The effects of intransitive competition on coexistence

Coexistence theory has been developed with an almost exclusive focus on interactions between two species, often ignoring more complex and indirect interactions, such as intransitive loops, that can emerge in competition networks. In fact, intransitive competition has typically been studied in isolation from other pairwise stabilising processes, and thus little is known about how intransitivity interacts with more traditional drivers of species coexistence such as niche partitioning. To integrate intransitivity into traditional coexistence theory, we developed a metric of growth rate when rare, , to identify and quantify the impact of intransitive competition against a backdrop of pairwise stabilising niche differences. Using this index with simulations of community dynamics, we demonstrate that intransitive loops can both stabilise or destabilise species coexistence, but the strength and importance of intransitive interactions are significantly affected by the length and the topology of these loops. We conclude by showing how can be used to evaluate effects of intransitivity in empirical studies. Our results emphasise the need to integrate complex mechanisms emerging from diverse interactions into our understanding of species coexistence.     

Dissecting the role of transitivity and intransitivity on coexistence in competing species networks

It is well established that intransitively assembled interaction networks can support the coexistence of competing species, while transitively assembled (hierarchical) networks are prone to species loss through competitive exclusion. However, as the number of species grows, the complexity of ecological interaction networks grows disproportionately, and species can get involved simultaneously in transitive and intransitive groups of interactions. In such complex networks, the effects of intransitivity on species persistence are not straightforward. Dissecting networks into intransitive/transitive components can help us to understand the complex role that intransitivity may play in supporting species diversity. We show through simulations that those species participating in the largest group of intransitive interactions (the core of the network) have high probabilities of persisting in the long term. However, participation in a group of intransitive interactions other than the core does not always improve persistence. Likewise, participating in transitive interactions does not always decrease persistence because certain species (the satellites) transitively linked to the core have also a high persistence probability. Therefore, when networks contain transitive and intransitive structures, as it can be expected in real ecological networks, the existence of a large intransitive core of species can have a disproportionate positive effect on species richness.     

Matrix models for quantifying competitive intransitivity from species abundance data

In a network of competing species, a competitive intransitivity occurs when the ranking of competitive abilities does not follow a linear hierarchy (A > B > C but C > A). A variety of mathematical models suggests that intransitive networks can prevent or slow down competitive exclusion and maintain biodiversity by enhancing species coexistence. However, it has been difficult to assess empirically the relative importance of intransitive competition because a large number of pairwise species competition experiments are needed to construct a competition matrix that is used to parameterize existing models. Here we introduce a statistical framework for evaluating the contribution of intransitivity to community structure using species abundance matrices that are commonly generated from replicated sampling of species assemblages. We provide metrics and analytical methods for using abundance matrices to estimate species competition and patch transition matrices by using reverse‐engineering and a colonization–competition model. These matrices provide complementary metrics to estimate the degree of intransitivity in the competition network of the sampled communities. Benchmark tests reveal that the proposed methods could successfully detect intransitive competition networks, even in the absence of direct measures of pairwise competitive strength. To illustrate the approach, we analyzed patterns of abundance and biomass of five species of necrophagous Diptera and eight species of their hymenopteran parasitoids that co‐occur in beech forests in Germany. We found evidence for a strong competitive hierarchy within communities of flies and parasitoids. However, for parasitoids, there was a tendency towards increasing intransitivity in higher weight classes, which represented larger resource patches. These tests provide novel methods for empirically estimating the degree of intransitivity in competitive networks from observational datasets. They can be applied to experimental measures of pairwise species interactions, as well as to spatio‐temporal samples of assemblages in homogenous environments or environmental gradients.     

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.     

Species interactions and random dispersal rather than habitat filtering drive community assembly during early plant succession

Theory on plant succession predicts a temporal increase in the complexity of spatial community structure and of competitive interactions: initially random occurrences of early colonising species shift towards spatially and competitively structured plant associations in later successional stages. Here we use long‐term data on early plant succession in a German post mining area to disentangle the importance of random colonisation, habitat filtering, and competition on the temporal and spatial development of plant community structure. We used species co‐occurrence analysis and a recently developed method for assessing competitive strength and hierarchies (transitive versus intransitive competitive orders) in multispecies communities. We found that species turnover decreased through time within interaction neighbourhoods, but increased through time outside interaction neighbourhoods. Successional change did not lead to modular community structure. After accounting for species richness effects, the strength of competitive interactions and the proportion of transitive competitive hierarchies increased through time. Although effects of habitat filtering were weak, random colonization and subsequent competitive interactions had strong effects on community structure. Because competitive strength and transitivity were poorly correlated with soil characteristics, there was little evidence for context dependent competitive strength associated with intransitive competitive hierarchies.     

Species coexistence, intransitivity, and topological variation in competitive tournaments

Competitive intransitivity occurs when species’ competitive abilities cannot be listed in a strict hierarchy, but rather form competitive loops, as in the game ‘Rock-Paper-Scissors’. Indices are useful for summarizing intransitivity in communities; however, as with most indices, a great deal of information is compressed into single number. So while recent ecological theory, experiments, and natural history observations demonstrate that competitive intransitivity can promote species coexistence, the consequence of variation in the ‘topology’ of competitive interactions that is not accounted for by intransitivity indices is much less well understood. We use a continuous analytical model and two complementary discrete lattice models (one spatially explicit, the other aspatial) to demonstrate that such variation does indeed greatly affect species coexistence. Specifically, we show that although intransitivity indices are good at capturing broad patterns of coexistence, communities with different levels of intransitivity can have equal coexistence, and communities with equal intransitivity can have different coexistence, due to underlying variation in competitive network topology.     

Reduction of species coexistence through mixing in a spatial competition model

Many ecological systems exhibit self-organized spatial patterns due to local interactions. Such patterns can promote species diversity and therefore serve as an important mechanism for biodiversity maintenance. Previous work has shown that when species interactions occurred at local spatial scales, species diversity was greatest when robust mosaic spatial patterns formed. Also, intransitive interactions led to the emergence of spiral patterns, frequently resulting in multispecies coexistence. In some instances, intransitive interactions reduced species diversity as the consequence of competitive hierarchies. Here, we extend and broaden this line of investigation and examine the role of global competition along a continuum ranging from spatial mosaics to spiral patterns. While previous models have predicted that species diversity is reduced when interactions occur over larger spatial scales, our model considers the effects of various levels of mixing on species diversity, in the context of various network structures as measured by the covariance of row and column sums of the competition matrix. First, we compare local competition (unmixed system) versus global competition (mixed systems) and show that greater species diversity is maintained under a positive covariance. Second, we show that under various levels of mixing, species diversity declines more rapidly under a negative covariance. Lastly, we demonstrate that time to extinction in our model occurs much more rapidly under a negative covariance.     

Competitive intransitivity promotes species coexistence

Using a spatially explicit cellular automaton model with local competition, we investigate the potential for varied levels of competitive intransitivity (i.e., nonhierarchical competition) to promote species coexistence. As predicted, on average, increased levels of intransitivity result in more sustained coexistence within simulated communities, although the outcome of competition also becomes increasingly unpredictable. Interestingly, even a moderate degree of intransitivity within a community can promote coexistence, in terms of both the length of time until the first competitive exclusion and the number of species remaining in the community after 500 simulated generations. These results suggest that modest levels of intransitivity in nature, such as those that are thought to be characteristic of plant communities, can contribute to coexistence and, therefore, community-scale biodiversity. We explore a potential connection between competitive intransitivity and neutral theory, whereby competitive intransitivity may represent an important mechanism for "ecological equivalence."     

Competitive interactions change the pattern of species co‐occurrences under neutral dispersal

Non‐random patterns of species segregation and aggregation within ecological communities are often interpreted as evidence for interspecific interactions. However, it is unclear whether theoretical models can predict such patterns and how environmental factors may modify the effects of species interactions on species co‐occurrence. Here we extend a spatially explicit neutral model by including competitive effects on birth and death probabilities to assess whether competition alone is able to produce non‐random patterns of species co‐occurrence. We show that transitive and intransitive competitive hierarchies alone (in the absence of environmental heterogeneity) are indeed able to generate non‐random patterns with commonly used metrics and null models. Moreover, even weak levels of intransitive competition can increase local species richness. However, there is no simple rule or consistent directional change towards aggregation or segregation caused by competitive interactions. Instead, the spatial pattern depends on both the type of species interaction and the strength of dispersal. We conclude that co‐occurrence analysis alone may not able to identify the underlying processes that generate the patterns.     

Intransitive competition is widespread in plant communities and maintains their species richness

Intransitive competition networks, those in which there is no single best competitor, may ensure species coexistence. However, their frequency and importance in maintaining diversity in real‐world ecosystems remain unclear. We used two large data sets from drylands and agricultural grasslands to assess: (1) the generality of intransitive competition, (2) intransitivity–richness relationships and (3) effects of two major drivers of biodiversity loss (aridity and land‐use intensification) on intransitivity and species richness. Intransitive competition occurred in > 65% of sites and was associated with higher species richness. Intransitivity increased with aridity, partly buffering its negative effects on diversity, but was decreased by intensive land use, enhancing its negative effects on diversity. These contrasting responses likely arise because intransitivity is promoted by temporal heterogeneity, which is enhanced by aridity but may decline with land‐use intensity. We show that intransitivity is widespread in nature and increases diversity, but it can be lost with environmental homogenisation.     

Intransitive competition and its effects on community functional diversity

Can competitive interactions be inferred from the analysis of community functional diversity patterns? Originally, at the scale of a community, competitive interactions were supposed to generate trait overdispersion patterns due to limiting similarity process. More recently, by highlighting the importance of competitive hierarchies, it has been shown that when only one resource limits species coexistence, competition can also lead to patterns of trait clustering. However, these two expectations (overdispersion and clustering) ignore potential multi‐species indirect competitive interactions, and especially intransitive competition. Indeed, little is yet known about intransitive competition and its influence on community's functional diversity. Here I propose a brief appraisal of empirical evidence for intransitive competition in nature, and an overview of the current understanding of this mechanism and its properties. I then demonstrate with a theoretical model that intransitive competitive interactions can actually generate random‐like functional diversity patterns. The variety of diversity patterns (overdispersion, clustering, randomness) that can emerge from diverse types of competitive interactions makes it difficult to identify the presence of competition in nature, potentially leading to an underestimation of its importance as a structuring force. New methodologies able to capture both simple and complex competition mechanisms are thus urgently needed.     

Disturbance, interspecific interaction and diversity in metapopulations

Metapopulation diversity patterns depend on the relations among the timescales of local biological interactions (predation, competition), the rates of dispersal among local populations and the patterns of disturbance. We investigate these relationships using a family of simple non-linear Markov chain models. We consider three models for interspecific competition; if the species are identified with early and late successional species, the models describe the facilitation, inhibition and tolerance models of ecological succession. By adding a third competing species we also compare transitive competitive hierarchies and intransitive competitive networks. Finally, we examine the effects of predation in mediating coexistence among competing prey species. In each model we find circumstances in which biotic or abiotic disturbance can increase both local and regional diversity, but those circumstances depend on the various timescales in the model in ways that arc neither obvious nor trivial.     

Using exclusion rate to unify niche and neutral perspectives on coexistence

The competitive exclusion principle is one of the most influential concepts in ecology. The classical formulation suggests a correlation between competitor species similarity and competition severity, leading to rapid competitive exclusion where species are very similar; yet neutral models show that identical species can persist in competition for long periods. Here, we resolve the conflict by examining two components of similarity – niche overlap and competitive similarity – and modeling the effects of each on exclusion rate (defined as the inverse of time to exclusion). Studying exclusion rate, rather than the traditional focus on binary outcomes (coexistence versus exclusion), allows us to examine classical niche and neutral perspectives using the same currency. High niche overlap speeds exclusion, but high similarity in competitive ability slows it. These predictions are confirmed by a well‐known model of two species competing for two resources. Under ecologically plausible scenarios of correlation between these two factors, the strongest exclusion rates may be among moderately similar species, while very similar and highly dissimilar competitors have very low exclusion rates. Adding even small amounts of demographic stochasticity to the model blurs the line between deterministic and probabilistic coexistence still further. Thus, focusing on exclusion rate, instead of on the binary outcome of coexistence versus exclusion, allows a variety of outcomes to result from competitive interactions. This approach may help explain species coexistence in diverse competitive communities and raises novel issues for future work.     

Realised niche changes in a native herbivore assemblage associated with the presence of livestock

Habitat partitioning is a common ecological mechanism to avoid competition among coexisting species, and the introduction of new species into existing assemblages can increase competitive pressures. However, situations of species in allopatry and sympatry only differing in species presence but not in environmental conditions are scarce. Thus, discerning whether niche segregation arises from competition or from different habitat preferences is usually unfeasible. Here, we analyse species’ habitat niches in an assemblage of native and introduced herbivores in southern Patagonia. We test if niche overlap is higher between native and domestic herbivores than among natives as expected from the relatively short time of coexistence, and we evaluate the effect of intra‐ and interspecific competition on niche breadth. We use a probabilistic multidimensional approach and null models to evaluate overlap and changes in niche dimensions. Overlap among native species is low as expected for species coexisting in evolutionary time. In native‐domestic species pairs, niche overlap was higher than among natives, although showing some niche segregation indicating niche differentiation in ecological time. Moreover, the presence of domestic species was associated with niche narrowing of both native and introduced species, revealing interspecific density‐dependent effects on their habitat niche during resource shortage periods.     

Heteromyopia and the spatial coexistence of similar competitors

Most spatial models of competing species assume symmetries in the spatial scales of dispersal and interactions. This makes analysis tractable, and has led to the conclusion that segregation of species in space does not promote coexistence. However, these symmetries leave parts of the parameter space uninvestigated. Using a moment‐approximation method, we present a spatial version of the Lotka–Volterra competition equations to investigate effects of removing symmetries in the distances over which individuals disperse and interact. Some spatial segregation of the species always comes about due to competition, and such segregation does not necessarily lead to coexistence. But, if interspecific competition occurs over shorter distances than intraspecific competition (heteromyopia), spatial segregation becomes strong enough to promote coexistence. Such coexistence is most likely when the species have similar dynamics, in contrast to the competition–colonization trade‐off that requires large competitive differences between species.     

Local‐scale spatial dynamics of ants in a temperate agroecosystem

At the local scale, spatial aggregations in ant distribution are often thought to be driven by competitive interactions among dominant ant species, although niche preferences and habitat heterogeneity might also lead to patchiness. Nevertheless, competitive interactions might be particularly important in agroecosystems that are structurally more homogeneous than natural habitats. The spatial patterns of ants in two Australian vineyards were investigated by intensive pitfall trapping to examine if non‐random patterns occur and whether these might be the result of competitive species interactions as well as the influence of woody vegetation adjacent to the vineyards. Null model analyses suggested competitive species interactions within ant assemblages that might have been driven by numerically dominant species, even though both positive and negative associations between these were found. Consistent spatial aggregations indicated significant spatial overlap in distributions of some species. Such overlap suggests that potential coexistence might be attributed to temporal partitioning or differences in foraging strategies. The presence of woody vegetation had a marked influence on ant assemblage structure and competitive interactions, and might facilitate coexistence by increasing resource heterogeneity. The implications of these findings for sampling strategies and ecological processes within vineyards are discussed.     

Emerging niche clustering results from both competition and predation

Understanding species coexistence has been a central question in ecology for decades, and the notion that competing species need to differ in their ecological niche for stable coexistence has dominated. Recent theoretical and empirical work suggests differently. Species can also escape competitive exclusion by being similar, leading to clusters of species with similar traits. This theory has so far only been explored under competition. By combining mathematical and numerical analyses, we reveal that competition and predation are equally capable to promote clusters of similar species in prey–predator communities, their relative importance being modulated by resource availability. We further show that predation has a stabilizing effect on clustering patterns, making the clusters more diverse. Our results merge different ecological theories and bring new light to the emergent neutrality theory by adding the perspective of trophic interactions. These results open new perspectives to the study of trait distributions in ecological interaction networks.     

Who is the top dog in ant communities? Resources,parasitoids, and multiple competitive hierarchies

A wide variety of animal communities are organized into interspecific dominance hierarchies associated with the control and harvest of food resources. Interspecific dominance relationships are commonly found to be linear. However, dominance relations within communities can form a continuum ranging from intransitive networks to transitive, linear dominance hierarchies. How interference competition affects community structure depends on the configuration of the dominance interactions among the species. This study explores how resource size and the trait-mediated indirect effect (TMIE) specialist phorid fly parasitoids exert on interference competition, affect the transitive nature of competitive interactions in an assemblage of woodland ants. I quantify the linearity of networks of interactions associated with large and small food resources in the presence and absence of phorid parasitoids. Two distinct, significantly linear dominance hierarchies exist within the ant assemblage depending on the size of the disputed resource. However, the presence of phorid fly parasitoids eliminates the linearity of both dominance hierarchies. The hosts phorid defense behaviors reduce the competitive asymmetries between the host and its subdominant competitors, increasing the indeterminacy in the outcome of competitive interactions. Thus, both resource size variation and phorid-induced TMIEs appear to facilitate coexistence in assemblages of scavenging ants.     

Frequency-dependent community dynamics driven by sexual interactions

Research in community ecology has tended to focus on trophic interactions (e.g., predation, resource competition) as driving forces of community dynamics, and sexual interactions have often been overlooked. Here we discuss how sexual interactions can affect community dynamics, especially focusing on frequency-dependent dynamics of horizontal communities (i.e., communities of competing species in a single ecological guild). By combining mechanistic and phenomenological models of competition, we place sexual reproduction into the framework of modern coexistence theory. First, we review how population dynamics of two species competing for two resources can be represented by the Lotka–Volterra competition model as well as frequency dynamics, and how niche differentiation and overlap produce negative and positive frequency-dependence (i.e., stable coexistence and priority effect), respectively. Then, we explore two situations where sexual interactions change the frequency-dependence in community dynamics: (1) reproductive interference, that is, negative interspecific interactions due to incomplete species recognition in mating trials, can promote positive frequency-dependence and (2) density-dependent intraspecific adaptation load, that is, reduced population growth rates due to adaptation to intraspecific sexual (or social) interactions, produces negative frequency-dependence. We show how reproductive interference and density-dependent intraspecific adaptation load can decrease and increase niche differences in the framework of modern coexistence theory, respectively. Finally, we discuss future empirical and theoretical approaches for studying how sexual interactions and related phenomena (e.g., reproductive interference, intraspecific adaptation load, and sexual dimorphism) driven by sexual selection and conflict can affect community dynamics.