Analysing the distance decay of community similarity in river networks using Bayesian methods

The distance decay of community similarity (DDCS) is a pattern that is widely observed in terrestrial and aquatic environments. Niche-based theories argue that species are sorted in space according to their ability to adapt to new environmental conditions. The ecological neutral theory argues that community similarity decays due to ecological drift. The continuum hypothesis provides an intermediate perspective between niche-based theories and the neutral theory, arguing that niche and neutral factors are at the opposite ends of a continuum that ranges from competitive to stochastic exclusion. We assessed the association between niche-based and neutral factors and changes in community similarity measured by Sorensen’s index in riparian plant communities. We assessed the importance of neutral processes using network distances and flow connection and of niche-based processes using Strahler order differences and precipitation differences. We used a hierarchical Bayesian approach to determine which perspective is best supported by the results. We used dataset composed of 338 vegetation censuses from eleven river basins in continental Portugal. We observed that changes in Sorensen indices were associated with network distance, flow connection, Strahler order difference and precipitation difference but to different degrees. The results suggest that community similarity changes are associated with environmental and neutral factors, supporting the continuum hypothesis.

A Call to Expand Avian Vocal Development Research

Birds are our best models to understand vocal learning – a vocal production ability guided by auditory feedback, which includes human language. Among all vocal learners, songbirds have the most diverse life histories, and some aspects of their vocal learning ability are well-known, such as the neural substrates and vocal control centers, through vocal development studies. Currently, species are classified as either vocal learners or non-learners, and a key difference between the two is the development period, extended in learners, but short in non-learners. But this clear dichotomy has been challenged by the vocal learning continuum hypothesis. One way to address this challenge is to examine both learners and canonical non-learners and determine whether their vocal development is dichotomous or falls along a continuum. However, when we examined the existing empirical data we found that surprisingly few species have their vocal development periods documented. Furthermore, we identified multiple biases within previous vocal development studies in birds, including an extremely narrow focus on (1) a few model species, (2) oscines, (3) males, and (4) songs. Consequently, these biases may have led to an incomplete and possibly erroneous conclusions regarding the nature of the relationships between vocal development patterns and vocal learning ability. Diversifying vocal development studies to include a broader range of taxa is urgently needed to advance the field of vocal learning and examine how vocal development patterns might inform our understanding of vocal learning.

Non-biodegradable objects may boost microbial growth in water bodies by harnessing bubbles

Given the ubiquity of bubbles and non-biodegradable wastes in aqueous environments, their transport through bubbles should be widely extant in water bodies. In this study, we investigate the effect of bubble-induced waste transport on microbial growth by using yeasts as model microbes and a silicone rubber object as model waste. Noteworthily, this object repeatedly rises and sinks in fluid through fluctuations in bubble-acquired buoyant forces produced by cyclic nucleation, growth and release of bubbles from object's surface. The rise–sink movement of the object gives rise to a strong bulk mixing and an enhanced resuspension of cells from the floor. Such spatially dynamic contaminant inside a nutrient-rich medium also leads to an increment in the total microbe concentration in the fluid. The enhanced concentration is caused by strong nutrient mixing generated by the object's movement which increases the nutrient supply to growing microbes and thereby, prolonging their growth phases. We confirm these findings through a theoretical model for cell concentration and nutrient distribution in fluid medium. The model is based on the continuum hypothesis and it uses the general conservation law which takes an advection–diffusion growth form. We conclude the study with the demonstration of bubble-induced digging of objects from model sand.

A Note on Congruences of Infinite Bounded Involution Lattices

We prove that an infinite (bounded) involution lattice and even pseudo-Kleene algebra can have any number of congruences between 2 and its number of elements or equalling its number of subsets, regardless of whether it has as many ideals as elements or as many ideals as subsets. Furthermore, when they have at most as many congruences as elements, these involution lattices and even pseudo-Kleene algebras can be chosen such that all their lattice congruences preserve their involutions, so that they have as many congruences as their lattice reducts. Under the Generalized Continuum Hypothesis, this means that an infinite (bounded) involution lattice and even pseudo-Kleene algebra can have any number of congruences between 2 and its number of subsets, regardless of its number of ideals. Consequently, the same holds for antiortholattices, a class of paraorthomodular Brouwer-Zadeh lattices. Regarding the shapes of the congruence lattices of the lattice{ ordered algebras in question, it turns out that, as long as the number of congruences is not strictly larger than the number of elements, they can be isomorphic to any nonsingleton well-ordered set with a largest element of any of those cardinalities, provided its largest element is strictly join-irreducible in the case of bounded lattice-ordered algebras and, in the case of antiortholattices with at least 3 distinct elements, provided that the predecessor of the largest element of that well-ordered set is strictly join{irreducible, as well; of course, various constructions can be applied to these algebras to obtain congruence lattices with different structures without changing the cardinalities in question. We point out sufficient conditions for analogous results to hold in an arbitrary variety.

Hilbert’s First Problem and the New Progress of Infinity Theory

In the 19th century, Cantor created the infinite cardinal number theory based on the "1-1 correspondence" principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of "whole is greater than part", and created another ruler for measuring infinite sets. At the same time, 16 the development of the infinity theory provides new ideas for solving Hilbert's first problem, and provides a new mathematical foundation for Cosmic Continuum Theory

Several results on compact metrizable spaces in $$\mathbf {ZF}$$

In the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

Distance decay of community similarity in river networks: a Bayesian approach

The distance decay of community similarity (DDCS) is a pattern that is widely observed in both terrestrial and aquatic environments. There are three major perspectives for explaining the DDCS. Niche-based theories argue that as environmental conditions change, species are sorted according to their ability to adapt to new environmental conditions and habitats. The ecological neutral theory argues that community similarity decays due to ecological drift. Finally, the continuum hypothesis argues that niche and neutral factors are at the opposite ends of a continuum that ranges from competitive exclusion to stochastic exclusion. Most studies on the DDCS have been conducted on terrestrial ecosytems, and there are few data for riparian plant communities in riparian ecosystems. Here we assessed the association between niche-based and neutral factors and changes in community similarity measured by Sorensen’s index. As neutral variables, we used network distances and flow connection, and as niche-based variables, we selected Strahler order differences and precipitation differences. We used a hierarchical Bayesian approach to assess which of these three perspectives best supported the results. We used a high-quality dataset composed of 338 vegetation censuses conducted in eleven river basins along a sizeable environmental gradient in continental Portugal. We observed that changes in Sorensen indices were associated with all four covariates but to different degrees. Overall, the results suggest that community similarity changes are associated with environmental and neutral factors, supporting the continuum hypothesis.

Hilbert's First Problem and the New Progress of Infinity Theory

In the 19th century, Cantor created the infinite cardinal number theory based on the "1-1 correspondence" principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of "whole is greater than part", and created another ruler for measuring infinite sets. The development of the infinity theory provides new ideas for solving Hilbert's first problem, and provides a new mathematical foundation for Cosmic Continuum Theory.

Hilbert's First Problem and the New Progress of Infinity Theory

In the 19th century, Cantor created the infinite cardinal number theory based on the "1-1 correspondence" principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of "whole is greater than part", and created another ruler for measuring infinite sets. The development of the infinity theory provides new ideas for solving Hilbert's first problem, and provides a new mathematical foundation for Cosmic Continuum Theory.

Hilbert' s First Problem and the New Progress of Infinity Theory

In the 19th century, Cantor created the infinite cardinal number theory based on the "1-1 correspondence" principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of "whole is greater than part", and created another ruler for measuring infinite sets. At the same time, the development of the infinity theory provides new ideas for solving Hilbert's first problem, and provides a new mathematical foundation for Cosmic Continuum Theory.