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A bounded version of the Lotka – Volterra model based on logistic differential equations is suggested to emulate cyclic behaviour in complex evolutionary and other systems. The model provides reasonable approximations for the so-called leaping cycles and other oscillational processes when the main state variables are limited by physical constraints. The model represents a basic model-building block that can be used in system dynamics and other frameworks and applications that require fundamental understanding and modelling of principal features of complex cyclic processes. Two application areas – technological progress and industrial safety – are specifically considered here. The model is shown to emulate techno-economic cycles reasonably well and give an appropriate qualitative description of risk and safety variations in the industrial environment. Simulations using the suggested model are quantitatively compared with the results of agent-based simulations. While a simple model cannot match all details of complex agent-based simulations of the risk and benefit dilemma, the bounded Lotka – Volterra model still gives a reasonable approximation of the process. The conceptual implications of the model are, nevertheless, significant, pointing to common cyclic mechanisms taking place in complex evolutionary systems that may belong to different branches of science. [ABSTRACT FROM AUTHOR]

Although plant–soil feedback (PSF) is being recognized as an important driver of plant recruitment, our understanding of its role in species coexistence in natural communities remains limited by the scarcity of experimental studies on multispecies assemblages. Here, we experimentally estimated PSFs affecting seedling recruitment in 10 co‐occurring Mediterranean woody species. We estimated weak but significant species‐specific feedback. Pairwise PSFs impose similarly strong fitness differences and stabilizing‐destabilizing forces, most often impeding species coexistence. Moreover, a model of community dynamics driven exclusively by PSFs suggests that few species would coexist stably, the largest assemblage with no more than six species. Thus, PSFs alone do not suffice to explain coexistence in the studied community. A topological analysis of all subcommunities in the interaction network shows that full intransitivity (with all species involved in an intransitive loop) would be rare but it would lead to species coexistence through either stable or cyclic dynamics. [ABSTRACT FROM AUTHOR]

Interactions among species are a fundamental aspect of biodiversity and drive ecosystem functioning and services. Species interactions include direct (pairwise) interactions among two species and indirect interactions that occur when a third species interacts and changes the pairwise direct interaction. In a three‐species interaction network, these interactions can be transitive (where one species outperforms all others) or intransitive (where each species outperforms another). Here, we investigate how direct and indirect interactions influence ecosystem functions in crop systems and how diversification and evolutionary adaptation can influence those interactions and therefore ecosystem functions.A common garden experiment was conducted with crop communities in monocultures, 2‐ and 3‐species mixtures that had either a common or no coexistence history (i.e. co‐adaptation) for the three previous years. Net, direct and indirect interaction intensities were estimated and compared between the diversity levels and coexistence histories. Furthermore, species interaction networks were inspected for transitive/intransitive interactions.We found evidence for less intense competition in mixtures and for reduced negative direct interaction intensity and enhanced facilitative effects upon co‐adaptation. We could further show that indirect interactions were generally less important for co‐adaptation than direct interactions. Additionally, we showed that co‐adaptation has the potential to shift interactions in the species interaction networks from competitive intransitive into pairwise competitive interactions where interactions occurred mainly between two species.Synthesis. Co‐adapted crop species with reduced negative interactions might have the potential to enhance productivity, especially in more diverse cropping systems. This supports the notion that intercropping is a vital part towards a more sustainable agriculture and one with further yield potential when developing cultivars optimised for growth in mixtures. [ABSTRACT FROM AUTHOR]

Species interactions are key drivers of biodiversity and ecosystem stability. Current theoretical frameworks for understanding the role of interactions make many assumptions which unfortunately, do not always hold in natural, diverse communities. This mismatch extends to annual plants, a common model system for studying coexistence, where interactions are typically averaged across environmental conditions and transitive competitive hierarchies are assumed to dominate. We quantify interaction networks for a community of annual wildflowers in Western Australia across a natural shade gradient at local scales. Whilst competition dominated, intraspecific and interspecific facilitation were widespread in all shade categories. Interaction strengths and directions varied substantially despite close spatial proximity and similar levels of local species richness, with most species interacting in different ways under different environmental conditions. Contrary to expectations, all networks were predominantly intransitive. These findings encourage us to rethink how we conceive of and categorize the mechanisms driving biodiversity in plant systems. [ABSTRACT FROM AUTHOR]

The seminal Bradley-Terry model exhibits transitivity, that is, the property that the probabilities of player A beating B and B beating C give the probability of A beating C, with these probabilities determined by a skill parameter for each player. Such transitive models do not account for different strategies of play between each pair of players, which gives rise to intransitivity. Various intransitive parametric models have been proposed but they lack the flexibility to cover the different strategies across n players, with the O (n 2) values of intransitivity modeled using O (n) parameters, while they are not parsimonious when the intransitivity is simple. We overcome their lack of adaptability by allocating each pair of players to one of a random number of K intransitivity levels, each level representing a different strategy. Our novel approach for the skill parameters involves having the n players allocated to a random number of A < n distinct skill levels, to improve efficiency and avoid false rankings. Although we may have to estimate up to O (n 2) unknown parameters for (A , K) we anticipate that in many practical contexts A + K < n . Our semiparametric model, which gives the Bradley-Terry model when (A = n − 1 , K = 0) , is shown to have an improved fit relative to the Bradley-Terry, and the existing intransitivity models, in out-of-sample testing when applied to simulated and American League baseball data. for the article areavailable online. [ABSTRACT FROM AUTHOR]

This short paper states a new objection against "spectrum arguments" for nontransitive betterness. It is shown that defenders of such arguments must reject one of two very plausible principles. [ABSTRACT FROM AUTHOR]

The present article studies the semantic-syntactic structure of polysemantic verbs, following the stratification of their meanings. Analyzing the syntactic neighborhoods of a certain polysemantic verb, with the matrix of obligatory thematic roles, characteristic for actantial, circumstantial or predicative relations, we notice that in the process of functioning, various transformational processes of a different nature take place. Following the research, it was found that these transformations modify the argumentative structure of the verb at the referential level, changing its semantic-syntactic structure, which allows it to pass from one semantic class to another to fully reveal its communicative role. Responsible for these would be the phenomenon of actantial derivation. Only two forms of actantial derivation were discussed – transitivization and intransitivization – given that transitivity, an unmarked semantic feature, influences the ability of the verb to accumulate meanings with different syntactic patterns. It was found that there is an obvious oscillation between the positive or negative marking of transitivity and the realization of a verb as intransitive or transitive. The phenomenon of free syntactic variation also participates in the diversification of the syntactic structure of a polysemantic verb, which allows the operation of semantically equivalent but syntactically different variants.

This review presents an overview of Lorenz models between 1960 and 2008, classified into six categories based on different types of Partial Differential Equations (PDEs). These models have made significant contributions to our understanding of chaos, the butterfly effect, attractor coexistence, and intransitivity (or "almost intransitivity") across various scientific fields. Type I models include the influential Lorenz 1963 model and generalized Lorenz models. The classical Lorenz model laid the groundwork for chaos theory by revealing the sensitivity to initial conditions and chaotic behavior. Generalized Lorenz models were developed to examine the dependence of chaos on the number of Fourier modes and to illustrate attractor coexistence. Type II models were derived from two-layer, quasi-geostrophic systems. These models investigated nonlinear oscillations and irregular solutions. Based on these models, in 1960, Lorenz first presented nonperiodic solutions. Type III models include the Lorenz 1960 and 1969 models, derived from a vorticity-conserved PDE. These models shed light on nonlinear oscillatory solutions, linearly unstable solutions, and the predictability estimates of the atmosphere. However, recent studies have raised doubts regarding the validity of the two-week predictability limit. Type IV models, based on shallow water equations, have advanced our understanding of the coexistence of slow and fast variables. Type V models, which include models not based on specific PDEs, include the Lorenz 1984 and 1996 models used for studying intransitivity and investigating data assimilation techniques. Type VI models, involving difference equations, have proven effective in demonstrating chaos and intransitivity across diverse fields. Interestingly, Lorenz's early work in 1964 and 1969 employed the Logistic map, appearing earlier than significant studies in the 1970s. In summary, the study of Lorenz models has deepened our understanding of chaos, attractor coexistence, and intransitivity (or "almost intransitivity"). Future research directions may involve exploring higher-dimensional models, utilizing advanced mathematical and computational techniques, and fostering interdisciplinary collaborations to further advance our comprehension and the prediction of capabilities regarding coexisting chaotic and nonchaotic phenomena, as well as regime changes. [ABSTRACT FROM AUTHOR]

Copyright of Djoussour El-maarefa is the property of Association of Arab Universities and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

When an individual is socially connected to two others, the resulting triplet can be closed (if the two social partners are themselves connected) or open (if they are not connected). The proportion of closed triplets, referred to as the binary network transitivity, is a classic measure of the level of interconnectedness of a social network. However, in any given triplet, if the closing link is weak, or indeed if any of the links in the triplet is weak, then the triplet should not contribute as much to network transitivity as if all three links were equally strong. I propose two ways to weight the contribution of each triplet according to the dissimilarity between the three links in the triplet. Empirically, the resulting new metrics conveyed information not picked up by any other network-level metric. I envision that this approach could prove useful in studies of triadic mechanisms, i.e., situations where pre-existing social ties influence the interactions with third parties. These metrics could also serve as repeatable synthetic variables that summarize information about the variability of the strength of social connections. • The transitivity of social networks is classically computed by summing over "triplet" contributions. • I weight the contribution of each triplet using the three links inside of it. • The resulting new metrics effectively captured information otherwise conveyed by 8 metrics, and more. • The new metrics are particularly geared towards studies into triadic mechanisms. [ABSTRACT FROM AUTHOR]

Understanding invasion mechanisms or identifying their potential outcomes has been a longstanding objective of invasion. Many recent empirical and theoretical works tend to frame a perspective of invasion biology within the field of coexistence theory. With increasing emphasis on indirect competitions, more researches hold that niche departure, intransitive loop structure or the integration of these two would be the potential mechanisms to promote native coexistence. But how invasion dynamics rely on these key properties of native competitive network is seldom investigated. Here, we introduce one alien species to a three-species competition system. By setting the structure of coexistence coefficient matrix, we consider three native coexistence mechanisms. After analyzing the equilibrium consequences of alien species invasion under these three mechanisms, we have found that (1) in the native communities supported by strong niche differentiation, alien species can certainly establish their population but would not pose great destruction to native species. (2) Invasion exclusion would happen in the community maintained by intransitive competition loop. However, whether alien species coexist with or exclude resident populations depends on both intraspecific and interspecific competition of invader. (3) The community assembled by the combination of these two mechanisms are most resistant to invasion, and where invasion consequences are more diverse. (4) Finally, the species long-term steady state and short-term respond always keep consistent. We have explicitly situated invasion process within the recent coexistence framework. Our results would broaden the understanding of invasion mechanisms and provide insights into the combination of invasion and coexistence theory. [ABSTRACT FROM AUTHOR]

• Ecological communities are frequently assumed to be structured according to the rules of interspecific competition. • When three or more species are involved, the usual tacit assumption that all competition is transitive may be violated. • Intransitive loops change some of the principles of the competition-based framework, since the intransitivity is oscillatory, a behavior that needs to be acknowledged. • It is likely that real communities will contain one or more intransitive structures, along with normal transitivities. • There are some theoretical constructs that emanate from the joint consideration of such intransitive and transitive structures. Based on the classical idea that no two species can occupy the same niche, ecological communities are frequently assumed to be structured according to the rules of interspecific competition, based on the intuition provided by the Lotka/Volterra competition equations in two dimensions. It has been noted that when three or more species are involved, the usual tacit assumption that all competition is transitive may be violated. Intransitive loops change some of the emergent principles of the competition-based framework of community structure. Since the intransitivity is oscillatory, the convenient stable equilibrium approach to communities is altered and oscillatory behavior of the system needs to be acknowledged. It is likely that real communities, especially if they are relatively large, will contain one or more intransitive structures, along with normal transitivities. Here we examine some theoretical constructs that emanate from the joint consideration of intransitive and transitive structures co-occurring in an ecological community. [ABSTRACT FROM AUTHOR]

When the estimated strength of social associations corresponds to the proportion of time spent together, strong links, those that take up most of the recorded time of individuals, are compulsorily transitive and tend to occur in clusters. However, I describe three ways in which the frequency and position of strong associations apparently offset the expected transitivity of strong links in published association networks from 26 species of vertebrates. Instead of occurring in groups of three, strong links were mostly isolated. When they did occur in clusters, the clusters were small. The phenomena increased in intensity as the overall number of links of all strengths and the overall network transitivity increased. Since stable transitive motifs are beneficial to cooperation, these results can help explain why cooperative behaviors are not more frequent than they are in group‐living vertebrates. Inversely, stable transitive motifs may be rare and small because the benefits of cooperation do not overcome the costs associated with these motifs. The summary statistics developed for this study captured information not conveyed by other network‐level metrics; thus they may help quantify the socio‐spatial structure of populations and potentially tease apart the environmental, species‐specific, and individual drivers. [ABSTRACT FROM AUTHOR]

Copyright of Nueva Revista de Filología Hispánica is the property of El Colegio de Mexico AC and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

When making decisions humans often violate the principlesof rational choice theory. Recent experiments, involving rapidexperiential decisions, uncovered a mechanism that is respon-sible for various rationality violations. According to this se-lective gating mechanism, incoming value samples are accu-mulated across time, but prior to their accumulation they areweighted in proportion to their momentary rank-order. Here,using a data-driven approach, I present a dynamic extensionof this mechanism, which involves potentially asymmetric in-hibition between the inputs. As a result, and contrary to theprevious selective gating implementation, the vigour of gatingis modulated by the difference between two value samples (adistance effect) as well as by the absolute magnitude of thesamples (a magnitude effect). This extension offers a supe-rior explanation to existing and new data; and links high-leveldecision phenomena with computational principles previouslydescribed in theories of selective attention and visual search.

Ranking of fuzzy numbers (FNs) is a key stage within fuzzy multicriteria decision analysis (FMCDA). However, the influence of FNs dependence on their ranking, including ranking alternatives within FMCDA, has not been studied yet. In this article, for studying such an influence, the widely used defuzzification-based fuzzy ranking methods, centroid index, and integral of means, along with their modifications, which are pairwise comparison defuzzification ranking methods, are explored. The authors argue that classical defuzzification ranking methods are intended to deal with independent FNs, whereas their modifications may be used for ranking of dependent FNs. It is provided a proof in which, pairwise comparison Yuan’s and defuzzification integral of means ranking methods, are equivalent when ordering independent and can differ when ordering dependent FNs; at the same time, Yuan’s and modified integral of means ranking methods are equivalent when ordering both independent and dependent FNs. Intransitivity of the two modified ranking methods when ordering dependent FNs as well as intransitivity of alternatives in FMCDA for fuzzy multiattribute value theory (FMAVT) as an example is proved. The distinctions in ranking of dependent FNs by all ranking methods under consideration are explored through ordering alternatives within FMAVT. For this, a real-life case study is considered, and the distinctions in ordering alternatives by classical and modified ranking methods are demonstrated. Statistical analysis of distinctions in ordering alternatives by FMAVT with different ranking methods is implemented with the use of Monte–Carlo simulation. The significance of distinctions for the choice and ranking multicriteria problems, as well as for justification of utilizing ranking methods under consideration in FMCDA, is discussed. [ABSTRACT FROM AUTHOR]

We propose a regret-based model that allows the separation of attitudes towards transitivity on triples of random variables that are close to each other and attitudes towards transitivity on triples that are far apart. This enables a theoretical reinterpretation of evidence related to intransitive behavior in the laboratory. When viewed through this paper's analysis, the experimental evidence need not imply intransitive behavior for large risky decisions such as investment choices and insurance. [ABSTRACT FROM AUTHOR]

The factors governing invasiveness and invasibility are important for understanding invasions in plant communities, but most previous work does not incorporate network‐level interaction structure. We addressed this gap by simulating perennial plant communities at multiple life stages that varied in species richness and interaction network structures (transitive and intransitive), characteristics associated with species coexistence, using a stochastic lattice model that incorporated local competition, facilitation, and dispersal. Resident communities were invaded with alien species that varied in their fecundity, dispersal, and competitive abilities. We found that community structures that are known to promote coexistence also increased invasibility; communities with intransitive interaction networks on the whole were more invasible than transitive communities. However, the interaction between species richness and network structure was complex, as intransitive communities with few species were relatively resistant and transitive communities with many species were relatively invasible. Thus, simple rules linking intransitivity and diversity may not reflect the complex relationships between community structure and dynamics that occur in more realistic spatial systems. Spatial patterns of clustering and segregation were associated with higher invasibility and successful invaders intensified these patterns in communities, particularly at large spatial scales. Invasiveness and alien species abundance were associated with species‐level characteristics (fecundity and dispersal), but community‐level characteristics were also important, particularly competitive tolerance to the resident community. These results emphasize the importance of a community‐level approach, involving network‐level structure and spatial patterns, in adding nuance to our understanding of invasions in plant communities. [ABSTRACT FROM AUTHOR]

The transitivity axiom is common to nearly all descriptive and normative utility theories of choice under risk. Contrary to both intuition and common assumption, the little-known 'Steinhaus-Trybula paradox' shows the relation 'stochastically greater than' will not always be transitive, in contradiction of Weak Stochastic Transitivity. We bespoke-design pairs of lotteries inspired by the paradox, over which individual preferences might cycle. We run an experiment to look for evidence of cycles, and violations of expansion/contraction consistency between choice sets. Even after considering possible stochastic but transitive explanations, we show that cycles can be the modal preference pattern over these simple lotteries, and we find systematic violations of expansion/contraction consistency.

Understanding the patterns of competitive and facilitative interactions within and among species in plant communities is a central goal of plant ecology, because these patterns determine species coexistence and community dynamics. Network theory provides tools that allow these patterns to be quantified, and can provide greater understanding of important community properties, including community stability, than can documenting pairwise species interactions.I characterized the interactions of multiple, co‐occurring invasive and native species in an old field woody plant community to build plant interaction networks at two different life stages. With the goal of identifying structural features that may operate to maintain species coexistence, I characterized the architecture of these networks at multiple scales: the entire network, the substructures that compose the network and species' roles within substructures.I found that species‐level pairwise interactions alone did not provide an accurate or sufficiently detailed picture of community structure. Rather, using a network approach, I identified substructures that have the potential to promote and hinder species coexistence in interactions among seedlings. Characterizing the nuances of network substructures was illuminating, as the size of the substructures and the pattern of interaction intensities within substructures influence the expected effects on species coexistence. Including interactions at multiple life stages was also important; the seedling species that benefited most from the nested structure of facilitative interactions with adults occupied subordinate roles in substructures with other seedlings. This role reversal at different life stages is a potential factor promoting coexistence in the community. Last, the network framework was useful for comparing species' roles between native and invasive members of the community, and the three invasive species in this system had different, life stage‐dependent strategies in interactions with co‐occurring plants.Synthesis. The interplay of network architecture and substructures within plant communities and among plants at different life stages is important for understanding species coexistence. In the plant community characterized in this study, there were several features that may promote coexistence, and these features were not observable in interactions within a single life stage or when considering pairwise interactions independently. [ABSTRACT FROM AUTHOR]

We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to 1/2, that a throw from one die is higher than the other. We build on a recent result of Polymath showing that three dice with i.i.d. faces drawn from the uniform distribution on { 1 , ... , n } and conditioned on the average of faces equal to (n + 1) / 2 are intransitive with asymptotic probability 1/4. We show that if dice faces are drawn from a non-uniform continuous mean zero distribution conditioned on the average of faces equal to 0, then three dice are transitive with high probability. We also extend our results to stationary Gaussian dice, whose faces, for example, can be the fractional Brownian increments with Hurst index H ∈ (0 , 1) . Second, we pose an analogous model in the context of Condorcet voting. We consider n voters who rank k alternatives independently and uniformly at random. The winner between each two alternatives is decided by a majority vote based on the preferences. We show that in this model, if all pairwise elections are close to tied, then the asymptotic probability of obtaining any tournament on the k alternatives is equal to 2 - k (k - 1) / 2 , which markedly differs from known results in the model without conditioning. We also explore the Condorcet voting model where methods other than simple majority are used for pairwise elections. We investigate some natural definitions of "close to tied" for general functions and exhibit an example where the distribution over tournaments is not uniform under those definitions. [ABSTRACT FROM AUTHOR]

In this paper, I develop three models for understanding plastic in the Plasticene epoch through readings of Arendt, Barthes, and Massumi. In the Ardentian model, plastic is made intransitive. It is withdrawn so far into the background of human experience as that which enables social and individual life of humans that it becomes the unthinkable. It can be argued that it is pushed to the background and made intransitive because of a certain image of the human and cyclical image of nature. The second model is Barthesian, and in it plastic becomes a signifying matter understood through a semiotic model. Plastic and products of plastic become signifiers in the ideological work of discourse. In the Massumian model, plastic is affective; it is a relational body in the process of becoming, simultaneously intensive and multiple in its eventfulness. [ABSTRACT FROM AUTHOR]

Biocrusts are critical components of drylands where they regulate a wide range of ecosystem functions, however, their response to the world‐wide phenomenon of shrub encroachment and to livestock grazing, the most extensive land use in drylands, is not well studied. Grazing by livestock and increases in shrub cover could influence biocrust communities directly via trampling or shading, or indirectly, by altering biotic interactions amongst biocrust taxa. The extent of these changes in biocrust cover, diversity and composition are poorly known.We used linear models and structural equation modelling to examine the direct effects of grazing and shrubs on biocrust community composition and the indirect effects mediated by changes in species interactions.Biocrust richness and cover increased with increasing shrub cover at the site level. This pattern occurred despite the negative response we found (lower cover and richness) under shrub patches versus open areas, which was consistent irrespective of the grazing level. Functional diversity and evenness were similar between shrubs and open at low grazing intensity, but at high grazing functional diversity was greater in the open. Competition between biocrust species was an important driver of their community assembly irrespective of shrub cover, grazing intensity or patch type. Structural equation models showed that the effects of grazing and shrub cover on functional evenness, functional diversity and richness were controlled by biotic interactions within the shrub microsites. In the open, however, these effects were either direct or mediated by changes in cover.Biocrust cover, species richness and functional diversity increase with shrub cover at the site scale, despite the negative effects at the microsite level. We demonstrate here that drivers of community assembly differ markedly at small spatial scales. Though biocrust communities were directly driven by environmental filtering in the open, biotic interactions played a fundamental role in their assembly when growing beneath shrubs. A free plain language summary can be found within the Supporting Information of this article. [ABSTRACT FROM AUTHOR]

The voting paradox occurs when a democratic society seeking to aggregate individual preferences into a social preference reaches an intransitive ordering. However it is not widely known that the paradox may also manifest for an individual aggregating over attributes of risky objects to form a preference over those objects. When this occurs, the relation 'stochastically greater than' is not always transitive and so transitivity need not hold between those objects. We discuss the impact of other decision paradoxes to address a series of philosophical and economic arguments against intransitive (cyclical) choice, before concluding that intransitive choices can be justified. [ABSTRACT FROM AUTHOR]

Birnbaum (2020) reanalyses the data from Butler and Pogrebna (2018) using his `true and error' test of choice patterns. His results generally support the evidence we presented in that paper. Here we reiterate the reasons for our agnosticism as to the direction any cycles might take, even though the paradox that motivated our study takes a `probable winner' direction. We conclude by returning to the potential significance of predictably intransitive preferences for decision theory generally.

Building on Goldman 2008 and 2009, which argue that objective values would be strange in coming in degrees but in no determinate number of degrees, this paper argues that related properties having to do with degrees of value make a further case against objective values. The properties of giving rise to intransitive orderings and being essentially comparative are explained by Larry Temkin in Rethinking the Good. He shows that "better than" is intransitively ordered. Many subjective states are too. But similar arguments for the intransitive orderings of intrinsic objective properties fail. Furthermore, subjective properties and states can change without these changes being explained by changes in their objects. This is similar to the essentially comparative nature of goodness. Given the analogies to subjective states and lack of analogies to objective properties that the present article points out, it argues that we should infer, as Temkin does not, that values are subjective. [ABSTRACT FROM AUTHOR]

The inference of pairwise competitive outcomes (PCO) and multispecies competitive ranks and intransitivity from empirical data is essential to evaluate how competition shapes plant communities. Three categories of methods, differing in theoretical background and data requirements, have been used: (a) theoretically sound coexistence theory‐based methods, (b) index‐based methods, and (c) 'process‐from‐pattern' methods. However, how they are related is largely unknown.In this study, we explored the relations between the three categories by explicitly comparing three representatives of them: (a) relative fitness difference (RFD), (b) relative yield (RY), and (c) a reverse‐engineering approach (RE). Specifically, we first conducted theoretical analyses with Lotka–Volterra competition models to explore their theoretical linkages. Second, we used data from a long‐term field experiment and a short‐term greenhouse experiment with eight herbaceous perennials to validate the theoretical findings.The theoretical analyses showed that RY or RE applied with equilibrium data indicated equivalent, or very similar, PCO respectively to RFD, but these relations became weaker or absent with data further from equilibrium. In line with this, both RY and RE converged with RFD in indicating PCO over time in the field experiment as the communities became closer to equilibrium. Moreover, the greenhouse PCO (far from equilibrium) were only similar to the field PCO of earlier rather than later years. Intransitivity was more challenging to infer because it could be reshuffled by even a small competitive shift among similar competitors. For example, the field intransitivity inferred by three methods differed greatly: no intransitivity was detected with RFD; intransitivity detected with RY and RE was poorly correlated, changed substantially over time (even after equilibrium) and failed to explain coexistence.Our findings greatly help the comparison and generalization of studies using different methods. For future studies, if equilibrium data are available, one can infer PCO and multispecies competitive ranks with RY or RE. If not, one should apply RFD with density gradient or time‐series data. Equilibria could be evaluated with T tests or standard deviations. To reliably infer intransitivity, one needs high quality data for a given method to first accurately infer PCO, especially among similar competitors. [ABSTRACT FROM AUTHOR]

Both behavioral and standard neoclassical economists place a heavy emphasis on the consistency of preferences. In particular, transitive preferences are considered a desideratum. This paper attempts to show that consistency at the level of individual choice may be pragmatically irrelevant. Consistently following an environmentally adapted rule can result in intransitive preferences without negative consequences for individual or social goals. I give three examples of this. Social scientists should look at intransitivity of choices as a challenge to offer better explanations rather than as a normative defect. [ABSTRACT FROM AUTHOR]

In this article, the second of a series of four articles that engage critically with the arguments of two recent and significant additions to the literature on critical realism (Bhaskar's Enlightened Common Sense: The Philosophy of Critical Realism and Bhaskar et al.'s Interdisciplinarity and Wellbeing: A Critical Realist General Theory of Interdisciplinarity), I present the results of a critical engagement with other categories of original or basic critical realism. Using the method of immanent critique and focusing mainly, but not exclusively, on the arguments of Enlightened Common Sense, I identify, and propose solutions to, a range of problems pertaining to the concepts of intransitivity, the domains of the real and the subjective, and the domain of the actual. In identifying and resolving these problems, my aim is to clarify and develop the categories of original critical realism and thereby ensure that critical realism as a whole is as effective an underlabourer for science as it can be. [ABSTRACT FROM AUTHOR]

The semantic analysis of verbs of the unwritten Akhvakh language, as one from avaro-ando-tsez group of Nakho-Dagestanian languages, is carried out in this paper. The syntax sentence construction in Dagestanian languages is inseparably linked with opposition of transitivity and intransitivity. Transitive languages form ergative constructions, and intransitive ones – absolute constructions. Based on the particular role of the lexical semantics of verbs in sentence formulating, the verbs of the Akhvakh language are classified into several lexical-semantic groups: transitive, intransitive, affective, labile. A significant number of verbs combine transitive and intransitive meanings. At the level of morphology the distinction between transitive and intransitive verbs by special markers (suffixes) is typical for the Akhvakh language. The causative forms of verbs, having a special place in the system of intransitive verbs, were also covered in this article.

This work considers reasons for and implications of discarding the assumption of transitivity—the fundamental postulate in the utility theory of von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology and economics. This work is intended as a common platform that allows us to discuss intransitivity in the context of different disciplines. The basic concepts and terms that are needed for consistent treatment of intransitivity in various applications are presented and analysed in a unified manner. The analysis points out conditions that necessitate appearance of intransitivity, such as multiplicity of preference criteria and imperfect (i.e., approximate) discrimination of different cases. The present work observes that with increasing presence and strength of intransitivity, thermodynamics gradually fades away leaving space for more general kinetic considerations. Intransitivity in competitive systems is linked to complex phenomena that would be difficult or impossible to explain on the basis of transitive assumptions. Human preferences that seem irrational from the perspective of the conventional utility theory, become perfectly logical in the intransitive and relativistic framework suggested here. The example of competitive simulations for the risk/benefit dilemma demonstrates the significance of intransitivity in cyclic behaviour and abrupt changes in the system. The evolutionary intransitivity parameter, which is introduced in the Appendix, is a general measure of intransitivity, which is particularly useful in evolving competitive systems.

Starting with the statement that the "Being is what-it-is," we have a new dilemma when we want to express something through a philosophical sentence. We will try to find out and to show how the structure of the verb, correlated with the judgement dresses up a double form: a passive one, and a reflexive one. We think the direction of transformation starts with the passive form and change into a reflexive one. This double loop of the verb, and the recent studies in judicative phenomenology, makes us to establish two new diathesis on the mental-structures of the verb: the judicative-diathesis and the pre-judicativediathesis. Finally, in the construction of the verbs "being" and "is," still persists the double fulfillment of the passive, and reflexive, to whom we can add the active form, because in ontical plane, the verb is let to activate something- the Being. The manner on how 'Being' is activated in judgement, is double: a pre-judicative way, and a judicative way. [ABSTRACT FROM AUTHOR]

Ordering fuzzy quantities is a challenging problem in fuzzy sets theory that has attracted the interest of many researchers. Despite the multiple indices introduced for this purpose and due to the fact that fuzzy quantities do not have a natural order, there is still a chance to provide a new approach for ranking this type of quantities from the acceptability and foundation point of view. This paper aims at developing a new approach to ranking fuzzy numbers (FNs),fuzzy rank acceptability analysis(FRAA), which not only implements a ranking of the FNs, but also provides adegree of confidencefor all ranks. Additionally, the FRAA can be efficiently implemented by using different fuzzy preference relations including both transitive and intransitive ones. Properties of FRAA ranking, their dependence on the fuzzy preference relations, and correspondence with the basic axioms for ranking FNs are analyzed. Finally, a comparison of the FRAA ranks to ranks from other methods is analyzed along with a discussion of the advantages of FRAA ranking. [ABSTRACT FROM AUTHOR]

This paper tested an assumption of the gradient model of split intransitivity put forward by Sorace (“Split Intransitivity Hierarchy” (SIH), 2000, 2004), namely that agentivity is a fundamental feature for unergatives but not for unaccusatives. According to this hypothesis, the animacy of the verb’s argument should affect the processing of unergative verbs to a greater extent than unaccusative verbs. By using eye-tracking methodology we monitored the online processing and integration costs of the animacy of the verb’s argument in intransitive verbs. We observed that inanimate subjects caused longer reading times only for unergative verbs, whereas the animacy of the verb’s argument did not influence the pattern of results for unaccusatives. In addition, the unergative verb data directly support the existence of gradient effects on the processing of the subject argument. [ABSTRACT FROM AUTHOR]

Biologists have long been interested in intransitive preferences: circular preferences in which options cannot be ranked and no single option dominates, similar to a game of rock-paper- scissors. Intransitive preferences violate rational decision-making, an assumption made by models of evolution by mate choice. Despite its potential importance in the study of sexual selection, few studies have tested for intransitive preferences. Even fewer have asked whether females differ in whether they choose mates transitively or intransitively and what factors might predict (in)transitive choice. Though intransitive choice is thought to be more common as options become more complex, this prediction is untested in animals. To fill this gap, we tested whether female Xiphophorus nigrensis swordtails can rank digitally animated males differing in size, courtship intensity, or both size and courtship intensity, and whether female responses were predicted by a female's age. Females choosing among males that varied only in size showed higher than expected levels of intransitivity, whereas females choosing among males that varied in their courtship or both properties did not. Older females were more likely to be irrational than younger females when evaluating male size, suggesting that experience modifies transitive decision-making processes. These results show that mate choice irrationality may vary by a female's experience and the signal characteristics during decision-making. [ABSTRACT FROM AUTHOR]

Abstract: Allelopathic species can alter biodiversity. Using simulated assemblages that are characterised by neutrality, lumpy coexistence and intransitivity, we explore relationships between within‐assemblage competitive dissimilarities and resistance to allelopathic species. An emergent behaviour from our models is that assemblages are more resistant to allelopathy when members strongly compete exploitatively (high competitive power). We found that neutral assemblages were the most vulnerable to allelopathic species, followed by lumpy and then by intransitive assemblages. We find support for our modeling in real‐world time‐series data from eight lakes of varied morphometry and trophic state. Our analysis of this data shows that a lake's history of allelopathic phytoplankton species biovolume density and dominance is related to the number of species clusters occurring in the plankton assemblages of those lakes, an emergent trend similar to that of our modeling. We suggest that an assemblage's competitive power determines its allelopathy resistance. [ABSTRACT FROM AUTHOR]

Aims Dune building processes are affected by interactions between the growth of ecosystem engineering dune grasses and environmental factors associated with disturbance such as sand burial and sea spray. Research investigating how species interactions influence dune community structure and functional trait responses in high abiotic stress environments is minimal. We investigated how species interactions influence the functional trait responses of three dominant dune grasses to common abiotic stressors. Methods We performed a multi-factorial greenhouse experiment by planting three common dune grasses (Ammophila breviligulata Fern., Uniola paniculata L. and Spartina patens Muhl.) in different interspecific combinations, using sand burial and sea spray as abiotic stressors. Sand burial was applied once at the beginning of the study. Sea spray was applied three times per week using a calibrated spray bottle. Morphological functional trait measurements (leaf elongation, maximum root length, aboveground biomass and belowground biomass) were collected at the end of the study. The experiment continued from May 2015 to August 2015. Important Findings Species interactions between A. breviligulata and U. paniculata negatively affected dune building function traits of A. breviligulata, indicating that interactions with U. paniculata could alter dune community structure. Furthermore, A. breviligulata had a negative interaction with S. patens, which decreased S. patens functional trait responses to abiotic stress. When all species occurred together, the interactions among species brought about coexistence of all three species. Our data suggest that species interactions can change traditional functional trait responses of dominant species to abiotic stress. [ABSTRACT FROM AUTHOR]

In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner, avoiding any unnecessary information. For this purpose, the new concept of representability is developed by means of partial functions, so that other common definitions of representability (i.e. (Richter-Peleg) multi-utility, Scott-Suppes representability, … ) are now particular cases in which the partial functions are actually functions. The paper also presents a collection of examples and propositions showing the advantages of this kind of representations, particularly in the case of partial orders and semiorders, as well as some results showing the connections between distinct kinds of representations. [ABSTRACT FROM AUTHOR]

The transitivity axiom is common to nearly all descriptive and normative utility theories of choice under risk. Contrary to both intuition and common assumption, the little-known 'Steinhaus-Trybula paradox' shows the relation 'stochastically greater than' will not always be transitive, in contradiction of Weak Stochastic Transitivity. We bespoke-design pairs of lotteries inspired by the paradox, over which individual preferences might cycle. We run an experiment to look for evidence of cycles, and violations of expansion/contraction consistency between choice sets. Even after considering possible stochastic but transitive explanations, we show that cycles can be the modal preference pattern over these simple lotteries, and we find systematic violations of expansion/contraction consistency. [ABSTRACT FROM AUTHOR]

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]