Limiting problems for a nonstandard viscous Cahn--Hilliard system with dynamic boundary conditions

This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of two-species phase segregation on an atomic lattice and was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp.105--118. The two unknowns are the phase parameter and the chemical potential. In contrast to previous investigations about this PDE system, we consider here a dynamic boundary condition for the phase variable that involves the Laplace-Beltrami operator and models an additional nonconserving phase transition occurring on the surface of the domain. We are interested to some asymptotic analysis and first discuss the asymptotic limit of the system as the viscosity coefficient of the order parameter equation tends to 0: the convergence of solutions to the corresponding solutions for the limit problem is proven. Then, we study the long-time behavior of the system for both problems, with positive or zero viscosity coefficient, and characterize the omega-limit set in both cases

Tertiary Climate Change and the Diversification of the Amazonian Gecko Genus Gonatodes (Sphaerodactylidae, Squamata)

The genus Gonatodes is a monophyletic group of small-bodied, diurnal geckos distributed across northern South America, Central America, and the Caribbean. We used fragments of three nuclear genes (RAG2, ACM4, and c-mos) and one mitochondrial gene (16S) to estimate phylogenetic relationships among Amazonian species of Gonatodes. We used Penalized Likelihood to estimate timing of diversification in the genus. Most cladogenesis occurred in the Oligocene and early Miocene and coincided with a burst of diversification in other South American animal groups including mollusks, birds, and mammals. The Oligocene and early Miocene were periods dominated by dramatic climate change and Andean orogeny and we suggest that these factors drove the burst of cladogenesis in Gonatodes geckos as well as other taxa. A common pattern in Amazonian taxa is a biogeographic split between the eastern and western Amazon basin. We observed two clades with this spatial distribution, although large differences in timing of divergence between the east–west taxon pairs indicate that these divergences were not the result of a common vicariant event

Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

Global existence for a nonstandard viscous Cahn--Hilliard system with dynamic boundary condition

In this paper, we study a model for phase segregation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically. In contrast to the existing literature about this PDE system, we consider here a dynamic boundary condition involving the Laplace-Beltrami operator for the order parameter. This boundary condition models an additional nonconserving phase transition occurring on the surface of the domain. Different well-posedness results are shown, depending on the smoothness properties of the involved bulk and surface free energies

A New Genus of Miniaturized and Pug-Nosed Gecko from South America (Sphaerodactylidae: Gekkota)

Sphaerodactyl geckos comprise five genera distributed across Central and South America and the Caribbean. We estimated phylogenetic relationships among sphaerodactyl genera using both separate and combined analyses of seven nuclear genes. Relationships among genera were incongruent at different loci and phylogenies were characterized by short, in some cases zero-length, internal branches and poor phylogenetic support at most nodes. We recovered a polyphyletic Coleodactylus, with Coleodactylus amazonicus being deeply divergent from the remaining Coleodactylus species sampled. The C. amazonicus lineage possessed unique codon deletions in the genes PTPN12 and RBMX while the remaining Coleodactylus species had unique codon deletions in RAG1. Topology tests could not reject a monophyletic Coleodactylus, but we show that short internal branch lengths decreased the accuracy of topology tests because there were not enough data along these short branches to support one phylogenetic hypothesis over another. Morphological data corroborated results of the molecular phylogeny, with Coleodactylus exhibiting substantial morphological heterogeneity. We identified a suite of unique craniofacial features that differentiate C. amazonicus not only from other Coleodactylus species, but also from all other geckos. We describe this novel sphaerodactyl lineage as a new genus, Chatogekko gen. nov. We present a detailed osteology of Chatogekko, characterizing osteological correlates of miniaturization that provide a framework for future studies in sphaerodactyl systematics and biology

Coming to America: Multiple Origins of New World Geckos

Geckos in the Western Hemisphere provide an excellent model to study faunal assembly at a continental scale. We generated a time-calibrated phylogeny, including exemplars of all New World gecko genera, to produce a biogeographic scenario for the New World geckos. Patterns of New World gecko origins are consistent with almost every biogeographic scenario utilized by a terrestrial vertebrate with different New World lineages showing evidence of vicariance, dispersal via temporary land bridge, overseas dispersal, or anthropogenic introductions. We also recovered a strong relationship between clade age and species diversity, with older New World lineages having more species than more recently arrived lineages. Our data provide the first phylogenetic hypothesis for all New World geckos and highlight the intricate origins and ongoing organization of continental faunas. The phylogenetic and biogeographical hypotheses presented here provide an historical framework to further pursue research on the diversification and assembly of the New World herpetofauna

Population Genetic Structure and Species Delimitation of a Widespread, Neotropical Dwarf Gecko

Amazonia harbors the greatest biological diversity on Earth. One trend that spans Amazonian taxa is that most taxonomic groups either exhibit broad geographic ranges or small restricted ranges. This is likely because many traits that determine a species range size, such as dispersal ability or body size, are autocorrelated. As such, it is rare to find groups that exhibit both large and small ranges. Once identified, however, these groups provide a powerful system for isolating specific traits that influence species distributions. One group of terrestrial vertebrates, gecko lizards, tends to exhibit small geographic ranges. Despite one exception, this applies to the Neotropical dwarf geckos of the genus Gonatodes. This exception, Gonatodes humeralis, has a geographic distribution almost 1,000,000 km2 larger than the combined ranges of its 30 congeners. As the smallest member of its genus and a gecko lizard more generally, G. humeralis is an unlikely candidate to be a wide-ranged Amazonian taxon. To test whether or not G. humeralis is one or more species, we generated molecular genetic data using restriction-site associated sequencing (RADseq) and traditional Sanger methods for samples from across its range and conducted a phylogeographic study. We conclude that G. humeralis is, in fact, a single species across its contiguous range in South America. Thus, Gonatodes is a unique clade among Neotropical taxa, containing both wide-ranged and range-restricted taxa, which provides empiricists with a powerful model system to correlate complex species traits and distributions. Additionally, we provide evidence to support species-level divergence of the allopatric population from Trinidad and we resurrect the name Gonatodes ferrugineus from synonymy for this population

The demography of the lizard Tropidurus torquatus (Squamata, Tropiduridae) in a highly seasonal Neotropical savanna

The demography of a population of Tropidurus torquatus was studied from March 1996 until December 1998, in the Cerrado biome of the Central Brazil, using the method of capture and recapture. Population size, number of incoming individuals in the population, and age structure varied seasonally, reflecting the reproductive cycle of the species. The instantaneous rate of population increase did not differ from zero throughout the study. In general, the permanence rate of juveniles and adults were low, indicating a large turnover of individuals in the population, with a maximum life expectancy of three years. The sex-ratio among adults was biased toward females. Since no bias was observed among juveniles and there was no difference in adults permanence between sexes, we suggestet that the biased adult sex-ratio resulted from a lower permanence of males during a short ontogenetic period, when secondary sexual characteristics develop. When compared to T. itambere, the studied population of T. torquatus attained a higher density and a greater female bias in the sex-ratio. In general, the studied population presented characteristics that, according to life history theory, should be associated with early age at maturity and polyginy: short life expectancy, high population turnover, and female biased sex-ratios