measurements within the evolutionary trend to propose a new metric for evaluating extremal hypotheses. A thorough review and synthesis of the extremal approach are additionally presented. The new method compares theoretical predictions against field-measured values to determine which extremal hypothesis is most effective in identifying the condition of dynamic equilibrium in a gravel-bed river. Channel width and depth are identified as the dependent stream variables that uniquely differentiate most extremal hypotheses from one another. The results indicate that extremal hypotheses based on energy metrics of the flow are most successful, with the strongest support for minimum kinetic energy and minimum specific stream power.