Massachusetts Institute of Technology, United States
The majority of research on species coexistence has been centered on the coexistence conditions of either 2-species in isolation or those of an entire multispecies system. However, species are seldom in isolation and ecological systems are continuously changing. Moreover, experimental work has shown that coexistence can be described as a probabilistic event when information about environments is missing. Thus, it is unclear whether traditional indicators of pairwise coexistence can be informative in general. To answer this question, we study the probability of pairwise coexistence within multispecies systems governed by Lotka-Volterra dynamics from a geometric and systems perspective. We derive analytically and numerically system-level indicators of long-term and short-term (transient) pairwise coexistence within multispecies systems, respectively. Using our proposed system-level indicators on theoretically-generated multispecies systems, we illustrate the effect of a system on changing the probabilities of pairwise coexistence. In addition, we use experimental data recording the frequency of pairwise coexistence of pairs of bacteria in isolation and within gut microbiota in order to illustrate the long-term and short-term effects of a system on changing the probability of pairwise coexistence.
We prove that traditional indicators of pairwise coexistence in isolation lose part of their informative value as the richness (dimension) of the system increases. Specifically, the coexistence constraints imposed on the parameters of a 2-species system (i.e., the pair in isolation) become weaker within multispecies systems, and new constraints emerge as a function of the parameters associated with the other species within the system. Next, we show that both the long-term and short-term effects of multispecies systems on the probability of pairwise coexistence are not homogeneous across pairs, but centered around their probability in isolation. Using the experimental data, we illustrate how our system-level indicators can be applied to understand long-term and short-term effects of the gut microbiota on the coexistence of each pair of bacteria. In sum, our work illustrates that traditional indicators of pairwise coexistence in isolation represent the expected probability of a pair under unknown changing environments. However, as soon as new information is available about a system, this expected probability needs to be replaced by a new expectation of pairwise coexistence conditional on the known system and the timescale of the dynamics.