Weak Congruence Research Articles

Closely coupled evolutionary history of ecto- and endosymbionts from two distantly related animal phyla.

The level of integration between associated partners can range from ectosymbioses to extracellular and intracellular endosymbioses, and this range has been assumed to reflect a continuum from less intimate to evolutionarily highly stable associations. In this study, we examined the specificity and evolutionary history of marine symbioses in a group of closely related sulphur-oxidizing bacteria, called Candidatus Thiosymbion, that have established ecto- and endosymbioses with two distantly related animal phyla, Nematoda and Annelida. Intriguingly, in the ectosymbiotic associations of stilbonematine nematodes, we observed a high degree of congruence between symbiont and host phylogenies, based on their ribosomal RNA (rRNA) genes. In contrast, for the endosymbioses of gutless phallodriline annelids (oligochaetes), we found only a weak congruence between symbiont and host phylogenies, based on analyses of symbiont 16S rRNA genes and six host genetic markers. The much higher degree of congruence between nematodes and their ectosymbionts compared to those of annelids and their endosymbionts was confirmed by cophylogenetic analyses. These revealed 15 significant codivergence events between stilbonematine nematodes and their ectosymbionts, but only one event between gutless phallodrilines and their endosymbionts. Phylogenetic analyses of 16S rRNA gene sequences from 50 Cand. Thiosymbion species revealed seven well-supported clades that contained both stilbonematine ectosymbionts and phallodriline endosymbionts. This closely coupled evolutionary history of marine ecto- and endosymbionts suggests that switches between symbiotic lifestyles and between the two host phyla occurred multiple times during the evolution of the Cand. Thiosymbion clade, and highlights the remarkable flexibility of these symbiotic bacteria.

Limited dispersal in an ectoparasitic mite, Laelaps giganteus, contributes to significant phylogeographic congruence with the rodent host, Rhabdomys.

To explore how biogeography, parasite life history and host vagility influences evolutionary codivergences, we followed a comparative phylogeography approach using a host-specific nonpermanent mite, Laelaps giganteus, that occurs on four rodent species within the genus Rhabdomys. A mtDNA COI haplotype network derived for 278 parasite specimens showed marked phylogeographic congruence with host distributions. Analysis of the less variable nuclear intron Tropomyosin was in part consistent with these results. Although distance-based cophylogenetic analyses in axparafit failed to support significant mtDNA codivergences (P≥0.02), event-based analyses revealed significant cophylogeny between sampling localities of Rhabdomys and Laelaps using core-pa (P=0.046) and jane (P=0.026; P=0.00). These findings, in conjunction with the weak congruence previously reported among the permanent ectoparasitic lice Polyplax and Rhabdomys, suggest that host-parasite intimacy is not the most important driver of significant codivergence in our study system. Instead, the more restricted dispersal ability of L.giganteus, when compared to Polyplax, resulted in stronger spatial structuring and this could have resulted in significant codivergence. Host switching occurred predominantly on the edges of host distributions and was probably facilitated by climate-induced range shifts. When host ranges shift, the phylogeographic structure of L.giganteus is not reflecting the host movements as most of the nest bound parasites do not disperse with the host (they miss the boat) and the genetic contribution of the few dispersing mite individuals is often overwhelmed by the large number of individuals already present in nests within the new environment (causing them to drown on arrival).

Arithmetic Groups, Base Change, and Representation Growth

Consider an arithmetic group $${\mathbf{G}(O_S)}$$ , where $${\mathbf{G}}$$ is an affine group scheme with connected, simply connected absolutely almost simple generic fiber, defined over the ring of S-integers O S of a number field K with respect to a finite set of places S. For each $${n \in \mathbb{N}}$$ , let $${R_n(\mathbf{G}(O_S))}$$ denote the number of irreducible complex representations of $${\mathbf{G}(O_S)}$$ of dimension at most n. The degree of representation growth $${\alpha(\mathbf{G}(O_S)) = \lim_{n \rightarrow\infty} \log R_n(\mathbf{G}(O_S)) / \log n}$$ is finite if and only if $${\mathbf{G}(O_S)}$$ has the weak Congruence Subgroup Property. We establish that for every $${\mathbf{G}(O_S)}$$ with the weak Congruence Subgroup Property the invariant $${\alpha(\mathbf{G}(O_S))}$$ is already determined by the absolute root system of $${\mathbf{G}}$$ . To show this we demonstrate that the abscissae of convergence of the representation zeta functions of such groups are invariant under base extensions $${K{\subset}L}$$ . We deduce from our result a variant of a conjecture of Larsen and Lubotzky regarding the representation growth of irreducible lattices in higher rank semi-simple groups. In particular, this reduces Larsen and Lubotzky’s conjecture to Serre’s conjecture on the weak Congruence Subgroup Property, which it refines.

The strength of cross‐taxon congruence in species composition varies with the size of regional species pools and the intensity of human disturbance

AbstractAimOur aims were to determine whether cross‐taxon congruence of species composition patterns varies across regions and human disturbance levels and to infer whether these patterns relate to the size of the regional species pool and the sorting of species along a gradient of human disturbance.LocationAlberta's Boreal and Grassland Natural Regions, Canada.MethodWe compiled presence–absence data of four biological groups (birds, vascular plants, bryophytes and mites) from low and high disturbance sites in upland habitat. The cross‐taxon congruence across ecoregion and disturbance levels was analysed using Mantel and Procrustes tests. We applied resampling without replacement to generate confidence intervals to test for significant differences in strength of congruency between disturbance levels and ecoregions. We performed indicator species analysis to highlight how the species‐level response to high and low disturbance influences the pattern in community‐level cross‐taxon congruence.ResultsCross‐taxon congruence was stronger when all sites were considered than when high and low disturbance sites were considered separately. Congruency was relatively stronger in high than low disturbance sites in the Boreal ecoregion, but the pattern was reversed in the Grassland ecoregion. More species were indicators of undisturbed habitat than of highly disturbed habitats for all biological groups except for birds. Overall, biological groups that were poorly represented in a region and/or with few characteristic indicator species showed weak congruence in those sites.Main conclusionsWe conclude that a longer disturbance gradient can promote cross‐taxon congruence by increasing the species pool characteristic of low or high disturbance levels. Moreover, regional context can influence (or even reverse) the relative strength of cross‐taxon congruence in high and low disturbance sites, which may explain the inconsistent strength of cross‐taxon congruence along the disturbance gradient. To use biodiversity surrogates across biogeographical regions, it is therefore important to account for the regional and disturbance‐level dependence of cross‐taxon congruence.

Representation of lattices by fuzzy weak congruence relations

Fuzzy (lattice valued) weak congruences of abstract algebras are investigated. For an algebra, the family of all such fuzzy relations is a complete lattice; its structure and cut properties are investigated and fully described. These fuzzy weak congruences are applied in representation of complete and algebraic lattices. A wider class of lattices can be represented in such a fuzzy framework, than in classical algebra. We prove that there is a straightforward representation of any complete lattice, using it as a co-domain. In a more general case, it is proved that several subdirect powers of lattices are also representable by fuzzy weak congruences.

Multifaceted diversity-area relationships reveal global hotspots of mammalian species, trait and lineage diversity.

To define biome-scale hotspots of phylogenetic and functional mammalian biodiversity (PD and FD, respectively) and compare them to 'classical' hotspots based on species richness (SR) only. Global. SR, PD & FD were computed for 782 terrestrial ecoregions using distribution ranges of 4616 mammalian species. We used a set of comprehensive diversity indices unified by a recent framework that incorporates the species relative coverage in each ecoregion. We build large-scale multifaceted diversity-area relationships to rank ecoregions according to their levels of biodiversity while accounting for the effect of area on each diversity facet. Finally we defined hotspots as the top-ranked ecoregions. While ignoring species relative coverage led to a relative good congruence between biome top ranked SR, PD and FD hotspots, ecoregions harboring a rich and abundantly represented evolutionary history and functional diversity did not match with top ranked ecoregions defined by species richness. More importantly PD and FD hotspots showed important spatial mismatches. We also found that FD and PD generally reached their maximum values faster than species richness as a function of area. The fact that PD/FD reach faster their maximal value than SR may suggest that the two former facets might be less vulnerable to habitat loss than the latter. While this point is expected, it is the first time that it is quantified at global scale and should have important consequences in conservation. Incorporating species relative coverage into the delineation of multifaceted hotspots of diversity lead to weak congruence between SR, PD and FD hotspots. This means that maximizing species number may fail at preserving those nodes (in the phylogenetic or functional tree) that are relatively abundant in the ecoregion. As a consequence it may be of prime importance to adopt a multifaceted biodiversity perspective to inform conservation strategies at global scale.

A note on representation of lattices by weak congruences

A weak congruence is a symmetric, transitive, and compatible relation. An element u of an algebraic lattice L is Δ-suitable if there is an isomorphism κ from L to the lattice of weak congruences of an algebra such that κ(u) is the diagonal relation. Some conditions implying the Δ-suitability of u are presented.

ON INTERRELATIONS BETWEEN FUZZY CONGRUENCE AXIOMS

In this paper we establish interrelations between fuzzy direct revelation axiom (FDRA), fuzzy transitive-closure coherence axiom (FTCCA), fuzzy consistent-closure coherence axiom (FCCCA) and fuzzy intermediate congruence axiom (FICA). We also establish their relationships with weak fuzzy congruence axiom (WFCA), strong fuzzy congruence axiom (SFCA) and weak axiom of fuzzy revealed preference (WAFRP). Condition for equivalence of fuzzy Arrow axiom (FAA) and weak fuzzy congruence axiom (WFCA) on arbitrary domain is also given.

Imprints of glacial history and current environment on correlations between endemic plant and invertebrate species richness

Aim We evaluate how closely diversity patterns of endemic species of vascular plants, beetles, butterflies, molluscs and spiders are correlated with each other, and to what extent similar environmental requirements or survival in common glacial refugia and comparable dispersal limitations account for their existing congruence. Location Austria. Methods We calculated pairwise correlations among species numbers of the five taxonomic groups in 1405 cells of a 3′ × 5′ raster (c. 35 km2) using the raw data as well as the residuals of regression models that accounted for: (1) environmental variables, (2) environmental variables and the occurrence of potential refugia during the Last Glacial Maximum, or (3) environmental variables, refugia and spatial filters. Results Pairwise cross-taxonomic group Spearman’s rank correlations in the raw data were significantly positive in most cases, but only moderate (0.3 < ρ < 0.5) to weak (ρ < 0.3) throughout. Correlations were closest between plants and beetles, plants and butterflies, and plants and snails, respectively, whereas the distribution of endemic spiders was largely uncorrelated with those of the other groups. Environmental variables explained only a moderate proportion of the variance in endemic richness patterns, and the response of individual groups to environmental gradients was only partly consistent. The inclusion of refugium locations and the spatial filters increased the goodness of model fit for all five taxonomic groups. Moreover, removing the effects of environmental conditions reduced congruence in endemic richness patterns to a lesser extent than did filtering the influence of refugium locations and spatial autocorrelation, except for spiders, which are probably the least dispersal-limited of the five groups. Main conclusions The moderate to weak congruence of endemic richness patterns clearly limits the usefulness of a surrogacy approach for designating areas for the protection of regional endemics. On the other hand, our results suggest that dispersal limitations still shape the distributions of many endemic plant, snail, beetle and butterfly species, even at the regional scale; that is, survival in shared refugia and subsequent restricted spread retain a detectable signal in existing correlations. Concentrating conservation efforts on well-known Pleistocene refugia hence appears to be a reasonable first step towards a strategy for protecting regional endemics of at least the less mobile invertebrate groups.

Cross-taxon congruence in tree, bird and bat species distributions at a moderate spatial scale across four tropical forest types in the Philippines

Indicator species groups are often used as surrogates for overall biodiversity in conservation planning because inventories of multiple taxa are rare, especially in the tropics where most biodiversity is found. At coarse spatial scales most studies show congruence in the distribution of species richness and of endemic and threatened species of different species groups. At finer spatial scale levels however, cross-taxon congruence patterns are much more ambiguous. In this study we investigated cross-taxon patterns in the distribution of species richness of trees, birds and bats across four tropical forest types in a ca. 100 × 35 km area in the Northern Sierra Madre region of Luzon Island, Philippines. A non-parametric species richness estimator (Chao1) was used to compensate for differential sample sizes, sample strategies and completeness of species richness assessments. We found positive but weak congruence in the distribution of all and endemic tree and bird and tree and bat species richness across the four forest types; strong positive congruence in the distribution of all and endemic bat and bird species richness and low or negative congruence in the distribution of globally threatened species between trees, birds and bats. We also found weak cross-taxon congruence in the complementarity of pairs of forest types in species richness between trees and birds and birds and bats but strong congruence in complementarity of forest pairs between trees and bats. This study provides further evidence that congruence in the distribution of different species groups is often ambiguous at fine to moderate spatial scales. Low or ambiguous cross-taxon congruence complicates the use of indicator species and species groups as a surrogate for biodiversity in general for local systematic conservation planning.

Characteristic triangles of closure operators with applications in general algebra

Our aim is to investigate groups and their weak congruence lattices in the abstract setting of lattices L with (local) closure operators C in the categorical sense, where L is regarded as a small category and C is a family of closure maps on the principal ideals of L. A useful tool for structural investigations of such “lattices with closure” is the so-called characteristic triangle, a certain substructure of the square L2. For example, a purely order-theoretical investigation of the characteristic triangle shows that the Dedekind groups (alias Hamiltonian groups) are precisely those with modular weak congruence lattices; similar results are obtained for other classes of algebras.

Algebraically closed algebras in certain small congruence distributive varieties

In a finitely generated congruence distributive variety satisfying a weak congruence extension property, the algebraically closed algebras are precisely updirected unions of maximal subdirectly irreducibles. The class of algebraically closed algebras of such a variety is elementary and definable by Horn sentences.

On the semidistributivity of elements in weak congruence lattices of algebras and groups

Weak congruence lattices and semidistributive congruence lattices are both recent topics in universal algebra. This motivates the main result of the present paper, which asserts that a finite group G is a Dedekind group if and only if the diagonal relation is a join-semidistributive element in the lattice of weak congruences of G. A variant in terms of subgroups rather than weak congruences is also given. It is pointed out that no similar result is valid for rings. An open problem and some results on the join-semidistributivity of weak congruence lattices are also included.

REMARKS ON CONGRUENCE OF 3-MANIFOLDS

We give two proofs that the 3-torus is not weakly d-congruent to #3S1 × S2, if d &gt; 2. We study how cohomology ring structure relates to weak congruence. We give an example of three 3-manifolds which are weakly 5-congruent but are not 5-congruent.

Phylogeny of Paramysis (Crustacea: Mysida) and the origin of Ponto-Caspian endemic diversity: Resolving power from nuclear protein-coding genes

The Ponto-Caspian (Black and Caspian seas) brackish-water fauna represents a special case of the endemic diversification in world’s ancient lakes; it also involves a hotspot of continental diversity in the predominantly marine mysid crustaceans. We explored the origins and history of the mysid diversification in a phylogenetic analysis of some 20 endemic Ponto-Caspian species mainly of the genus Paramysis and their marine congeners, using sequences of two nuclear protein-coding genes, two nuclear rRNA genes, the mitochondrial COI gene and morphological data. A nearly completely resolved phylogeny was recovered, with no indication of rapid diversification bursts. Deep divergences were found among the main endemic clades, attesting to a long independent faunal history in the continental Paratethys waters. The current marine Paramysis species make a monophyletic cluster secondarily derived from the continental Paratethyan (Ponto-Caspian) Paramysis ancestors. The good phylogenetic resolution was mainly due to the two nuclear protein-coding genes, opsin and EPRS, here for the first time applied to peracarid systematics. In contrast, ‘conventional’ mtDNA and nuclear rRNA genes provided poor topological resolution and weak congruence of divergence rates. The two nuclear protein-coding genes had more congruent rates of evolution, and were about 10–15 times slower than the mitochondrial COI gene.

A note on atomistic weak congruence lattices

It is proved that a codistributive element in an atomistic algebraic lattice has a complement, implying that kernels of the related homomorphisms coincide. Some applications to weak congruence lattices of algebras are presented. In particular, necessary and sufficient conditions under which the weak congruence lattice of an algebra is atomistic are given.

INTUITIONISTIC FUZZY WEAK CONGRUENCES ON A SEMIRING

We introduce the concept of intuitionistic fuzzy weak congruence on a semiring and obtain the relation between intuitionistic fuzzy weak congruence and intuitionistic fuzzy ideal of a semiring. Also we define and investigate intuitionistic fuzzy quotient semiring of a semiring over an intuitionistic fuzzy ideal or over an intuitionistic fuzzy weak congruence.

Arrow’s Axiom and Full Rationality for Fuzzy Choice Functions

A classical result for crisp choice functions shows the equivalence between Arrow axiom and the property of full rationality. In this paper we study a fuzzy form of Arrow axiom formulated in terms of the subsethood degree and of the degree of equality (of fuzzy sets). We prove that a fuzzy choice function satisfies Fuzzy Arrow Axiom if and only if it is (fuzzy) full rational. We also show that these conditions are also equivalent with weak and strong fuzzy congruence axioms WFCA and SFCA. It is studied the Arrow index, a new concept that indicates the degree to which a fuzzy choice function satisfies the Fuzzy Arrow Axiom.

A Note on Triangular Schemes for Weak Congruences

Some geometrical methods, the so called Triangular Schemes and Principles, are introduced and investigated for weak congruences of algebras. They are analogues of the corresponding notions for congruences. Particular versions of Triangular Schemes are equivalent to weak congruence modularity and to weak congruence distributivity. For algebras in congruence permutable varieties, stronger properties—Triangular Principles—are equivalent to weak congruence modularity and distributivity.

Congruence Distributivity in Goursat and Mal’cev Categories

We characterize the congruence distributive property for the Goursat and regular Mal’cev categories in terms of preservation of the intersection by direct images. This splits a previous characterization for the exact Mal’cev categories in two cases: plain congruence distributive property and weak congruence distributive property.