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Functional traits offer a potential avenue to generalize and forecast the impacts of changing competition on plant communities, including changing outcomes of competition among species that currently interact (current competition) or that will interact in the future following range shifts (novel competition). However, it remains unclear how well traits explain variation in the outcomes of current and novel competition as well as the underlying processes determining coexistence or competitive exclusion, under changing climate. Here, we interacted pairs of high and low‐elevation species in three sites across an elevation gradient in the Swiss Alps. For each species pair, we quantified the population‐level outcomes of competition (invasion growth rates), relative fitness differences, and niche overlap and related these to 15 functional traits that were measured in each site. Most traits were significantly associated with invasion growth rates at the low elevation, where species had greater relative fitness differences, but these associations were much weaker towards higher elevations. This appears to be because traits, particularly those associated with light competition, captured species' relative fitness differences at lower elevations, but not at the high elevation site, highlighting that the predictive ability of traits can depend on environmental context. The amplified relative fitness differences towards lower elevations suggest that climate warming may increase the likelihood of competitive exclusion. In addition, novel competitors tended to show greater niche overlap than current competitors, leading to stronger overall competitive effects. However, in general, trait differences predicted competitive outcomes of novel and current competitors similarly well, suggesting that traits can predict interactions between species that do not yet interact. Our study reinforces the importance of considering changing interactions for predicting species responses to climate change and provides experimental evidence supporting the usefulness of functional trait differences in forecasting the impacts of future plant interactions under changing climate. [ABSTRACT FROM AUTHOR]

Major theories regarding microbe‐mediated plant community dynamics assume that plant species cultivate distinct microbial communities. However, few studies empirically assess the role of species‐associated microbial community dissimilarity in plant competitive dynamics.In this study, we paired a competition experiment between eight annual forbs with characterisation of species‐associated fungal communities to assess whether mycobiome dissimilarity is associated with pairwise competitive dynamics.Using a quantitative approach informed by modern coexistence theory, we found that fungal dissimilarity was correlated with both increased stabilising niche differences and fitness inequalities. Additionally, we found that the probability of coexistence increased with mycobiome dissimilarity.When subsetting the community into different fungal functional groups (pathotrophs, saprotrophs, symbiotrophs), overall relationships between dissimilarity and competitive dynamics were independent of these functional groups.Synthesis. These results suggest that fungal community divergence may play an important role in mediating plant competitive dynamics. Although fungal community dissimilarity is associated with both niche and fitness differences, complex biotic and/or abiotic interactions below‐ground may result in an observed correlation between fungal community dissimilarity and plant coexistence. Ultimately, this study suggests a novel approach to better understanding how microbiome dissimilarity may impact host community dynamics. [ABSTRACT FROM AUTHOR]

Plant–soil feedback (PSF), the reciprocal interaction between plants and their soil environment, is a fundamental ecological process that can influence coexistence and functional structure in plant communities. Current theory establishes that PSF may enhance diversity or lead to exclusion depending on whether soil conditioning disproportionately benefits heterospecific or conspecific individuals. However, a more complete picture of the impact of PSF requires understanding how PSF interacts with competition. To that end, here we propose an integrated mathematical model combining trait‐based competition and soil‐explicit PSF. Contrary to the current paradigm, we find that soil conditioning that disproportionately favours conspecific individuals can promote coexistence. Additionally, we show that priority effects are common when soil‐conditioning species differ in their edaphic preferences. These effects can allow species with large differences in competitive ability to coexist under certain soil conditions. Our results provide testable predictions tying community‐level functional patterns in plant communities to PSF and competition. [ABSTRACT FROM AUTHOR]

Just as plants attack heterospecific competitors with allelopathic phytotoxins, they also attack conspecifics with phytotoxins to inhibit seedling germination and growth (autotoxicity). As a result, for many plant species, autotoxicity limits offspring germination and growth proximate to parental plants—consequently reducing deleterious density dependent effects. Autotoxicity appears to vary across species, but it also may vary within species. We tested autotoxicity and variability in six ecotypes of the model plant, Arabidopsis thaliana, using allelopathy bioassays. We found that autotoxic impacts varied across the Eurasian and African ecotypes, and the negative effects on conspecific root growth were greater from above-than belowground exudate. In half the ecotypes, root growth decreased 71% in seedlings treated with exudate from the same ecotype than when treated with exudate from other ecotypes. That the ecotypes limited themselves more than they did other ecotypes is consistent with coexistence theory, which assumes species limit themselves more than others. Moreover, it is consistent with negative density dependent theories that suggest seedling mortality is highest near conspecific adults. Finally, the variation in autotoxicity across ecotypes suggests that intraspecific genetic variability and/or local habitat influence autotoxic intensity. It is well recognized that phytotoxic effect (allelopathy and autotoxicity) varies interspecifically but ecotype-level effects suggests that plants may exhibit greater intraspecific variation in autotoxicity than currently recognized. [ABSTRACT FROM AUTHOR]

Interspecific competition is widely considered a powerful process underlying species coexistence and ecological community structure. Although coexistence theory predicts stronger competition between more ecologically similar species, empirical support has largely relied on inferring competition from patterns of species co-occurrence. Coexistence theory also posits that species can only coexist when individuals compete more with conspecifics than with other species, however, few field studies—particularly in reptiles—have simultaneously estimated the strength of both intra- and interspecific competition among co-occurring species. Using an array of 12 experimental plots, we manipulated species presence and population size by plot of three native Anolis lizard species to empirically estimate the strength of competition on one anole species driven by two other species of varying ecological similarity. We observed that the strength of competition—as determined by relative growth rates and gravidity—was highly predictable and correlated to ecological similarity. Interspecific competition was strongest among species of highest ecological similarity, and intraspecific competition—induced by the addition or removal of conspecifics—was consistently the most intense. By employing direct experimental manipulations, our study provides an empirical investigation of the strength of competition as it relates to ecological similarity. [ABSTRACT FROM AUTHOR]

The competition-colonization (CC) trade-off is a well-studied coexistence mechanism for metacommunities. In this setting, it is believed that the coexistence of all species requires their traits to satisfy restrictive conditions limiting their similarity. To investigate whether diverse metacommunities can assemble in a CC trade-off model, we study their assembly from a probabilistic perspective. From a pool of species with parameters (corresponding to traits) sampled at random, we compute the probability that any number of species coexist and characterize the set of species that emerges through assembly. Remarkably, almost exactly half of the species in a large pool typically coexist, with no saturation as the size of the pool grows, and with little dependence on the underlying distribution of traits. Through a mix of analytical results and simulations, we show that this unlimited niche packing emerges as assembly actively moves communities toward overdispersed configurations in niche space. Our findings also apply to a realistic assembly scenario where species invade one at a time from a fixed regional pool. When diversity arises de novo in the metacommunity, richness still grows without bound, but more slowly. Together, our results suggest that the CC trade-off can support the robust emergence of diverse communities, even when coexistence of the full species pool is exceedingly unlikely. [ABSTRACT FROM AUTHOR]

Work on the Lake Victoria cichlids Pundamilia nyererei (red dorsum males, deeper water), Pundamilia pundamilia (blue males, shallower water) and related species pairs has provided insights into processes of speciation. Here, we investigate the female mating behaviour of 5 Pundamilia species and 4 of their F1 hybrids through mate choice trials and paternity testing. Complete assortative mating was observed among all sympatric species. Parapatric species with similar depth habitat distributions interbred whereas other parapatric and allopatric species showed complete assortative mating. F1 hybrids mated exclusively with species accepted by females of the parental species. The existence of complete assortative mating among some currently allopatric species suggests that pre-existing mating barriers could be sufficient to explain current patterns of co-existence, although, of course, many other factors may be involved. Regardless of the mechanism, mating preferences may influence species distribution in potentially hybridizing taxa, such as in the adaptive radiation of cichlid fish. We suggest that this at least partly explains why some species fail to establish breeding populations in locations where they are occasionally recorded. Our results support the notion that the mating preferences of potentially cross-breeding species ought to be included in coexistence theory. [ABSTRACT FROM AUTHOR]

Intraspecific trait variation is ubiquitous and is likely to influence species coexistence. Despite theoretical progress, empirical work on the effects of intraspecific variation on the dynamics of competing species is rare. This is because of the formidable empirical requirements necessary to link intraspecific variation in species' functional traits with intraspecific variation in the demographic and competitive rates that mediate coexistence. Here we partially overcome these challenges to determine how intraspecific variation in reproductive phenology in a native Californian annual plant species Lasthenia californica affects its ability to coexist with two non‐native species Bromus madritensis and Lactuca serriola that display contrasting phenological patterns. Using data from a field experiment, we empirically parameterize a model of competitive population dynamics, accounting for the effects of intraspecific phenological trait variation on the native species' response to both intra‐ and interspecific competition. We find that intraspecific variation in phenology drives differences in the native species' response to competition. Moreover, simulations of the parameterized model show that this variation improves the competitive performance of the native species. This occurs because of the effects of nonlinear averaging mediated by a nonlinear, concave‐up competition function that is a general feature of competition across a wide range of taxa. While intraspecific variation improves competitive performance, we also find that the magnitude of the benefit is predicted to be insufficient to prevent competitive exclusion against the non‐native species with early phenogy Bromus. Against the second non‐native species with later phenology Lactuca, intraspecific variation is predicted to result in coexistence where competitive exclusion would otherwise occur, but we could not rule out alternative qualitative outcomes for this interaction. [ABSTRACT FROM AUTHOR]

Explaining the maintenance of diverse species assemblages is a central goal of ecology and conservation. Recent coexistence mechanisms highlight the role of dispersal as a source of the differences that allow similar species to coexist. Here, we propose a new mechanism for species coexistence that is based on dispersal differences, and on the geometry of the habitat patch. In a finite habitat patch with complex boundaries, species with different dispersal abilities will arrange themselves in stable, concentric patterns of dominance. Species with superior competitive and dispersal abilities will dominate the interior of the patch, with inferior species at the periphery. We demonstrate and explain the mechanism on a simple one-dimensional domain, and then on two-dimensional habitat patches with realistic geometries. Finally, we use metrics from landscape ecology to demonstrate that habitat patches with more complex geometries can more easily support coexistence. The factors that underpin this new coexistence mechanism—different dispersal abilities and habitat patches with complex geometries—are common to many marine and terrestrial ecosystems, and it is therefore possible that the mechanism is a common factor supporting diverse species assemblages. [ABSTRACT FROM AUTHOR]

The ability of native communities to maintain invasion resistance in the face of environmental changes is crucial for biodiversity conservation. However, previous studies have primarily focused on the inhibitive effects experienced by invaders, providing limited insights into the ultimate outcome of resistance.In this study, we integrated modern coexistence theory into biotic resistance research to investigate the impact of nutrient enrichment on the resistance of Phragmites australis marshes to Spartina alterniflora invasion in the Yangtze estuary saltmarshes of China.Our results demonstrated that under non‐enriched conditions, successful invasion resistance was facilitated by stable coexistence between native and invasive species in the field. This prediction of invasion resistance aligned with the distribution dynamics of the two species in the Yangtze estuary saltmarshes over the past two decades. However, nutrient enrichment was likely to lead to a fundamental shift in their coexistence and ultimately, the failure of resistance.Synthesis and applications. Integrating modern coexistence theory into biotic resistance studies advances the assessment of invasion resistance by shifting from quantifying relative strength to predicting explicit resistance outcomes. Ecosystem managers can draw explicit conclusions about the potential establishment and impact of invaders by analysing observational or experimental data within the framework of modern coexistence theory. This information aids in identifying the most efficient strategies for addressing invasive species. [ABSTRACT FROM AUTHOR]

Ecological differences between coexisting species within plant communities can be assessed by considering functional and phylogenetic dissimilarities either separately or in a complementary way. Here, we studied (a) the potential overlap between functional (FD) and phylogenetic diversities (PD) and (b) their combined and unique roles in explaining community assembly patterns across different temperate vegetation types and across functional traits representing multiple dimensions of plant strategy (plant size, leaf, floral and reproductive, clonal and bud bank traits).We tested the strength of the PD–FD relationship within and across vegetation types and functional traits (Pearson correlations) and tested whether it depended on the strength of the phylogenetic signal (Pagel's lambda and Blomberg's K). We tested deviations from random expectations in FD and 'decoupled FD' (i.e. functional dissimilarity after accounting for the effect of phylogenetic distances between species) to reveal the importance of ecological differences for community assembly.PD–FD correlations were predominantly significant but rarely strong, and largely depended on the studied functional trait and vegetation type. Phylogenetic signals were partially but inconsistently related to the overlap between FD and PD.Community assembly patterns tended to shift from under‐dispersion (FD lower than random expectations) towards over‐dispersion (FD higher than random expectations) when functional distances were decoupled from phylogenetic distances indicating that species within the same clade were dissimilar to each other regarding their traits. However, we found the opposite pattern as well, mainly for floral and below‐ground traits, which indicated functional differentiation across clades.Synthesis. Decoupling functional and phylogenetic differences between species might provide further information on plant community assembly: showing cases where the strongest ecological differentiation between coexisting species occurs between phylogenetically related species rather than between phylogenetically unrelated ones. [ABSTRACT FROM AUTHOR]

Phosphorus, Iron and Aluminum are the key elements in solar cell materials and typically difficult to remove during MG-Si refining process. The evaluations of their thermodynamic properties in Si dilute solutions are crucial for the possibility and efficiency of impurities elimination process. In the present study, the activities and self-interaction parameters of P、Fe and Al in molten Si at 1723-1873 K were investigated by applying the models of mass action concentrations for Si-P、Si-Fe and Si-Al Binary Solution. The activities of Fe, Al with a mass concentration range of 1–2000 ppmw and P with a mass concentration range of 1–100 ppmw in dilute Si-based solutions are calculated by the model. The effects of temperature and impurity concentration on the thermodynamic properties of Si-based binary solutions were also determined by the models. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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Classic ecological theory explains species coexistence in variable environments. While spatial variation is often treated as an intrinsic feature of a landscape, it may be shaped and even generated by the resident community. All species modify their local environment to some extent, driving changes that can feed back to affect the composition and coexistence of the community, potentially over timescales very different from population dynamics. We introduce a simple nested modeling framework for community dynamics in heterogeneous environments, including the possible evolution of heterogeneity over time due to community-environment feedbacks. We use this model to derive analytical conditions for species coexistence in environments where heterogeneity is either fixed or shaped by feedbacks. Among other results, our approach reveals how dispersal and environmental specialization interact to shape realized patterns of habitat association and demonstrates that environmental feedbacks can tune landscape conditions to allow the stable coexistence of any number of species. Our flexible modeling framework helps explain feedback dynamics that arise in a wide range of ecosystems and offers a generic platform for exploring the interplay between species and landscape diversity. [ABSTRACT FROM AUTHOR]

Plant–arbuscular mycorrhizal fungal (AMF) associations can mediate soil resources among competing plants to influence plant resource capture and fitness, making AMF a potential agent of plant coexistence. We assessed plant coexistence, via niche and fitness differences, using six plant species varying in their mycorrhizal status. We grew the species in 15 competitive pairs with or without AMF. Effects of AMF on coexistence were determined by parametrizing pair-wise Lotka–Volterra plant competition models. Responses of the six plant species to AMF were determined by comparing the shoot biomass of single plants grown in the absence of any competition with AMF to the shoot biomass without AMF. The inoculation with AMF reduced the fitness differences between competitors, but the degree of AMF-mediated coexistence depended on the identity of the competing plant species. A greater AMF response difference between competing plant species reduced niche overlap and increased coexistence. These results show that while AMF generally reduce fitness differences, the equalizing effect of AMF is not always strong enough to overcome a competitive imbalance due to niche overlap and thus does not always lead to coexistence. Instead, it is the intrinsic growth response of different plant species to AMF, which can predict reduced niche overlap that in turn leads to coexistence. This implies that mycorrhizal dependence is a plant strategy to reduce niche overlap with competitors, thus allowing for greater coexistence. [ABSTRACT FROM AUTHOR]

Understanding the effects of evolution on emergent population properties such as intrinsic growth rates, species abundances or resilience is not only a key theoretical question, but has major empirical implications, for instance in conservation, agroecology and invasion ecology. Evolution can also lead to polymorphism based on niche differentiation among different phenotypes. The present article has three aims. First, we clarify the evolutionary scenarios allowing for optimization of population growth rate and abundance. Second, we relate the eco‐evolutionary emergence of polymorphism to the niche‐overlap and fitness‐ratio sensu coexistence theory. Third, we discuss whether properties of polymorphic populations can be optimized due to niche‐displacement among phenotypes. We revisit previous theoretical results on eco‐evolutionary optimization and link them with our Lotka–Volterra framework. Depending on how the traits under selection affect species intrinsic growth rates or ecological interactions, we uncover three scenarios, ranging from the optimization of all three properties to no optimization and link evolutionary dynamics to coexistence theory. Optimization is, in general, incompatible with niche differentiation sensu coexistence theory and, therefore, with the emergence of polymorphism. Niche displacement between resident and mutant phenotypes, and potentially polymorphism, only arise when we do not expect optimality to hold. Finally, we show how our approach can be generalized to coevolutionary scenarios. In the discussion, we propose biological scenarios and traits that may fall into our three scenarios. Although it is possible to find traits for which optimality is expected, for the majority of the cases optimization arguments do not hold. We also provide practical applications of our results in conservation, agroecology, harvesting and invasion ecology. [ABSTRACT FROM AUTHOR]

Competition is among the most important factors regulating plant population and community dynamics, but we know little about how different vital rates respond to competition and jointly determine population growth and species coexistence. We conducted a field experiment and parameterised integral projection models to model the population growth of 14 herbaceous plant species in the absence and presence of neighbours across an elevation gradient (284 interspecific pairs). We found that suppressed individual growth and seedling establishment contributed the most to competition‐induced declines in population growth, although vital rate contributions varied greatly between species and with elevation. In contrast, size‐specific survival and flowering probability and seed production were frequently enhanced under competition. These compensatory vital rate responses were nearly ubiquitous (occurred in 92% of species pairs) and significantly reduced niche overlap and stabilised coexistence. Our study highlights the importance of demographic processes for regulating population and community dynamics, which has often been neglected by classic coexistence theories. [ABSTRACT FROM AUTHOR]

For millennia, societies have tried to find ways to sustain people's livelihoods by setting rules to equitably and sustainably access, harvest and manage common pools of resources (CPR) that are productive and rich in species. But what are the elements that explain historical successes and failures? Elinor Ostrom suggested that it depends on at least eight axiomatic principles of good governance, whereas empirical results suggest that these principles are not sufficient to describe them, especially when applied to CPRs that possess great social and ecological diversity. The aim of this article is to explore the behavior of a mathematical model of multi-species forest dynamics that respects the foundations of ecology and Ostrom's governance theory, in order to detect possible constraints inherent to the functioning of these complex systems. The model reveals that fundamental structural laws of compatibilities between species life-history traits are indeed constraining the level of co-existence (average and variance) between a diversity of co-vulnerable timber resource users (RU) and of competing tree species. These structural constraints can also lead to unexpected outcomes. For instance in wetter forest commons, opening up the access to as many diverse RUs as there are competing tree species, produces a diversity of independently-controlled disturbances on species, collectively improving the chances of coexistence between species with different life-history traits. Similar benefits are observed on forest carbon and on profits from timber harvesting. However in drier forest commons, the same benefits cannot be observed, as predicted on the basis of the constraining laws. The results show that the successes and failures of certain management strategies can be reasonably explained by simple mechanistic theories from ecology and the social-ecological sciences, which are themselves constrained by fundamental ecological invariants. If corroborated, the results could be used, in conjunction with Ostrom's CPR theory, to understand and solve various human-nature coexistence dilemmas in complex social-ecological systems. [ABSTRACT FROM AUTHOR]

For millennia, societies have tried to find ways to sustain people’s livelihoods by setting rules to equitably and sustainably access, harvest and manage common pools of resources (CPR) that are productive and rich in species. But what are the elements that explain historical successes and failures? Elinor Ostrom suggested that it depends on at least eight axiomatic principles of good governance, whereas empirical results suggest that these principles are not sufficient to describe them, especially when applied to CPRs that possess great social and ecological diversity. The aim of this article is to explore the behavior of a mathematical model of multi-species forest dynamics that respects the foundations of ecology and Ostrom’s governance theory, in order to detect possible constraints inherent to the functioning of these complex systems. The model reveals that fundamental structural laws of compatibilities between species life-history traits are indeed constraining the level of co-existence (average and variance) between a diversity of co-vulnerable timber resource users (RU) and of competing tree species. These structural constraints can also lead to unexpected outcomes. For instance in wetter forest commons, opening up the access to as many diverse RUs as there are competing tree species, produces a diversity of independently-controlled disturbances on species, collectively improving the chances of coexistence between species with different life-history traits. Similar benefits are observed on forest carbon and on profits from timber harvesting. However in drier forest commons, the same benefits cannot be observed, as predicted on the basis of the constraining laws. The results show that the successes and failures of certain management strategies can be reasonably explained by simple mechanistic theories from ecology and the social-ecological sciences, which are themselves constrained by fundamental ecological invariants. If corroborated, the results could be used, in conjunction with Ostrom’s CPR theory, to understand and solve various human-nature coexistence dilemmas in complex social-ecological systems.

Pathogen coexistence depends on ecological processes operating at both within and between‐host scales, making it difficult to quantify which processes may promote or prevent coexistence. Here, we propose that adapting modern coexistence theory—traditionally applied in plant communities—to pathogen systems provides an exciting approach for examining mechanisms of coexistence operating across different spatial scales. We first overview modern coexistence theory and its mechanistic decomposition; we subsequently adapt the framework to quantify how spatial variation in pathogen density, host resources and immunity, and their interaction may promote pathogen coexistence. We apply this derivation to an example two pathogen, multiscale model comparing two scenarios with generalist and strain‐specific immunity: one with demographic equivalency among pathogens and one with demographic trade‐offs among pathogens. We then show how host–pathogen feedbacks generate spatial heterogeneity that promote pathogen coexistence and decompose those mechanisms to quantify how each spatial heterogeneity contributes to that coexistence. Specifically, coexistence of demographically equivalent pathogens occurs due to spatial variation in host resources, immune responses, and pathogen aggregation. With a competition–colonization trade‐off, the superior colonizer requires spatial heterogeneity to coexist, whereas the superior competitor does not. Finally, we suggest ways forward for linking theory and empirical tests of coexistence in disease systems. [ABSTRACT FROM AUTHOR]

Resource competition theory predicts coexistence and exclusion patterns based on species' R *s, the minimum resource values required for a species to persist. A central assumption of the theory is that all species have equal access to resources. However, many systems are characterized by preemption exploitation, where some species deplete resources before their competitors can access them (e.g., asymmetric light competition, contest competition among animals). We hypothesized that coexistence under preemption requires an R *-preemption trade-off—that is, the species with the priority access should have a higher R * (lower "efficiency"). Thus, we developed an extension of resource competition theory to investigate partial and total preemption (in the latter, the preemptor is unaffected by species with lower preemption rank). We found that an R *-preemption trade-off is a necessary condition for coexistence in all models. Moreover, under total preemption, the trade-off alone is sufficient for coexistence. In contrast, under partial preemption, more conditions are needed, which restricts the parameter space of coexistence. Finally, we discuss the implications of our finding for seemingly distinct trade-offs, which we view as special cases of the R *-preemption trade-off. These trade-offs include the digger-grazer trade-off, the competition-colonization trade-off, and trade-offs related to light competition between trees and understories. [ABSTRACT FROM AUTHOR]

Janzen–Connell effects (JCEs), specialised predation of seeds and seedlings near conspecific trees, are hypothesised to maintain species richness. While previous studies show JCEs can maintain high richness relative to neutral communities, recent theoretical work indicates JCEs may weakly inhibit competitive exclusion when species exhibit interspecific fitness variation. However, recent models make somewhat restrictive assumptions about the functional form of specialised predation—that JCEs occur at a fixed rate when offspring are within a fixed distance of a conspecific tree. Using a theoretical model, I show that the functional form of JCEs largely impacts their ability to maintain coexistence. If predation pressure increases additively with adult tree density and decays exponentially with distance, JCEs maintain considerably higher species richness than predicted by recent models. Loosely parameterising the model with data from a Panamanian tree community, I elucidate the conditions under which JCEs are capable of maintaining high species richness. [ABSTRACT FROM AUTHOR]

Recent developments in understanding and predicting species responses to climate change have emphasised the importance of both environmental variability and consideration of the wider biotic community. However, to date, the interaction between the two has received less attention. Both theoretical and empirical results suggest that the combined effect of environmental variability and interspecific interactions can have strong impacts on existing range limits. Here we explore how competitive interactions and temporal variability can interact with the potential to strongly influence range shift dynamics. We highlight the need to understand these between‐process interactions in order to predict how species will respond to global change. In particular, future research will need to move from evaluating possibilities to quantifying their impact. We emphasise the value and utility of empirically parameterised models to determine the direction and relative importance of these forces in natural systems. [ABSTRACT FROM AUTHOR]

A calculation model of activity for CaO–SiO2–MgO–Al2O3–TiO2 slag is established according to molecular-ion coexistence theory of slag structure to calculate the activities of Al2O3, SiO2, and TiO2 in the slag. The possibility of TiO2 reduction in the slag during refining is analyzed by thermodynamics and verified by laboratory and industrial experiments. Both theoretical analysis and laboratory experimental results show that the content of TiO2 in the ladle slag significantly influences the Ti content in molten steel. When the content of the dissolved aluminum in molten steel is 0.030–0.050%, the TiO2 content in the ladle slag should be controlled below 0.3% to prevent TiO2 reduction. The critical content of TiO2 decreases with an increasing amount of the dissolved aluminum in molten steel. In addition, silicon should be used as a deoxidizer during diffused deoxidization because aluminum as a deoxidizer would lead to the reduction of TiO2. The industrial experiments confirm the results of the laboratory experiments and thermodynamics analysis.

Modern coexistence theory (MCT) holds the potential to study the ability of species to avoid extinction (i.e. to persist) across community types but is rarely applied beyond pairs of competing species. Here, we show that this limitation can be overcome by mapping species according to their niche () and fitness differences (). This application provides three main benefits to study processes of multispecies persistence across trophic levels. First, mapping introduces a novel categorization of species and communities according to the high‐level processes at play: frequency dependence (negative or positive), the occurrence of positive species interactions (facilitation and mutualism) and whether persistence is possible without the presence of other species because of trophic interactions, such as herbivory or predation. Therefore, this mapping can be seen as a toolbox to describe how species persistence depends on species interactions. Second, mapping facilitates studying how species persistence responds to environmental changes that shift intrinsic growth rates and the strength and sign of species interactions. Third, mapping has the potential to foster synthesis across community types because it can accommodate co‐occurrence of positive, negative and neutral interactions between species. We, therefore, argue that mapping can promote collaboration across sub‐fields, as it provides a common concept to link disparate ecological communities. [ABSTRACT FROM AUTHOR]

That species must differ ecologically is often viewed as a fundamental condition for their stable coexistence in biological communities. Yet, recent work has shown that ecologically equivalent species can coexist when reproductive interactions and sexual selection regulate population growth. Here, we review theoretical models and highlight empirical studies supporting a role for reproductive interactions in maintaining species diversity. We place reproductive interactions research within a burgeoning conceptual framework of coexistence theory, identify four key mechanisms in intra- and interspecific interactions within and between sexes, speculate on novel mechanisms, and suggest future research. Given the preponderance of sexual reproduction in nature, our review suggests that this is a neglected path towards explaining species diversity when traditional ecological explanations have failed. Understanding how species diversity is maintained has implications for both applied and basic sciences. Species coexistence in biological communities is frequently thought to require ecological niche differentiation between species. Recent developments have shown that ecological differences are not necessary, and that sexual selection and other reproductive interactions can promote coexistence in the absence of ecological differentiation. The key mechanisms that generate coexistence along with their empirical support are highlighted. A more expansive and mechanistic view of mechanisms promoting coexistence may help to resolve how diverse groups can persist in the absence of ecological differences. [ABSTRACT FROM AUTHOR]

Mutualisms are ubiquitous in nature and are thought to play important roles in the maintenance of biodiversity. For biodiversity to be maintained, however, species must coexist in the face of competitive exclusion. Chesson's coexistence theory provides a mechanistic framework for evaluating coexistence, yet mutualisms are conspicuously absent from coexistence theory and there are no comparable frameworks for evaluating how mutualisms affect the coexistence of competiting species. To address this conceptual gap, I develop theory predicting how multitrophic mutualisms mediate the coexistence of species competing for mutualistic commodities and other limiting resources using the niche and fitness difference concepts of coexistence theory. I demonstrate that failing to account for mutualisms can lead to erroneous conclusions. For example, species might appear to coexist on resources alone, when the simultaneous incorporation of mutualisms actually drives competitive exclusion, or competitive exclusion might occur under resource competition, when in fact, the incorporation of mutualisms generates coexistence. Existing coexistence theory cannot therefore be applied to mutualisms without explicitly considering the underlying biology of the interactions. By discussing how the metrics derived from coexistence theory can be quantified empirically, I show how this theory can be operationalized to evaluate the coexistence consequences of mutualism in natural communities. [ABSTRACT FROM AUTHOR]

Forecasting the impacts of climate change on species persistence in diverse natural communities requires a way to account for indirect effects mediated through species interactions. In particular, we expect species to experience major changes in competition as they track favorable climates. Here, we combine experimental data with a recently developed theoretical framework based on coexistence theory to measure the impact of climate‐driven range shifts on alpine plant persistence under climate change. We transplanted three co‐dominant alpine perennial species to five elevations, creating a maximum of 5°C increase in average growing‐season temperature. We statistically modeled species' demographic rates in response to the environment and interpolated species' intrinsic ranges—the environmental mapping of reproduction in the absence of competition. We used low‐density population growth rates—species' initial rate of invasion into an established community—as a metric of persistence. Further analysis of low‐density growth rates (LGRs) allowed us to parse the direct impacts of climate change from indirect impacts mediated by shifting competition. Our models predict qualitatively different range shifts for each species based on the climate conditions under which growth rates are maximized and where they are zero. Overall, climate change is predicted to increase the intrinsic (competition free) growth rates of all species, as warmer and wetter conditions increase the favorability of alpine habitat. However, these benefits are entirely negated by increased competition arising from greater overlap between competitors in their intrinsic ranges. Species were highly dispersal limited, which can prevent species from tracking shifting intrinsic ranges by reducing population spread rates. Yet dispersal limitation also promoted species' persistence because it promotes persistence mechanisms. Our study demonstrates the complex pathways by which climate change impacts species' persistence by altering their competitive environment, and highlights how a persistence framework based on LGRs can help disentangle impacts. [ABSTRACT FROM AUTHOR]

Speciation is frequently initiated but rarely completed, a phenomenon hypothesized to arise due to the failure of nascent lineages to persist. Although a failure to persist often has ecological causes, key gaps exist between ecological and evolutionary theories that, if filled, would clarify when and why speciation succeeds or fails. Here, we apply ecological coexistence theory to show how the alignment between different forms of niche opportunity and niche use shape the initiation, progression, and completion of speciation. Niche evolution may drive coexistence or competitive exclusion, and an ability to coexist ecologically may help or hinder speciation. Our perspective allows progress towards unifying the origin and maintenance of species diversity across the tree of life. Speciation is the process by which new species are formed, shaped by ecological conditions within which lineages live and evolve. We argue that the distribution of available resources within and among regions dictates if and how speciation will be initiated, as well as whether newly formed lineages will persist ecologically. Lineages may diverge to use different resource types, but whether divergence confers niche differentiation or a competitive asymmetry depends on resource availability in the location of secondary contact. Coexistence may sometimes help and sometimes halt speciation, depending on its timing relative to reproductive isolation, and may frequently fail due to stochastic extinction. Speciation modes emerge as a consequence of how different forms of ecological opportunity shape microevolutionary processes, giving rise to new persistent species at different rates. [ABSTRACT FROM AUTHOR]

Seasonal compositional changes in plankton communities are usually considered as species replacements. Given the enormous number of individuals integrating the communities and our limited capacity to count and determine most of them, we likely observe only alternative population peaks of some of the coexisting species. The contemporary coexistence theory addresses coexistence in communities of competing species, considering relative fitness inequalities and stabilising niche differences as components of average long‐term growth rates. Here, we experimentally show that the response patterns predicted by the theory occur when varying nutrient pulses fertilise the planktonic community.We used gently self‐filling 100‐L enclosures to minimise the disturbance of the initial community and different pulse P and N additions to manipulate the apparently species‐poor epilimnetic community of an ultraoligotrophic P‐limited lake. We measured and compared the protist species growth response to gradients of P enrichment and N stoichiometric imbalance. The P and N levels used in most treatments were within the oligotrophic seasonal and inter‐annual variations of the lake and were higher in a few extreme treatments that provided mesotrophic conditions of the remote regions affected by N atmospheric contamination. We alternatively replicated all treatments using ammonium or nitrate as the N source.Most protist species, recorded in this lake across seasons in previous studies, were recovered, indicating a persistent assemblage of species that is seasonally hidden from observation. Recovery included some rare species observed only in the slush layers of the seasonal snow and ice cover. The coexistence‐stabilising mechanisms were indicated by treatment response features, such as frequency‐dependent growth, inverse relationship between fitness inequality and niche differentiation proxies, high‐rank taxonomic levels clustering across the limiting‐nutrient gradient but segregation at the species level according to the type of N supply and resting stage development depending on nutrient conditions. The response similarities between autotrophic and heterotrophic organisms indicate a network of interactions that may reinforce coexistence.Synthesis. The results indicate that many planktonic protist species in oligotrophic waters can show stable long‐term non‐equilibrium coexistence by alternately recovering from very low densities when episodic nutrient enrichments, of varying P and N amounts and composition, occur. [ABSTRACT FROM AUTHOR]

Half a century ago, Janzen and Connell hypothesized that the high tree species diversity in tropical forests is maintained by specialized natural enemies. Along with other mechanisms, these can cause conspecific negative density dependence (CNDD) and thus maintain species diversity. Numerous studies have measured proxies of CNDD worldwide, but doubt about its relative importance remains. We find ample evidence for CNDD in local populations, but methodological limitations make it difficult to assess if CNDD scales up to control community diversity and thereby local and global biodiversity patterns. A combination of more robust statistical methods, new study designs, and eco-evolutionary models are needed to provide a more definite evaluation of the importance of CNDD for geographic variation in plant species diversity. Stabilizing conspecific negative density dependence (CNDD) is a classical explanation for diversity maintenance in species-rich ecosystems, particularly in tropical forests. Fifty years after Janzen and Connell popularized this idea, a plethora of empirical evidence suggests that CNDD can be found at all latitudes and for many tree species. On closer inspection, however, it is still unclear if locally measured density effects are indeed stabilizing community dynamics and, moreover, if they have a causal effect on large-scale diversity and abundance patterns, such as the latitudinal diversity gradient. More robust and comparable CNDD estimates are needed, coupled with a theoretical research program that aims at understanding the role of CNDD for coexistence in stochastic multispecies communities as well as macroecological and macroevolutionary diversity patterns. [ABSTRACT FROM AUTHOR]

Conspecific negative density dependence (CNDD) has been highlighted as a main driver of biodiversity maintenance. However, while there is general consensus on the scale‐dependent and interacting nature of ecological processes, there is limited knowledge about the relative importance of CNDD across spatial scales and on its interaction with other processes, such as dispersal and immigration. While many studies have detected CNDD at local scales, it remains unknown whether its effects on biodiversity maintenance scale‐up to landscapes and regions. Here, we use a generic dynamic and spatially‐explicit simulation model to assess the interacting relative effects of local‐scale CNDD and immigration from a metacommunity for biodiversity maintenance across spatial scales. For this purpose, we systematically varied immigration rates, the average strength and the variation of CNDD among species. We found that CNDD only determined species richness in strongly isolated communities with little or no interspecific variation in CNDD. In closed communities, plausible interspecific variation in CNDD led to a strong reduction in species richness. In open communities, realistic levels of immigration overwhelmed the effects of CNDD on diversity maintenance. From these results, we suggest that local CNDD is unlikely to be a main driver of biodiversity in real communities, especially at larger spatial scales. This study provides a first step towards improved integration of local‐scale coexistence theory with large‐scale metacommunity theory and highlights the importance of considering the interacting and scale‐dependent nature of ecological processes. [ABSTRACT FROM AUTHOR]

Ecological theory produces opposing predictions about whether differences in the timing of life-history transitions, or "phenology," promote or limit coexistence. Phenological separation is predicted to create temporal niche differences, increasing coexistence, yet phenological separation could also competitively favor one species, increasing fitness differences and hindering coexistence. We experimentally manipulated relative germination timing, a critical phenological event, of two annual grass species, Vulpia microstachys and V. octoflora , to test these contrasting predictions. We parameterized a competition model to estimate within-season niche differences, fitness differences, and coexistence and to estimate coexistence when year-to-year fluctuations of germination timing occur. Increasing germination separation caused parallel changes in niche and fitness differences, with the net effect of weakening within-year coexistence. Both species experienced a competitive advantage by germinating earlier, and a 4-day head start allowed the generally inferior competitor to exclude the otherwise superior competitor. The overall consequence of germination separation was to limit coexistence within a given year, although year-to-year variation in the relative timing of germination was sufficient to support long-term coexistence. Our results clarify how phenological differences structure competitive interactions and highlight the need to quantify year-to-year variation in these differences to better understand species coexistence. [ABSTRACT FROM AUTHOR]

Coexistence and food web theory are two cornerstones of the long‐standing effort to understand how species coexist. Although competition and predation are known to act simultaneously in communities, theory and empirical study of these processes continue to be developed largely independently. Here, we integrate modern coexistence theory and food web theory to simultaneously quantify the relative importance of predation and environmental fluctuations for species coexistence. We first examine coexistence in a theoretical, multitrophic model, adding complexity to the food web using machine learning approaches. We then apply our framework to a stochastic model of the rocky intertidal food web, partitioning empirical coexistence dynamics. We find the main effects of both environmental fluctuations and variation in predator abundances contribute substantially to species coexistence. Unexpectedly, their interaction tends to destabilise coexistence, leading to new insights about the role of bottom‐up vs. top‐down forces in both theory and the rocky intertidal ecosystem. [ABSTRACT FROM AUTHOR]

Competition for limiting resources is among the most fundamental ecological interactions and has long been considered a key driver of species coexistence and biodiversity. Species' minimum resource requirements, their R*s, are key traits that link individual physiological demands to the outcome of competition. However, a major question remains unanswered--to what extent are species' competitive traits able to evolve in response to resource limitation? To address this knowledge gap, we performed an evolution experiment in which we exposed Chlamydomonas reinhardtii for approximately 285 generations to seven environments in chemostats that differed in resource supply ratios (including nitrogen, phosphorus and light limitation) and salt stress. We then grew the ancestors and descendants in a common garden and quantified their competitive abilities for essential resources. We investigated constraints on trait evolution by testing whether changes in resource requirements for different resources were correlated. Competitive abilities for phosphorus improved in all populations, while competitive abilities for nitrogen and light increased in some populations and decreased in others. In contrast to the common assumption that there are trade-offs between competitive abilities for different resources, we found that improvements in competitive ability for a resource came at no detectable cost. Instead, improvements in competitive ability for multiple resources were either positively correlated or not significantly correlated. Using resource competition theory, we then demonstrated that rapid adaptation in competitive traits altered the predicted outcomes of competition. These results highlight the need to incorporate contemporary evolutionary change into predictions of competitive community dynamics over environmental gradients. [ABSTRACT FROM AUTHOR]

In a recent modeling study ("Limiting Similarity? The Ecological Dynamics of Natural Selection among Resources and Consumers Caused by Both Apparent and Resource Competition") that appeared in the April 2019 issue of The American Naturalist , Mark A. McPeek argued that ecologically equivalent species may emerge via competition-induced trait convergence, in conflict with naive expectations based on the limiting similarity principle. Although the emphasis on the possibility of the convergence of competitors is very timely, here we show that the proposed mechanism will only lead to actual coexistence in the converged state for specially chosen fine-tuned parameter settings. It is therefore not a robust mechanism for the evolution of ecologically equivalent species. We conclude that invoking trait convergence as an explanation for the co-occurrence of seemingly fully equivalent species in nature would be premature. [ABSTRACT FROM AUTHOR]

Pollination is thought to be under positive density‐dependence, destabilising plant coexistence by conferring fitness disadvantages to rare species. Such disadvantage is exacerbated by interspecific competition but can be mitigated by facilitation and intraspecific competition. However, pollinator scarcity should enhance intraspecific plant competition and impose disadvantage on common over rare species (negative density‐dependence, NDD). We assessed pollination proxies (visitation rate, pollen receipt, pollen tubes) in a generalised plant community and related them to conspecific and heterospecific density, expecting NDD and interspecific facilitation due to the natural pollinator scarcity. Contrary to usual expectations, all proxies indicated strong intraspecific competition for common plants. Moreover interspecific facilitation prevailed and was stronger for rare than for common plants. Both NDD and interspecific facilitation were modulated by specialisation, floral display and pollinator group. The combination of intraspecific competition and interspecific facilitation fosters plant coexistence, suggesting that pollination can be a niche axis maintaining plant diversity. [ABSTRACT FROM AUTHOR]

Invasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno- and phenotypic intra-tumour heterogeneity, an alternative hypothesis presents itself: could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the context of acid-mediated invasion. We assume tumour expansion is obstructed by stroma which inhibits growth and extra-cellular matrix (ECM) which blocks cancer cell movement. Further, we assume that there are two types of cancer cells: (i) a glycolytic phenotype which produces acid that kills stromal cells and (ii) a matrix-degrading phenotype that locally remodels the ECM. We extend the Gatenby–Gawlinski reaction–diffusion model to derive a system of five coupled reaction–diffusion equations to describe the resulting invasion process. We characterise the spatially homogeneous steady states and carry out a simulation study in one spatial dimension to determine how the tumour develops as we vary the strength of competition between the two phenotypes. We find that overall tumour growth is most extensive when both cell types can stably coexist, since this allows the cells to locally mix and benefit most from the combination of traits. In contrast, when inter-species competition exceeds intra-species competition the populations spatially separate and invasion arrests either: (i) rapidly (matrix-degraders dominate) or (ii) slowly (acid-producers dominate). Overall, our work demonstrates that the spatial and ecological relationship between a heterogeneous population of tumour cells is a key factor in determining their ability to cooperate. Specifically, we predict that tumours in which different phenotypes coexist stably are more invasive than tumours in which phenotypes are spatially separated. [ABSTRACT FROM AUTHOR]

A fundamental challenge in ecology is to identify the processes which explain how species come to occupy diverse communities. There is uncertainty about whether community composition arises through deterministic processes, whereby trait differences between species make them more or less adapted to certain environmental conditions. We tested the capacity for deterministic processes to explain the long-term dynamics of phytoplankton community structure in Lake Müggelsee—a shallow and eutrophic lake in Berlin, Germany using a trait-based approach. We developed a null model representing random processes alone by generating a time series of random trait distributions derived from the observed long-term data. We determined the extent to which deterministic processes lead to nonrandom patterns in phytoplankton communities by comparing the resulting null-trait distributions with the observed trait distributions in the long-term data. We found that phytoplankton communities fell along a gradient from random to nonrandom trait distributions, suggesting that deterministic processes alone do not fully describe the community structure. Nonrandom patterns were observed in communities with high species richness and during late spring as well as early winter. But neither species richness nor seasonality explained nonrandom patterns consistently for different metrics and traits given the high relevance of random trait distribution patterns. Thus, deterministic and stochastic processes may be needed to fully explain the structure of phytoplankton communities under changing environmental conditions. [ABSTRACT FROM AUTHOR]

In order to study the thermodynamic conditions of iron resources recycled from oxidized molten nickel slag, a calculation model of apeo activity in CaO-FeO-MgO-SiO2 slag system was established，which was used to investigate the influence of binary basicity and MgO content on aFe0 activity in the slag at 1 723 K. The thermodynamic possibilities of oxidation of Fe to Fe3O4 in nickel slag at 1 723 K were analyzed, and the experimental verification was carried out. The results show that the activity o£ aFeo increases first and then decreases with the increase of the basicity, and reaches the maximum value at basicity of 1. 1. When the oxidation temperature was above 1 723 K, the K& of Fe3O4 being further oxidized to Fe2 O3 was less than 0，which could inhibit the formation of Fe2O3. After the molten oxidation process for nickel slag, the iron component is mainly enriched in the magnetite phase, and the average particle size of the magnetite particles is about 52 pm，which paves a way for magnetic separation of the magnetite phase in nickel slags. [ABSTRACT FROM AUTHOR]

The effect of alkaline oxide content,optical basicity,total iron content in slag and temperature on the measured slag phosphate capacity was investigated through the calculation and analysis of the slag phosphate capacity during the converter dephosphorization process combined with previous study. The relationship between phosphate capacity and composition of slag was fitted according to the production data. In addition,different prediction models of phosphate capacity were compared and analyzed from previous studies. Based on the coexistence theory,the prediction model of phosphate capacity in slag system was established,and the error analysis shows that the prediction model is accurate and credible,which can provide a theoretical guidance for the field production.

A thermodynamic model is proposed for calculating the mass action concentration of structural units in the Al-Ti binary melt system based on the atom-molecule coexistence theory. The standard equilibrium constants of reactions for forming three associated molecules as Al3Ti,Al Ti,and Al11Ti5 in the Al-Ti binary melt system at the temperature of 2073 to 2273 K are calculated based on the activity reported in the literature,and the expressions of the standard molar Gibbs free energy change of reactions are obtained.Meanwhile,the calculated mass action concentrations NAl and NTi of Al and Ti are compared with the reported activities of both Al and Ti in the full composition range of the Al-Ti binary melt system at different temperatures from the literature. The results show that the calculated mass action concentrations NAl and NTi are in agreement with the activities aAl and aTi in the reported literature. The relationship between the calculated mass action concentration Ni and the calculated equilibrium amount of substance ni of Al3Ti and Al11Ti5 in the Al-Ti binary melt system is rod-type. However,the relationship between the calculated mass action concertation NAlTi and the calculated equilibrium amount of substance nAlTi in this binary melt system is spindle-type.

Abstract: Over 40 years after the introduction of the concept into ecology, intransitive (i.e. non‐hierarchical) competition remains overlooked by ecological theory, despite theoretical work showing it could be a major driver of species coexistence. This special feature presents six studies, including models, reviews, experimental studies and large‐scale observational studies. Collectively, these studies help to (i) link intransitive competition with short‐ and long‐term coexistence and with other ecological patterns, (ii) evaluate the conditions under which intransitivity is more common and (iii) determine how best to quantify the degree of intransitivity. The studies in this special feature show the generality of intransitive competition in nature, explore interactions between intransitivity and other coexistence mechanisms, and illustrate the effect of environmental conditions (drought, shade, fertility) on intransitivity and coexistence. They also show which metrics best quantify intransitivity and highlight the importance of adopting a more continuous view of competition as varying from strongly transitive to strongly intransitive. The studies also examine relationships between intransitivity and functional diversity and explore the evolution of intransitivity over time. Synthesis. The studies presented here advance the field by integrating intransitive competition into species coexistence and general ecological theory. We also highlight important research gaps that will hopefully inspire the next generation of studies in this topic. [ABSTRACT FROM AUTHOR]

Abstract: Recent evidence suggests that intransitive competition (as in the game “rock‐paper‐scissors,” and in contrast to transitive or hierarchical competition) may be common in natural plant communities. This is important as theoretical analyses indicate that intransitivity promotes species coexistence. However, while intransitivity is common, competitive relationships among many species in communities may vary from transitive to highly intransitive. With increasing numbers of species, variation in competitive interrelationships among species can take on vastly more variable topologies. Consequently, several indices can be used to capture topological variation that is relevant to the prediction of species coexistence. Different indices capture different elements of topological variation. In addition, evidence indicates that these indices vary in their capacity to predict coexistence, and that variation not captured by these indices also contributes to variation in species coexistence. We used aspatial and spatial competition models to explore how well different indices (Slater's i, Kendall and Babington Smith's d, Monsuur and Storcken's ν, Bezembinder's ρ and Bezembinder's δ′, plus two binary indices we call “unbeatability” [u] and “always‐beatability” [a]) predict coexistence under the full spectrum of competitive tournament topologies for three to eight species, and a large sample of existing tournament topologies for nine species. All indices explored were generally better at predicting short‐term coexistence (i.e. the number of generations until the first extinction) compared to long‐term coexistence (i.e. generations until monoculture or long‐term species richness in aspatial and spatial models respectively). Indices also differed in performance: Kendall and Babington Smith's d (a measure of the number intransitive cycles among an assemblage's three‐species subsets that has also been reformulated as the relative intransitivity index) was the best predictor of short‐term coexistence; in terms of long‐term coexistence, the best predictor was typically d or u, the latter indicating the presence or absence of a species capable of outcompeting all its competitors. Synthesis. The indices employed here capture different elements of topological variation. Existing indices that capture aspects of intransitive competition vary in their capacity to predict coexistence in competition models. The more continuous nature of Kendall and Babington Smith's d index likely contributed to its robust performance; likewise, the ability of unbeatability to detect intransitivities involving the strongest competitors helps explain its success. [ABSTRACT FROM AUTHOR]

Abstract: Indirect biotic interactions—such as intransitive competition—are increasingly recognized as being important in shaping ecological patterns in natural systems. Over long time‐scales, such indirect interactions may affect the evolution of species phenotypes, which in turn can modify these interactions, thereby begetting eco‐evolutionary feedbacks. If indirect intransitive interactions can emerge in situ during lineage diversification, they could profoundly affect species’ phenotypic diversity, temporal stability, and subsequent diversification rates. We address these questions by investigating the conditions under which indirect intransitive competition can emerge from a lineage diversifying in sympatry. We use an adaptive dynamics model to study the ecological and evolutionary properties of this lineage under different scenarios where competition for resources between phenotypes varies in strength and (a)symmetry. Results show that weak‐intransitive competition can emerge during the sympatric diversification of a single lineage. “Weak‐intransitivity” here refers to situations where species interactions are not perfectly transitive, that is, there is no strict hierarchy in species competitive abilities. The strength of such weak‐intransitivity increases when the competition between phenotypes increases in strength and asymmetry. The strength of intransitivity also correlates with other system properties. We notably found that the strength of intransitivity increases with the number of phenotypes, and that greater intransitivity correlates with the evolution of greater functional trait divergences between phenotypes, greater resistance to invasion by new phenotypes but lower resistance to disturbances as well as slower evolutionary rates. Synthesis. This theoretical exploration of the evolution of intransitive competition provides the first formal bridge between the ecological and evolutionary aspects of intransitive competition. We show that, when competitive interactions are strong enough, weak‐intransitive competition is more likely to emerge through adaptive diversification than from a random community assembly. Intransitive competition is, therefore, not only restricted to between‐species interactions but can also function as a regulator of diversification within species, thereby affecting lineage functional diversity, and ecological and evolutionary stability. [ABSTRACT FROM AUTHOR]