Understanding the impact of third-party species on pairwise coexistence

Abstract

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.

On the limits to invasion prediction using coexistence outcomes

“…Then, the probabilities can be approximated by the frequencies that certain species compositions persist together over a finite period of time and threshold for species extinction (Deng et al, 2022).…”

“…Formally, the feasibility domain D F (C, S) of a species collection C (C ⊆ S, C ̸ = ∅) in a multispecies community S characterized by an interaction matrix A, can be represented by (Deng et al, 2022)…”

“…This classification can also be reached via simulations after a given period of time assuming a given threshold for extinction (Deng et al, 2022). We simulate the gLV model (Eq.…”

“…The analytic calculation, however, is valid only in the idealized theoretical limit of an infinite number of experimental trials and time steps (Deng et al, 2022). Hence, we use a numerical approximation using simulations to make our analysis more comparable to the finite nature of lab/field experiments or observations (Deng et al, 2022). For this purpose, for each community A , we randomly and uniformly sample 1000 vectors of effective growth rates θ inside the feasibility domain of residents in isolation .…”

Integrating metabolic scaling and coexistence theories

“…We have proposed a tractable and scalable integration of metabolic scaling theory [4] and coexistence theories [26][27][28][29] in order to systematically link metabolic scaling relationships at the population level and the persistence of ecological communities under different environmental conditions [40,43,44].…”