Conservative force fields in non-Gaussian statistics

In this Letter, we determine the kappa-distribution function for a gas in the presence of an external field of force described by a potential U(r). In the case of a dilute gas, we show that the kappa-power law distribution including the potential energy factor term can rigorously be deduced in the framework of kinetic theory with basis on the Vlasov equation. Such a result is significant as a preliminary to the discussion on the role of long range interactions in the Kaniadakis thermostatistics and the underlying kinetic theory. (C) 2008 Elsevier B.V. All rights reserved.

Molecular Systematics of Noctuoidea (Insecta, lepidoptera)

In this thesis, I conduct a series of molecular systematic studies on the large phytophagous moth superfamily Noctuoidea (Insecta, Lepidoptera) to clarify deep divergences and evolutionary affinities of the group, based on material from every zoogeographic region of the globe. Noctuoidea are the most speciose radiations of butterflies and moths on earth, comprising about a quarter of all lepidopteran diversity. The general aim of these studies was to apply suitably conservative genetic markers (DNA sequences of mitochondrial—mtDNA—and nuclear gene— nDNA—regions) to reconstruct, as the initial step, a robust skeleton phylogenetic hypothesis for the superfamily, then build up robust phylogenetic frameworks for those circumscribed monophyletic entities (i.e., families), as well as clarifying the internal classification of monophyletic lineages (subfamilies and tribes), to develop an understanding of the major lineages at various taxonomic levels within the superfamily Noctuoidea, and their inter-relationships. The approaches applied included: i) stabilizing a robust family-level classification for the superfamily; ii) resolving the phylogeny of the most speciose radiation of Noctuoidea: the family Erebidae; iii) reconstruction of ancestral feeding behaviors and evolution of the vampire moths (Erebidae, Calpinae); iv) elucidating the evolutionary relationships within the family Nolidae and v) clarifying the basal lineages of Noctuidae sensu stricto. Thus, in this thesis I present a wellresolved molecular phylogenetic hypothesis for higher taxa of Noctuoidea consisting of six strongly supported families: Oenosandridae, Notodontidae, Euteliidae, Erebidae, Nolidae, and Noctuidae. The studies in my thesis highlight the importance of molecular data in systematic and phylogenetic studies, in particular DNA sequences of nuclear genes, and an extensive sampling strategy to include representatives of all known major lineages of entire world fauna of Noctuoidea from every biogeographic region. This is crucial, especially when the model organism is as species-rich, highly diverse, cosmopolitan and heterogeneous as the Noctuoidea, traits that represent obstacles to the use of morphology at this taxonomic level.

Molecular clock or erratic evolution? A tale of two genes.

We have investigated the evolution of glycerol-3-phosphate dehydrogenase (Gpdh). The rate of amino acid replacements is 1 x 10(-10)/site/year when Drosophila species are compared. The rate is 2.7 times greater when Drosophila and Chymomyza species are compared; and about 5 times greater when any of those species are compared with the medfly Ceratitis capitata. This rate of 5 x 10(-10)/site/year is also the rate observed in comparisons between mammals, or between different animal phyla, or between the three multicellular kingdoms. We have also studied the evolution of Cu,Zn superoxide dismutase (Sod). The rate of amino acid replacements is about 17 x 10(-10)/site/year when comparisons are made between dipterans or between mammals, but only 5 x 10(-10) when animal phyla are compared, and only 3 x 10(-10) when the multicellular kingdoms are compared. The apparent decrease by about a factor of 5 in the rate of SOD evolution as the divergence between species increases can be consistent with the molecular clock hypothesis by assuming the covarion hypothesis (namely, that the number of amino acids that can change is constant, but the set of such amino acids changes from time to time and from lineage to lineage). However, we know of no model consistent with the molecular clock hypothesis that would account for the increase in the rate of GPDH evolution as the divergence between species increases.

Large-scale DNA sequencing in taxonomy and conservation : a case study with the mayfly family Heptageniidae (Ephemeroptera) in the Alps and Madagascar

Les larves aquatiques d'éphémères (Ephemeroptera) colonisent toutes les eaux douces du monde et sont couramment utilisées comme bio-indicateurs de la qualité de l'eau. Le genre Rhithrogena (Heptageniidae) est le deuxième plus diversifié chez les éphémères, et plusieurs espèces européennes ont une distribution restreinte dans des environnements alpins sensibles. Les espèces de Rhithrogena ont été classées en "groupes d'espèces" faciles à identifier. Cependant, malgré leur importance écologique et en terme de conservation, beaucoup d'espèces présentent des différences morphologiques ambiguës, suggérant que lataxonomie actuelle ne refléterait pas correctement leur diversité évolutive. De plus, aucune information sur leurs relations, leur origine, le taux de spéciation ou les mécanismes ayant provoqué leur remarquable diversification dans les Alpes n'est disponible. Nous avons d'abord examiné le statut spécifique d'environ 50% des espèces européennes de Rhithrogena en utilisant un large échantillonnage de populations alpines incluant 22 localités typiques, ainsi qu'une analyse basée sur le modèle général mixte de Yule et de coalescence (GMYC) appliqué à un gène mitochondrial standard (coxl) et à un gène nucléaire développé spécifiquement pour cette étude. Nous avons observé un regroupement significatif des séquences coxl en 31 espèces potentielles, et nos résultats ont fortement suggéré la présence d'espèces cryptiques et de fractionnements taxonomiques excessifs chez les Rhithrogena. Nos analyses phylogénétiques ont démontré la monophylie de quatre des six groupes d'espèces reconnus présents dans notre échantillonnage. La taxonomie ADN développée dans cette étude pose les bases d'une future révision de ce genre important mais cryptique en Europe. Puis nous avons mené une étude phylogénétique multi-gènes entre les espèces européennes de Rhithrogena. Les données provenant de trois gènes nucléaires et de deux gènes mitochondriaux ont été largement concordantes, et les relations entre les espèces bien résolues au sein de la plupart des groupes d'espèces dans une analyse combinant tous les gènes. En l'absence de points de calibration extérieurs tels que des fossiles, nous avons appliqué à nos données mitochondriales une horloge moléculaire standard pour les insectes, suggérant une origine des Rhithrogena alpins à la limite Oligocène / Miocène. Nos résultats ont montré le rôle prépondérant qu'ont joué les glaciations du quaternaire dans leur diversification, favorisant la spéciation d'au moins la moitié des espèces actuelle dans les Alpes. La biodiversité et le taux d'endémisme à Madagascar, notamment au niveau de la faune des eaux douces, sont parmi les plus extraordinaires et les plus menacés au monde. On pense que beaucoup d'espèces d'éphémères sont restreintes à un seul bassin versant (microendémisme) dans les zones forestières, ce qui les rendrait particulièrement sensibles à la réduction et à la dégradation de leur habitat. Mis à part deux espèces décrites, Afronurus matitensis et Compsoneuria josettae, les Heptageniidae sont pratiquement inconnus à Madagascar. Les deux genres ont une distribution discontinue en Afrique, à Madagascar et en Asie du Sud-Est, et leur taxonomie complexe est régulièrement révisée. L'approche standard pour comprendre leur diversité, leur endémisme et leur origine requerrait un échantillonnage étendu sur plusieurs continents et des années de travaux taxonomiques. Pour accélérer le processus, nous avons utilisé des collections de musées ainsi que des individus fraîchement collectés, et appliqué une approche combinant taxonomie ADN et phylogénie. L'analyses GMYC du gène coxl a délimité 14 espèces potentielles à Madagascar, dont 70% vraisemblablement microendémiques. Une analyse phylogénique incluant des espèces africaines et asiatiques portant sur deux gènes mitochondriaux et quatre gènes nucléaires a montré que les Heptageniidae malgaches sont monophylétiques et groupe frère des Compsoneuria africains. L'existence de cette lignée unique, ainsi qu'un taux élevé de microendémisme, mettent en évidence leur importance en terme de conservation. Nos résultats soulignent également le rôle important que peuvent jouer les collections de musées dans les études moléculaires et en conservation. - Aquatic nymphs of mayflies (Ephemeroptera) colonize all types of freshwaters throughout the world and are extensively used as bio-indicators of water quality. Rhithrogena (Heptageniidae) is the second most species-rich genus of mayflies, and several European species have restricted distributions in sensitive Alpine environments and therefore are of conservation interest. The European Rhithrogena species are arranged into "species groups" that are easily identifiable. However, despite their ecological and conservation importance, ambiguous morphological differences among many species suggest that the current taxonomy may not accurately reflect their evolutionary diversity. Moreover, no information about their relationships, origin, timing of speciation and mechanisms promoting their successful diversification in the Alps is available. We first examined the species status of ca. 50% of European Rhithrogena diversity using a widespread sampling scheme of Alpine species that included 22 type localities, general mixed Yule- coalescent (GMYC) model analysis of one standard mitochondrial (coxl) and one newly developed nuclear marker. We observed significant clustering of coxl into 31 GMYC species, and our results strongly suggest the presence of both cryptic diversity and taxonomic oversplitting in Rhithrogena. Phylogenetic analyses recovered four of the six recognized species groups in our samples as monophyletic. The DNA taxonomy developed here lays the groundwork for a future revision of this important but cryptic genus in Europe. Then we conducted a species-level, multiple-gene phylogenetic study of European Rhithrogena. Data from three nuclear and two mitochondrial loci were broadly congruent, and species-level relationships were well resolved within most species groups in a combined analysis. In the absence of external calibration points like fossils, we applied a standard insect molecular clock hypothesis to our mitochondrial data, suggesting an origin of Alpine Rhithrogena in the Oligocene / Miocene boundary. Our results highlighted the preponderant role that quaternary glaciations played in their diversification, promoting speciation of at least half of the current diversity in the Alps. Madagascar's biodiversity and endemism are among the most extraordinary and endangered in the world. This includes the island's freshwater biodiversity, although detailed knowledge of the diversity, endemism, and biogeographic origin of freshwater invertebrates is lacking. Many mayfly species are thought to be restricted to single river basins (microendemic species) in forested areas, making them particularly sensitive to habitat reduction and degradation. The Heptageniidae are practically unknown in Madagascar except for two described species, Afronurus matitensis and Compsoneuria josettae. Both genera have a disjunct distribution in Africa, Madagascar and Southeast Asia, and a complex taxonomic status still in flux. The standard approach to understanding their diversity, endemism, and origin would require extensive field sampling on several continents and years of taxonomic work. Here we circumvent this using museum collections and freshly collected individuals in a combined approach of DNA taxonomy and phylogeny. The cox/-based GMYC analysis revealed 14 putative species on Madagascar, 70% of which potentially microendemics. A phylogenetic analysis that included African and Asian species and data from two mitochondrial and four nuclear loci indicated the Malagasy Heptageniidae are monophyletic and sister to African Compsoneuria. The observed monophyly and high microendemism highlight their conservation importance. Our results also underline the important role that museum collections can play in molecular studies, especially in critically endangered biodiversity hotspots like Madagascar.

Models of DNA sequence evolution

Models of DNA sequence evolution and methods for estimating evolutionary distances are needed for studying the rate and pattern of molecular evolution and for inferring the evolutionary relationships of organisms or genes. In this dissertation, several new models and methods are developed.^ The rate variation among nucleotide sites: To obtain unbiased estimates of evolutionary distances, the rate heterogeneity among nucleotide sites of a gene should be considered. Commonly, it is assumed that the substitution rate varies among sites according to a gamma distribution (gamma model) or, more generally, an invariant+gamma model which includes some invariable sites. A maximum likelihood (ML) approach was developed for estimating the shape parameter of the gamma distribution $(\alpha)$ and/or the proportion of invariable sites $(\theta).$ Computer simulation showed that (1) under the gamma model, $\alpha$ can be well estimated from 3 or 4 sequences if the sequence length is long; and (2) the distance estimate is unbiased and robust against violations of the assumptions of the invariant+gamma model.^ However, this ML method requires a huge amount of computational time and is useful only for less than 6 sequences. Therefore, I developed a fast method for estimating $\alpha,$ which is easy to implement and requires no knowledge of tree. A computer program was developed for estimating $\alpha$ and evolutionary distances, which can handle the number of sequences as large as 30.^ Evolutionary distances under the stationary, time-reversible (SR) model: The SR model is a general model of nucleotide substitution, which assumes (i) stationary nucleotide frequencies and (ii) time-reversibility. It can be extended to SRV model which allows rate variation among sites. I developed a method for estimating the distance under the SR or SRV model, as well as the variance-covariance matrix of distances. Computer simulation showed that the SR method is better than a simpler method when the sequence length $L>1,000$ bp and is robust against deviations from time-reversibility. As expected, when the rate varies among sites, the SRV method is much better than the SR method.^ The evolutionary distances under nonstationary nucleotide frequencies: The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, I developed formulas for correcting the estimation biases of the paralinear and LogDet distances. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, I developed a method for estimating the variance-covariance matrix of the paralinear distance, so that statistical tests of phylogenies can be conducted when the nucleotide frequencies are nonstationary. Third, a new method for testing the molecular clock hypothesis was developed in the nonstationary case. ^

Symmetry in chemistry from the hydrogen atom to proteins

The last 2 decades have seen discoveries in highly excited states of atoms and molecules of phenomena that are qualitatively different from the “planetary” model of the atom, and the near-rigid model of molecules, characteristic of these systems in their low-energy states. A unified view is emerging in terms of approximate dynamical symmetry principles. Highly excited states of two-electron atoms display “molecular” behavior of a nonrigid linear structure undergoing collective rotation and vibration. Highly excited states of molecules described in the “standard molecular model” display normal mode couplings, which induce bifurcations on the route to molecular chaos. New approaches such as rigid–nonrigid correlation, vibrons, and quantum groups suggest a unified view of collective electronic motion in atoms and nuclear motion in molecules.

Estimation of evolutionary distances under stationary and nonstationary models of nucleotide substitution

Estimation of evolutionary distances has always been a major issue in the study of molecular evolution because evolutionary distances are required for estimating the rate of evolution in a gene, the divergence dates between genes or organisms, and the relationships among genes or organisms. Other closely related issues are the estimation of the pattern of nucleotide substitution, the estimation of the degree of rate variation among sites in a DNA sequence, and statistical testing of the molecular clock hypothesis. Mathematical treatments of these problems are considerably simplified by the assumption of a stationary process in which the nucleotide compositions of the sequences under study have remained approximately constant over time, and there now exist fairly extensive studies of stationary models of nucleotide substitution, although some problems remain to be solved. Nonstationary models are much more complex, but significant progress has been recently made by the development of the paralinear and LogDet distances. This paper reviews recent studies on the above issues and reports results on correcting the estimation bias of evolutionary distances, the estimation of the pattern of nucleotide substitution, and the estimation of rate variation among the sites in a sequence.

Reinforcing and expanding the predictions of the disturbance vicariance hypothesis in Amazonian harlequin frogs: A molecular phylogenetic and climate envelope modelling approach

The disturbance vicariance hypothesis (DV) has been proposed to explain speciation in Amazonia, especially its edge regions, e. g. in eastern Guiana Shield harlequin frogs (Atelopus) which are suggested to have derived from a cool-adapted Andean ancestor. In concordance with DV predictions we studied that (i) these amphibians display a natural distribution gap in central Amazonia; (ii) east of this gap they constitute a monophyletic lineage which is nested within a pre-Andean/western clade; (iii) climate envelopes of Atelopus west and east of the distribution gap show some macroclimatic divergence due to a regional climate envelope shift; (iv) geographic distributions of climate envelopes of western and eastern Atelopus range into central Amazonia but with limited spatial overlap. We tested if presence and apparent absence data points of Atelopus were homogenously distributed with Ripley's K function. A molecular phylogeny (mitochondrial 16S rRNA gene) was reconstructed using Maximum Likelihood and Bayesian Inference to study if Guianan Atelopus constitute a clade nested within a larger genus phylogeny. We focused on climate envelope divergence and geographic distribution by computing climatic envelope models with MaxEnt based on macroscale bioclimatic parameters and testing them by using Schoener's index and modified Hellinger distance. We corroborated existing DV predictions and, for the first time, formulated new DV predictions aiming on species' climate envelope change. Our results suggest that cool-adapted Andean Atelopus ancestors had dispersed into the Amazon basin and further onto the eastern Guiana Shield where, under warm conditions, they were forced to change climate envelopes. © 2010 The Author(s).

Testing the Cambrian explosion hypothesis by using a molecular dating technique

Molecular studies have the potential to shed light on the origin of the animal phyla by providing independent estimates of the divergence times, but have been criticized for failing to account adequately for variation in rate of evolution. A method of dating divergence times from molecular data addresses the criticisms of earlier studies and provides more realistic, but wider, confidence intervals. The data are not compatible with the Cambrian explosion hypothesis as an explanation for the origin of metazoan phyla, and provide additional support for an extended period of Precambrian metazoan diversification.

Molecular phylogeny analysis of fiddler crabs: test of the hypothesis of increasing behavioral complexity in evolution.

The current phylogenetic hypothesis for the evolution and biogeography of fiddler crabs relies on the assumption that complex behavioral traits are assumed to also be evolutionary derived. Indo-west Pacific fiddler crabs have simpler reproductive social behavior and are more marine and were thought to be ancestral to the more behaviorally complex and more terrestrial American species. It was also hypothesized that the evolution of more complex social and reproductive behavior was associated with the colonization of the higher intertidal zones. Our phylogenetic analysis, based upon a set of independent molecular characters, however, demonstrates how widely entrenched ideas about evolution and biogeography led to a reasonable, but apparently incorrect, conclusion about the evolutionary trends within this pantropical group of crustaceans. Species bearing the set of "derived traits" are phylogenetically ancestral, suggesting an alternative evolutionary scenario: the evolution of reproductive behavioral complexity in fiddler crabs may have arisen multiple times during their evolution. The evolution of behavioral complexity may have arisen by coopting of a series of other adaptations for high intertidal living and antipredator escape. A calibration of rates of molecular evolution from populations on either side of the Isthmus of Panama suggest a sequence divergence rate for 16S rRNA of 0.9% per million years. The divergence between the ancestral clade and derived forms is estimated to be approximately 22 million years ago, whereas the divergence between the American and Indo-west Pacific is estimated to be approximately 17 million years ago.

Quantifying the complexity of chaos in multibasin multidimensional dynamics of molecular systems

The simulated classical dynamics of a small molecule exhibiting self-organizing behavior via a fast transition between two states is analyzed by calculation of the statistical complexity of the system. It is shown that the complexity of molecular descriptors such as atom coordinates and dihedral angles have different values before and after the transition. This provides a new tool to identify metastable states during molecular self-organization. The highly concerted collective motion of the molecule is revealed. Low-dimensional subspaces dynamics is found sensitive to the processes in the whole, high-dimensional phase space of the system. © 2004 Wiley Periodicals, Inc.

Approach to chaos in ultracold atomic and molecular physics: Statistics of near-threshold bound states for Li+CaH and Li+CaF

We calculate near-threshold bound states and Feshbach resonance positions for atom–rigid-rotor models of the highly anisotropic systems Li+CaH and Li+CaF. We perform statistical analysis on the resonance positions to compare with the predictions of random matrix theory. For Li+CaH with total angular momentum J=0 we find fully chaotic behavior in both the nearest-neighbor spacing distribution and the level number variance. However, for J>0 we find different behavior due to the presence of a nearly conserved quantum number. Li+CaF (J=0) also shows apparently reduced levels of chaotic behavior despite its stronger effective coupling. This may indicate the development of another good quantum number relating to a bending motion of the complex. However, continuously varying the rotational constant over a wide range shows unexpected structure in the degree of chaotic behavior, including a dramatic reduction around the rotational constant of CaF. This demonstrates the complexity of the relationship between coupling and chaotic behavior.

The four hexamerin genes in the honey bee: structure, molecular evolution and function deduced from expression patterns in queens, workers and drones

Background: Hexamerins are hemocyanin-derived proteins that have lost the ability to bind copper ions and transport oxygen; instead, they became storage proteins. The current study aimed to broaden our knowledge on the hexamerin genes found in the honey bee genome by exploring their structural characteristics, expression profiles, evolution, and functions in the life cycle of workers, drones and queens. Results: The hexamerin genes of the honey bee (hex 70a, hex 70b, hex 70c and hex 110) diverge considerably in structure, so that the overall amino acid identity shared among their deduced protein subunits varies from 30 to 42%. Bioinformatics search for motifs in the respective upstream control regions (UCRs) revealed six overrepresented motifs including a potential binding site for Ultraspiracle (Usp), a target of juvenile hormone (JH). The expression of these genes was induced by topical application of JH on worker larvae. The four genes are highly transcribed by the larval fat body, although with significant differences in transcript levels, but only hex 110 and hex 70a are re-induced in the adult fat body in a caste-and sex-specific fashion, workers showing the highest expression. Transcripts for hex 110, hex 70a and hex70b were detected in developing ovaries and testes, and hex 110 was highly transcribed in the ovaries of egg-laying queens. A phylogenetic analysis revealed that HEX 110 is located at the most basal position among the holometabola hexamerins, and like HEX 70a and HEX 70c, it shares potential orthology relationship with hexamerins from other hymenopteran species. Conclusions: Striking differences were found in the structure and developmental expression of the four hexamerin genes in the honey bee. The presence of a potential binding site for Usp in the respective 5' UCRs, and the results of experiments on JH level manipulation in vivo support the hypothesis of regulation by JH. Transcript levels and patterns in the fat body and gonads suggest that, in addition to their primary role in supplying amino acids for metamorphosis, hexamerins serve as storage proteins for gonad development, egg production, and to support foraging activity. A phylogenetic analysis including the four deduced hexamerins and related proteins revealed a complex pattern of evolution, with independent radiation in insect orders.

A molecular phylogeny and the evolution of nest architecture and behavior in Trigona s.s. (Hymenoptera : Apidae : Meliponini)

Stingless bees exhibit extraordinary variation in nest architecture within and among species. To test for phylogenetic association of behavioral traits for species of the Neotropical stingless bee genus Trigona s.s., a phylogenetic hypothesis was generated by combining sequence data of 24 taxa from one mitochondrial (16S rRNA) and four nuclear gene fragments (long-wavelength rhodopsin copy 1 (opsin), elongation factor-1 alpha copy F2, arginine kinase, and 28S rRNA). Fifteen characteristics of the nest architecture were coded and tested for phylogenetic association. Several characters have significant phylogenetic signal, including type of nesting substrate, nest construction material, and hemipterophily, the tending of hemipteroid insects in exchange for sugar excretions. Phylogenetic independent habits encountered in Trigona s.s. include coprophily and necrophagy.