On the limits to invasion prediction using coexistence outcomes

Abstract

The dynamics of ecological communities in nature are typically characterized by probabilistic, sequential assembly processes (i.e., adding species across time). Because of technical or practical limitations, however, the majority of theoretical and experimental studies have focused on the outcomes derived from simultaneous assembly processes (i.e., having all species included at once). Therefore, it has become central to understand the extent to which the outcomes from such simultaneous processes can be translated into analogous outcomes from sequential processes relevant for systems in nature. This translation requires a non-trivial integration of coexistence and invasion theories. Here, we provide this integration under a geometric and probabilistic Lotka-Volterra framework. We illustrate our integration by estimating and comparing the probability of analogous outcomes between these different assembly processes. 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, as well as between exclusion probability and replacement probability. These results provide a guiding framework and testable theoretical predictions regarding the translatability of probabilistic outcomes between simultaneous and sequential processes when communities are represented by Lotka-Volterra dynamics under environmental uncertainty.