The persistence of virtually every single species depends on both the presence of other species and the specific environmental conditions in a given location. Because in natural settings many of these conditions are unknown, research has been centered on finding the fraction of possible conditions (probability) leading to species coexistence. The focus has been on the persistence probability of an entire multispecies community (formed of either two or more species). However, the methodological and philosophical question has always been whether we can observe the entire community and, if not, what the conditions are under which an observed subset of the community can persist as part of a larger multispecies system. Here, we derive long-term (using analytical calculations) and short-term (using simulations and experimental data) system-level indicators of the effect of third-party species on the coexistence probability of a pair (or subset) of species under unknown environmental conditions. We demonstrate that the fraction of conditions incompatible with the possible coexistence of a pair of species tends to become vanishingly small within systems of increasing numbers of species. Yet, the probability of pairwise coexistence in isolation remains approximately the expected probability of pairwise coexistence in more diverse assemblages. In addition, we found that when third-party species tend to reduce (resp. increase) the coexistence probability of a pair, they tend to exhibit slower (resp. faster) rates of competitive exclusion. Long-term and short-term effects of the remaining third-party species on all possible specific pairs in a system are not equally distributed, but these differences can be mapped and anticipated under environmental uncertainty.

The persistence of virtually every single species depends on both the presence of other species and the heterogeneous environmental conditions. Because in natural settings many of these conditions are unknown, research has been centered on finding the fraction of possible conditions (probability) leading to species coexistence. The focus has been on the coexistence probability of two species in isolation or that of an entire multispecies system. However, it is unclear how a system can affect differently the coexistence expectation of each of its constituent pairs. Here, we derive long-term (using analytical calculations) and short-term (using simulations and experimental data) system-level indicators of the effect of multispecies systems on pairwise coexistence under unknown environmental conditions. We demonstrate that the fraction of conditions incompatible with the possible coexistence of a pair of species in isolation tends to become vanishingly small within systems of increasing numbers of species. Yet, the fraction of conditions allowing pairwise coexistence in isolation remains approximately the center of the probability distribution of pairwise coexistence across all possible systems. While the likelihood of short-term survival is always greater than or equal to that of long-term survival, we found in general stronger (resp. weaker) short-term buffering effects within systems than in isolation under negative (resp. positive) long-term effects. We show that both long-term and short-term effects of a system are not equally distributed across all of its possible pairs, but these differences can be mapped and anticipated under environmental uncertainty.Author SummaryIt is debated whether the frequency at which two species coexist in isolation or within a single environmental context is representative of their coexistence expectation within larger systems and across different environmental conditions. Here, using analytical calculations, simulations, and experimental data, we show how multispecies systems can provide the opportunity of pairwise coexistence regardless of whether a pair of species cannot coexist in isolation across different environmental conditions. However, we show that this opportunity is not homogeneously granted across all pairs within the same system. We provide a framework to understand and map the long-term and short-term effects that a system has on the coexistence of each of its constituent pairs. Our work can have useful applications in bio-restoration and bio-medicine subject to unknown environmental conditions.

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.