An algorithm to compute the strength of competing interactions in the Bering Sea based on pythagorean fuzzy hypergraphs

The networks of various problems have competing constituents, and there is a concern to compute the strength of competition among these entities. Competition hypergraphs capture all groups of predators that are competing in a community through their hyperedges. This paper reintroduces competition hypergraphs in the context of Pythagorean fuzzy set theory, thereby producing Pythagorean fuzzy competition hypergraphs. The data of real-world ecological systems posses uncertainty, and the proposed hypergraphs can efficiently deal with such information to model wide range of competing interactions. We suggest several extensions of Pythagorean fuzzy competition hypergraphs, including Pythagorean fuzzy economic competition hypergraphs, Pythagorean fuzzy row as well as column hypergraphs, Pythagorean fuzzy k-competition hypergraphs, m-step Pythagorean fuzzy competition hypergraphs and Pythagorean fuzzy neighborhood hypergraphs. The proposed graphical structures are good tools to measure the strength of direct and indirect competing and non-competing interactions. Their aptness is illustrated through examples, and results support their intrinsic interest. We propose algorithms that help to compose some of the presented graphical structures. We consider predator-prey interactions among organisms of the Bering Sea as an application: Pythagorean fuzzy competition hypergraphs encapsulate the competing relationships among its inhabitants. Specifically, the algorithm which constructs the Pythagorean fuzzy competition hypergraphs can also compute the strength of competing and non-competing relations of this scenario.

A framework of decision making based on bipolar fuzzy competition hypergraphs

Bipolarity plays a key role in different domains such as technology, social networking and biological sciences for illustrating real-world phenomenon using bipolar fuzzy models. In this article, novel concepts of bipolar fuzzy competition hypergraphs are introduced and discuss the application of the proposed model. The main contribution is to illustrate different methods for the construction of bipolar fuzzy competition hypergraphs and their variants. Authors study various new concepts including bipolar fuzzy row hypergraphs, bipolar fuzzy column hypergraphs, bipolar fuzzy k-competition hypergraphs, bipolar fuzzy neighborhood hypergraphs and strong hyperedges. Besides, we develop some relations between bipolar fuzzy k-competition hypergraphs and bipolar fuzzy neighborhood hypergraphs. Moreover, authors design an algorithm to compute the strength of competition among companies in business market. A comparative analysis of the proposed model is discuss with the existing models such bipolar fuzzy competition graphs and fuzzy competition hypergraphs.

Competition between native and non-native plants.

The introduction of species to new locations leads to novel competitive interactions between resident native and newly-arriving non-native species. The nature of these competitive interactions can influence the suitability of the environment for the survival, reproduction and spread of non-native plant species, and the impact those species have on native plant communities. Indeed, the large literature on competition among plants reflects its importance in shaping the composition of plant communities, including the invasion success of non-native species. While competition and invasion theory have historically developed in parallel, the increasing recognition of the synergism between the two themes has led to new insights into how non-native plant species invade native plant communities, and the impacts they have on those plant communities. This chapter provides an entry point into the aspects of competition theory that can help explain the success, dominance and impacts of invasive species. It focuses on resource competition, which arises wherever the resources necessary for establishment, survival, reproduction and spread are in limited supply. It highlights key hypotheses developed in invasion biology that relate to ideas of competition, outlines biotic and abiotic factors that influence the strength of competition and species' relative competitive abilities, and describes when and how competition between non-native and native plant species can influence invasion outcomes. Understanding the processes that influence the strength of competition between non-native and native plant species is a necessary step towards understanding the causes and consequences of biological invasions.

The Simple Economics of Wholesale Price-Parity Agreements: The Case of the Airline Tickets Distribution Industry*

This paper clarifies the differences between retail and wholesale price-parity agreements in vertical industries. In contrast to traditional wide and narrow retail price-parity arrangements, the competitive effects of wholesale price-parity depend on the complexity of the vertical supply chain, the business model operated by sellers and distributors, and the strength of competition between direct and indirect distribution channels. While retail price-parity agreements are almost always anticompetitive, wholesale price-parity agreements may positively affect consumer welfare when direct and indirect distribution channels are close substitutes. To demonstrate the relevance of our analysis for competition policy, we illustrate our findings by referring to an industry that has recently attracted policy and regulatory interest on both sides of the Atlantic: the airline ticket distribution industry. We find that, in this industry, while wholesale price-parity agreements always harm airlines, Global Distribution Systems (GDSs) have preferences more aligned with consumers: when consumers benefit from these provisions, GDSs benefit too. JEL: K21, L13, L40

Microbial species interactions determine community diversity in fluctuating environments

Microorganisms often live in environments that fluctuate between mild and harsh conditions. Although such fluctuations are bound to cause local extinctions and affect species diversity, it is unknown how diversity changes at different fluctuation rates and how this relates to changes in species interactions. Here, we use a mathematical model describing the dynamics of resources, toxins, and microbial species in a chemostat where resource supplies switch. Over most of the explored parameter space, species competed, but the strength of competition peaked at either low, high, or intermediate switching rates depending on the species’ sensitivity to toxins. Importantly, however, the strength of competition in species pairs was a good predictor for how community diversity changed over the switching rate. In sum, predicting the effect of environmental switching on competition and community diversity is difficult, as species’ properties matter. This may explain contradicting results of earlier studies on the intermediate disturbance hypothesis.

An Extension of Fuzzy Competition Graph and Its Uses in Manufacturing Industries

Competition graph is a graph which constitutes from a directed graph (digraph) with an edge between two vertices if they have some common preys in the digraph. Moreover, Fuzzy competition graph (briefly, FCG) is the higher extension of the crisp competition graph by assigning fuzzy value to each vertex and edge. Also, Interval-valued FCG (briefly, IVFCG) is another higher extension of fuzzy competition graph by taking each fuzzy value as a sub-interval of the interval [ 0 , 1 ] . This graph arises in many real world systems; one of them is discussed as follows: Each and every species in nature basically needs ecological balance to survive. The existing species depends on one another for food. If there happens any extinction of any species, there must be a crisis of food among those species which depend on that extinct species. The height of food crisis among those species varies according to their ecological status, environment and encompassing atmosphere. So, the prey to prey relationship among the species cannot be assessed exactly. Therefore, the assessment of competition of species is vague or shadowy. Motivated from this idea, in this paper IVFCG is introduced and several properties of IVFCG and its two variants interval-valued fuzzy k-competition graphs (briefly, IVFKCG) and interval-valued fuzzy m-step competition graphs (briefly, IVFMCG) are presented. The work is helpful to assess the strength of competition among competitors in the field of competitive network system. Furthermore, homomorphic and isomorphic properties of IVFCG are also discussed. Finally, an appropriate application of IVFCG in the competition among the production companies in market is presented to highlight the relevance of IVFCG.

Disturbance-induced changes in size-structure promote coral biodiversity

Reef-building coral assemblages are typically species-rich, yet the processes maintaining coral biodiversity remain poorly understood. Disturbance has long been believed to promote coral species coexistence by reducing the strength of competition. However, such disturbance-induced effects have since been shown to be insufficient on their own to prevent competitive exclusion. Nevertheless, Modern Coexistence Theory has revealed other mechanisms by which disturbance and, more generally, environmental variation can favour coexistence. Here, we formulate, calibrate, and analyze a size-structured, stochastic coral competition model using field data from two common colony morphologies. These two coral morphologies, tabular and digitate, differ in their size-dependent vulnerability to dislodgement caused by wave action. We confirm that fluctuations in wave action can promote coral species coexistence. However, using a recently proposed partitioning framework, we show that, contrast to previous expectations, temporal variability in strength of competition did not promote coexistence. Instead, coexistence was enabled by differential fluctuations in size-dependent mortality among competitors. Frequent and intense disturbances resulted in monocultures of digitate corals, which are more robust to wave action than tabular corals. In contrast, infrequent or weak disturbances resulted in monocultures of tabular corals. Coexistence was only possible under intermediate levels of disturbance frequency and intensity. Given the sensitivity of coexistence to disturbance frequency and intensity, anthropogenic changes in disturbance regimes are likely to affect biodiversity in coral assemblages in ways that are not predictable from single population models.