The three-species problem: Incorporating competitive asymmetry and intransitivity in modern coexistence theory

While natural communities can contain hundreds of species, modern coexistence theory focuses primarily on species pairs. Alternatively, the structural stability approach considers the feasibility of equilibria, gaining scalability to larger communities but sacrificing information about dynamic stability. Three-species competitive communities are a bridge to more-diverse communities. They display novel phenomena while remaining amenable to mathematical analysis, but remain incompletely understood. Here, we combine these approaches to identify the key quantities that determine three-species competition outcomes. We show that pairwise niche overlap and fitness differences are insufficient to completely characterize competitive outcomes, which requires a strictly triplet-wise quantity: cyclic asymmetry, which underlies intransitivity. Low pairwise niche overlap stabilizes the triplet, while high fitness differences promote competitive exclusion. The effect of cyclic asymmetry on stability is complex and depends on pairwise niche overlap. In summary, we elucidate how pairwise niche overlap, fitness differences and cyclic asymmetry determine three-species competition outcomes.

The unimodal intransitivity-fertility relationship is not mediated by demographic trade-offs in a subtropical forest

Intransitive competition has long been acknowledged as a potential mechanism favoring species coexistence. However, its prevalence, variance along environmental gradients, and possible underlying mechanisms (trade-offs) in plant communities (especially in forests) has seldom been examined. A recently developed "reverse-engineering" approach based on Markov Chain allowed us to estimate the competitive transition matrices and competitive intransitivity from observational abundance data. Using this approach, we estimated competitive intransitivity of five dominant species in a subtropical forest and then related it to soil fertility (soil organic matter and soil pH) and demographic trade-offs (growth-survival and stature-recruitment trade-offs). In our forest plot, intransitive competition was common among the dominant species and peaked at the intermediate level of soil organic matter. Neither the growth-survival trade-off nor the stature-recruitment trade-off was positively related to competitive intransitivity. Our study for the first time empirically supported the unimodal intransitivity-fertility relationship in forests, which, however, was not mediated by the two demographic trade-offs in our plot.

Habitat loss alters effects of intransitive higher-order competition on biodiversity: a new metapopulation framework

Recent studies have suggested that intransitive competition, as opposed to hierarchical competition, allows more species to coexist. Furthermore, it is recognized that the prevalent paradigm, which assumes that species interactions are exclusively pairwise, may be insufficient. More importantly, whether and how habitat loss, a key driver of biodiversity loss, can alter these complex competition structures (and therefore species coexistence) remain unclear. We thus present a new, simple yet comprehensive metapopulation framework that can account for any competition pattern and more complex higher-order interactions (HOIs) among species. We find that competitive intransitivity increases community diversity and that HOIs generally enhance this effect. Essentially, intransitivity promotes species richness by preventing the dominance of a few species, unlike the hierarchical competition, while HOIs facilitate species coexistence through stabilizing community fluctuations. However, variation in species' vital rates and habitat loss can weaken or even reverse such higher-order effects, as their interaction can lead to a more rapid decline in competitive intransitivity under HOIs. Thus, it is essential to correctly identify the most appropriate interaction model for a given system before models are used to inform conservation efforts. Overall, our simple model framework provides a more parsimonious explanation for biodiversity maintenance than the existing theory.

Ecological drift and competitive interactions predict unique patterns in temporal fluctuations of population size

Recent studies have highlighted the importance of higher-order competitive interactions in stabilizing population dynamics in multi-species communities. But how does the structure of competitive hierarchies affect population dynamics and extinction processes? We tackled this important question by using spatially explicit simulations of ecological drift (10 species in a homogeneous landscape of 64 patches) in which birth rates were influenced by interspecific competition. Specifically, we examined how transitive (linear pecking orders) and intransitive (pecking orders with loops) competitive hierarchies affected extinction rates and population dynamics in simulated communities through time. In comparison to a pure neutral model, an ecological drift model including transitive competition increased extinction rates, caused synchronous density-dependent population fluctuations, and generated a white-noise distribution of population sizes. In contrast, the drift model with intransitive competitive interactions decreased extinctions rates, caused asynchronous (compensatory) density-dependent population fluctuations, and generated a brown noise distribution of population sizes. We also explored the effect on community stability of more complex patterns of competitive interactions in which pairwise competitive relationships were assigned probabilistically. These probabilistic competition models also generated density-dependent trajectories and a brown noise distribution of population sizes. However, extinction rates and the degree of population synchrony were comparable to those observed in purely neutral communities. Collectively, our results confirm that intransitive competition has a strong and stabilizing effect on local populations in species-poor communities. This effect wanes with increasing species richness. Empirical assemblages characterized by brown spectral noise, density-dependent regulation, and asynchronous (compensatory) population fluctuations may indicate a signature of intransitive competitive interactions.

Intransitivity is infrequent and fails to promote annual plant coexistence without pairwise niche differences

Intransitive competition is often projected to be a widespread mechanism of species coexistence in ecological communities. However, it is unknown how much of the coexistence we observe in nature results from this mechanism when species interactions are also stabilized by pairwise niche differences. We combined field-parameterized models of competition among 18 annual plant species with tools from network theory to quantify the prevalence of intransitive competitive relationships. We then analyzed the predicted outcome of competitive interactions with and without pairwise niche differences. Intransitive competition was found for just 15-19% of the 816 possible triplets, and this mechanism was never sufficient to stabilize the coexistence of the triplet when the pair-wise niche differences between competitors were removed. Of the transitive and intransitive triplets, only four were predicted to coexist and these were more similar in multidimensional trait space defined by 11 functional traits than non-coexisting triplets. Our results argue that intransitive competition may be less frequent than recently posed, and that even when it does operate, pairwise niche differences may be key to possible coexistence.

Facilitation as a ubiquitous driver of biodiversity

Models describing the biotic drivers that create and maintain biological diversity within trophic levels have focused primarily on negative interactions (i.e. competition), leaving marginal room for positive interactions (i.e. facilitation). We show facilitation to be a ubiquitous driver of biodiversity by first noting that all species use resources and thus change the local biotic or abiotic conditions, altering the available multidimensional niches. This can cause a shift in local species composition, which can cause an increase in beta, and sometimes alpha, diversity. We show that these increases are ubiquitous across ecosystems. These positive effects on diversity occur via a broad host of disparate direct and indirect mechanisms. We identify and unify several of these facilitative mechanisms and discuss why it has been easy to underappreciate the importance of facilitation. We show that net positive effects have a long history of being considered ecologically or evolutionarily unstable, and we present recent evidence of its potential stability. Facilitation goes well beyond the common case of stress amelioration and it probably gains importance as community complexity increases. While biodiversity is, in part, created by species exploiting many niches, many niches are available to exploit only because species create them.