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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]

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]

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]

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]

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]

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]

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.

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]

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]

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]

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]

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]

According to the ion and molecule coexistence theory (IMCT) for molten slags and corresponding phase diagrams, a thermodynamic model for the evaluation of mass action concentrations (designated by Ni for structure unit i) for La2O3-Al2O3, La2O3-Al2O3-CaF2, La2O3-Al2O3-CaF2-CaO, La2O3-Al2O3-CaF2-MgO and La2O3-Al2O3-CaF2-CaO-MgO slag systems for electroslag remelting (ESR) has been formulated. The influencing factors for the mass action concentration of La2O3, such as mass fraction of Al2O3, CaF2, CaO and MgO and temperature, were investigated. The results show that when the mole fraction of La2O3 is at 0.495, the mass action concentration of La2O3 · Al2O3 achieves its maximum value 0.946 in the La2O3-Al2O3 binary slag. In a composition area of La2O3: 10wt% ∼ 45wt%, Al2O3: 0wt% ∼ 50wt% and CaF2: 20wt% ∼ 70wt% of the La2O3-Al2O3-CaF2 ternary slag at 1873 K, the results show that the calculated values of NLa2O3 are in good agreement with the reported measured values of aLa2O3. The iso-curves of NLa2O3 is also drawn from the calculated results, which reveals that the mass action concentration of La2O3 decreases with the increasing of the Al2O3 and CaF2 content, and Al2O3 is stronger than CaF2 in decreasing the mass action concentration of La2O3. However, in La2O3-Al2O3-CaF2-CaO, La2O3-Al2O3-CaF2-MgO and La2O3-Al2O3-CaF2-CaO-MgO slag systems, the mass action concentration of La2O3 increases with the increasing of the MgO and CaO content, and CaO is stronger than MgO in increasing the mass action concentration of La2O3. In addition, the mass action concentration of La2O3 increases with the increasing temperature at the composition of 30wt%La2O3, 10wt%Al2O3, 40wt%CaF2, 10wt%MgO and 10wt%CaO.

According to the ion and molecule coexistence theory (IMCT) for molten slags and corresponding phase diagrams, a thermodynamic model for the evaluation of mass action concentrations (designated by Ni for structure unit i) for Ce2O3-Al2O3, CaO-Al2O3-Ce2O3 and CaO-Al2O3-SiO2-Ce2O3 slag systems has been formulated. The results show that when the mole fraction of Ce2O3 is at 0.49 in the binary slag, the mass action concentration of Ce2O3·Al2O3 achieves its maximum value 0.90. In a composition area of CaO/Al2O3 (mass fraction ratio) from 0.7 to 1.5 and Ce2O3 content (mass fraction) from 0 to 45% of the ternary slag at 1773 K, the results show that trends of calculated NAl2O3 are in good agreement with reported measured trends of aAl2O3. The iso-curves of NCe2O3 and NCaO are also drawn from the calculated results. A thermodynamic model of the equilibrium between 55.83%CaO-23%Al2O3-11.17%SiO2-10%Ce2O3 quaternary slag and molten steel containing aluminum has been further discussed. Results indicate that certain content of Ce would be dissolved in steel, which increases with the increasing of temperature and aluminum content, and when the aluminum content is 0.02%, the corresponding cerium content is in the range of 1.87 to 13.30 ppm at 1873 K. In summary, using Ce2O3 to replace Al2O3 can effectively reduce NAl2O3, certain content of Ce can dissolved in steel.

Recent theory predicts that stochastic dilution effects may result in species-rich communities with statistically independent species spatial distributions, even if the underlying ecological processes structuring the community are driven by deterministic niche differences. Stochastic dilution is a consequence of the stochastic geometry of biodiversity where the identities of the nearest neighbors of individuals of a given species are largely unpredictable. Under such circumstances, the outcome of deterministic species interactions may vary greatly among individuals of a given species. Consequently, nonrandom patterns in the biotic neighborhoods of species, which might be expected from coexistence or community assembly theory (e.g., individuals of a given species are neighbored by phylogenetically similar species), are weakened or do not emerge, resulting in statistical independence of species spatial distributions. We used data on phylogenetic and functional similarity of tree species in five large forest dynamics plots located across a gradient of species richness to test predictions of the stochastic dilution hypothesis. To quantify the biotic neighborhood of a focal species we used the mean phylogenetic (or functional) dissimilarity of the individuals of the focal species to all species within a local neighborhood. We then compared the biotic neighborhood of species to predictions from stochastic null models to test if a focal species was surrounded by more or less similar species than expected by chance. The proportions of focal species that showed spatial independence with respect to their biotic neighborhoods increased with total species richness. Locally dominant, high-abundance species were more likely to be surrounded by species that were statistically more similar or more dissimilar than expected by chance. Our results suggest that stochasticity may play a stronger role in shaping the spatial structure of species rich tropical forest communities than it does in species poorer forests. These findings represent an important step towards understanding the factors that govern the spatial configuration of local biotic communities. The stochastic dilution effect is a simple geometric mechanism that can explain why species' spatial distributions in species-rich communities approximate independence from their biotic neighborhood, even if deterministic niche processes are in effect. [ABSTRACT FROM AUTHOR]

The massive release of captive-bred native species ("intentional release") is a pervasive method to enhance wild populations of commercial and recreational species. However, such external inputs may disrupt the sensitive species interactions that allow competing species to coexist, potentially compromising long-term community stability. Here, we use theory and long-term data of stream fish communities to show that intentional release destabilizes community dynamics with limited demographic benefit to the enhanced species. Our theory predicted that intentional release intensifies interspecific competition, facilitating the competitive exclusion of unenhanced species that otherwise stably coexist. In parallel, the excessive input of captive-bred individuals suppressed the natural recruitment of the enhanced species via intensified within-species competition. Consequently, the ecological community with the intentional release is predicted to show reduced community density with unstable temporal dynamics. Consistent with this prediction, stream fish communities showed greater temporal fluctuations and fewer taxonomic richness in rivers with the intensive release of hatchery salmon-a major fishery resource worldwide. Our findings alarm that the current overreliance on intentional release may accelerate global biodiversity loss with undesired consequences for the provisioning of ecosystem services.