Abstract: The dynamics of ecological communities in nature are typically characterized by probabilistic, sequential assembly processes (i.e., invasion dynamics). Because of technical challenges, however, the majority of theoretical and experimental studies have focused on the outcomes derived from simultaneous assembly processes (i.e., coexistence dynamics). Therefore, it has become central to understand the extent to which the outcomes from such simultaneous processes can be used to predict analogous outcomes from sequential processes relevant for systems in nature. Here, we study the limits to this predictability under a geometric and probabilistic Lotka-Volterra framework. We show that while survival probability in simultaneous assembly can be fairly closely translated into colonization probability in sequential assembly, the translation is less precise between community persistence and community augmentation, and worse between exclusion probability and replacement probability. These results provide a guiding and testable theoretical framework regarding the (lack of) translatability of outcomes between simultaneous and sequential processes when communities are represented by Lotka-Volterra dynamics under environmental uncertainty.
