Semiclassical propagator for SU(n) coherent states

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)We present a detailed derivation of the semiclassical propagator in the SU(n) coherent state representation. In order to provide support for immediate physical applications, we restrict this work to the fully symmetric irreducible representations, which are suitable for the treatment of bosonic dynamics in n modes, considering systems with conservation of total particle number. The derivation described here can be easily extended to other classes of coherent states, thus representing an alternative approach to previously published methods. (C) 2011 American Institute of Physics. [doi:10.1063/1.3583996]525Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP [2008/09491-9, 2009/11032-5

Allopatry increases the balance of phylogenetic trees during radiation under neutral speciation

The shape of a phylogenetic tree is defined by the sequence of speciation events, represented by its branching points, and extinctions, represented by branch interruptions. In a neutral scenario of parapatry and isolation by distance, species tend to branch off the original population one after the other, leading to highly unbalanced trees. In this case the degree of imbalance, measured by the normalized Sackin index, grows linearly with species richness. Here we claim that moderate values of imbalance for trees with large number of species can occur if the geographic distribution involves more than one deme (allopatry) and speciation is parapatric within demes. The combined values of balance (normalized Sackin index) and species richness provide an estimate of how many demes were involved in the process if it happened in such neutral scenario. We also show that the spatial division in demes moderately slows down the diversification process, portraying a neutral mechanism for structuring the branch length distribution of phylogenetic trees

Trace formula for systems with spin from the coherent state propagator

We present a detailed derivation of the trace formula for a general Hamiltonian with two degrees of freedom where one of them is canonical and the other a spin. Our derivation starts from the semiclassical formula for the propagator in a basis formed by the product of a canonical and a spin coherent states and is valid in the limit h -> 0, j ->infinity with jh constant. The trace formula, obtained by taking the trace and the Fourier transform of the coherent state propagator, is compared to others found in the literature. (c) 2007 American Institute of Physics.481

Mean-field approximation to a spatial host-pathogen model

We study the mean-field approximation to a simple spatial host-pathogen model that has been shown to display interesting evolutionary properties. We show that previous derivations of the mean-field equations for this model are actually only low-density approximations to the true mean-field limit. We derive the correct equations and the corresponding equations including pair correlations. The process of invasion by a mutant type of pathogen is also discussed.674

The role of sex separation in neutral speciation

Neutral speciation mechanisms based on isolation by distance and sexual selection, termed topopatric, have recently been shown to describe the observed patterns of abundance distributions and species-area relationships. Previous works have considered this type of process only in the context of hermaphrodic populations. In this work we extend a hermaphroditic model of topopatric speciation to populations where individuals are explicitly separated into males and females. We show that for a particular carrying capacity speciation occurs under similar conditions, but the number of species generated decreases as compared to the hermaphroditic case. Evolution results in fewer species having more abundant populations.Comment: 18 pages + 8 figure

Frequency-dependent selection predicts patterns of radiations and biodiversity

Most empirical studies support a decline in speciation rates through time, although evidence for constant speciation rates also exists. Declining rates have been explained by invoking niche-filling processes, whereas constant rates have been attributed to non-adaptive processes such as sexual selection, mutation, and dispersal. Trends in speciation rate and the processes underlying it remain unclear, representing a critical information gap in understanding patterns of global diversity. Here we show that the speciation rate is driven by frequency dependent selection. We used a frequency-dependent and DNA sequence-based model of populations and genetic-distance-based speciation, in the absence of adaptation to ecological niches. We tested the frequency-dependent selection mechanism using cichlid fish and Darwin's finches, two classic model systems for which speciation rates and richness data exist. Using negative frequency dependent selection, our model both predicts the declining speciation rate found in cichlid fish and explains their species richness. For groups like the Darwin's finches, in which speciation rates are constant and diversity is lower, the speciation rate is better explained by a model without frequency-dependent selection. Our analysis shows that differences in diversity are driven by larger incipient species abundance (and consequent lower extinction rates) with frequency-dependent selection. These results demonstrate that mutations, genetic-distance-based speciation, sexual and frequency-dependent selection are sufficient not only for promoting rapid proliferation of new species, but also for maintaining the high diversity observed in natural systems

Genus Paracoccidioides: Species Recognition and Biogeographic Aspects

Background: Paracoccidioidomycosis is a systemic mycosis caused by Paracoccidioides brasiliensis (species S1, PS2, PS3), and Paracoccidioides lutzii. This work aimed to differentiate species within the genus Paracoccidioides, without applying multilocus sequencing, as well as to obtain knowledge of the possible speciation processes. Methodology/Principal Findings: Single nucleotide polymorphism analysis on GP43, ARF and PRP8 intein genes successfully distinguished isolates into four different species. Morphological evaluation indicated that elongated conidia were observed exclusively in P. lutzii isolates, while all other species (S1, PS2 and PS3) were indistinguishable. To evaluate the biogeographic events that led to the current geographic distribution of Paracoccidioides species and their sister species, Nested Clade and Likelihood Analysis of Geographic Range Evolution (LAGRANGE) analyses were applied. The radiation of Paracoccidioides started in northwest South America, around 11–32 million years ago, as calculated on the basis of ARF substitution rate, in the BEAST program. Vicariance was responsible for the divergence among S1, PS2 and P. lutzii and a recent dispersal generated the PS3 species, restricted to Colombia. Taking into account the ancestral areas revealed by the LAGRANGE analysis and the major geographic distribution of L. loboi in the Amazon basin, a region strongly affected by the Andes uplift and marine incursions in the Cenozoic era, we also speculate about the effect of these geological events on the vicariance between Paracoccidioides and L. loboi. Conclusions/Significance: The use of at least 3 SNPs, but not morphological criteria, as markers allows us to distinguish among the four cryptic species of the genus Paracoccidioides. The work also presents a biogeographic study speculating on how these species might have diverged in South America, thus contributing to elucidating evolutionary aspects of the genus Paracoccidioides

Does Sex Speed Up Evolutionary Rate and Increase Biodiversity?

Most empirical and theoretical studies have shown that sex increases the rate of evolution, although evidence of sex constraining genomic and epigenetic variation and slowing down evolution also exists. Faster rates with sex have been attributed to new gene combinations, removal of deleterious mutations, and adaptation to heterogeneous environments. Slower rates with sex have been attributed to removal of major genetic rearrangements, the cost of finding a mate, vulnerability to predation, and exposure to sexually transmitted diseases. Whether sex speeds or slows evolution, the connection between reproductive mode, the evolutionary rate, and species diversity remains largely unexplored. Here we present a spatially explicit model of ecological and evolutionary dynamics based on DNA sequence change to study the connection between mutation, speciation, and the resulting biodiversity in sexual and asexual populations. We show that faster speciation can decrease the abundance of newly formed species and thus decrease long-term biodiversity. In this way, sex can reduce diversity relative to asexual populations, because it leads to a higher rate of production of new species, but with lower abundances. Our results show that reproductive mode and the mechanisms underlying it can alter the link between mutation, evolutionary rate, speciation and biodiversity and we suggest that a high rate of evolution may not be required to yield high biodiversity