A major challenge in ecological research is to identify the tolerance of ecological communities to external perturbations. Modern Coexistence Theory (MCT) has been widely adopted as a framework to investigate the tolerance to perturbations in relative reductions of per capita growth rates, often using metrics that explicitly eliminate the independent role of intrinsic growth rates. More recently, the Structural Approach (SA) was introduced to investigate the tolerance of communities to perturbations in intrinsic growth rates as a function of the strength of intraspecific and interspecific competition. Because the external perturbations are likely to happen in both intrinsic growth rates and competition strengths, no framework alone can fully disentangle the effects of external perturbations. Here we combine MCT and SA to disentangle the tolerance in coexistence and priority effects of a pair of competing species when subject to perturbations in intrinsic growth rates and competition strengths. Through this combination, we reveal the emergence of a key trade‐off. increasing the tolerance to perturbations in intrinsic growth rates typically decreases the tolerance in competition strengths, and vice versa. Furthermore, this trade‐off is stronger under coexistence than under priority effects. We test this combined framework on competing pairs of 18 California annual plant species. For both coexistence and priority effects, we find that the tolerance to perturbations in intrinsic growth rates is maximized instead of that to perturbations in competition strengths in the studied annual plant communities. Our combined framework of MCT and SA illustrates that it is possible to disentangle the impact of different external perturbations on the persistence of species. Importantly, our findings show that species interactions may reveal whether communitiesare dominated either by changes in intrinsic growth rates or competition strengths. Overall, this combined framework can open a new perspective to understand and predict the response of populations to changing environmental conditions.