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Aim: Statistical model comparison has become common in historical biogeography, enabled by the R package BioGeoBEARS, which implements several models in a common framework, allowing models to be compared with standard likelihood‐based methods of statistical model comparison. Ree and Sanmartín (Journal of Biogeography, 45, 741–749, 2018) critiqued the comparison of Dispersal–Extinction–Cladogenesis (DEC) and a modification of it, DEC+J, which adds the process of jump dispersal at speciation. DEC+J provides highly significant improvements in model fit on most (although not all) datasets. They claim that the comparison is statistically invalid for a variety of reasons. I analyse the key claims made by the critique. Location: Simulated data. Taxon: Simulated data. Methods: Likelihood calculations are checked by comparison between programs and by‐hand calculations, and by summing likelihoods across all possible datasets. Model adequacy of DEC versus DEC+J is checked by a simulation/inference experiment. Results: Mistakes in the critique's example likelihood calculations are demonstrated. DEC+J fits better on datasets because the DEC model is statistically inadequate in the common situation when most species have geographical ranges of single areas; the DEC model requires long residence times of multi‐area ranges, and when these are not observed, a model that does produce such data patterns, such as DEC+J, prevails. More fundamentally, statistical comparison of DEC and DEC+J produces identical log‐likelihood differences to statistical comparison of two submodels of ClaSSE where extinction rates are fixed to 0. Main Conclusions: DEC fails a basic model adequacy check for understandable reasons, while DEC+J does not. As Ree and Sanmartín recommend ClaSSE models as valid for comparison, the comparison of DEC and DEC+J is statistically valid according to their own criteria. [ABSTRACT FROM AUTHOR]

Detailed knowledge of the thermal behavior of heat storage tanks is necessary for the design and operation of heat supply systems. Storage models enable to simulate the development of the thermal stratification, the thermal losses, the loading and unloading behavior. This article presents a model approach for large‐scale tank stores. It is based on the Lagrange formulation, which is well suited for analyzing variable fill levels. Variable material properties enable the calculation of the thermal expansion of the storage medium. This approach can be used, for example, to model stores with a floating lid. [ABSTRACT FROM AUTHOR]

One of the reasons for the success of the finite element method in Solid Mechanics, among other Applied Sciences, is its versatility to deal with bodies of arbitrary shape. In case the problem at hand is modeled by second‐order partial differential equations with Dirichlet conditions prescribed on a curvilinear boundary, method's isoparametric version for meshes consisting of curved triangles or tetrahedra has been mostly employed to recover the optimal approximation properties known to hold for polygonal or polyhedral domains and methods of order greater than one based on standard straight‐edged elements. However, besides algebraic and geometric inconveniences, the isoparametric technique is limited in scope, since its extension to degrees of freedom other than function values is not straightforward. In previous work the author introduced a simple alternative, which bypasses the above drawbacks without eroding qualitative approximation properties. Among other advantages, it can do without curved elements and is based only on polynomial Algebra. The purpose of this paper is two‐fold: On the one hand the mathematical foundations of this method are established, in the framework of a model Poisson problem solved with Lagrange elements; in particular optimal‐rate error estimates both in energy norm and in the mean‐square sense are demonstrated and a numerical comparison with the isoparametric technique is carried out. On the other hand this study is extended to Hermite elements with normal‐derivative degrees of freedom for solving the equation modeling the bending of clamped thin plates with a curvilinear edge. [ABSTRACT FROM AUTHOR]

The kernel gradient free (KGF) smoothed particle hydrodynamics (SPH) method is a modified finite particle method (FPM) which has higher order accuracy than the conventional SPH method. In KGF-SPH, no kernel gradient is required in the whole computation, and this leads to good flexibility in the selection of smoothing functions and it is also associated with a symmetric corrective matrix. When modeling viscous incompressible flows with SPH, FPM or KGF-SPH, it is usual to approximate the Laplacian term with nested approximation on velocity, and this may introduce numerical errors from the nested approximation, and also cause difficulties in dealing with boundary conditions. In this paper, an improved KGF-SPH method is presented for modeling viscous, incompressible fluid flows with a novel discrete scheme of Laplacian operator. The improved KGF-SPH method avoids nested approximation of first order derivatives, and keeps the good feature of 'kernel gradient free'. The two-dimensional incompressible fluid flow of shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, the original KGF-SPH and improved KGF-SPH. The numerical results show that the improved KGF-SPH with the novel discrete scheme of Laplacian operator are more accurate than SPH, and more stable than FPM and the original KGF-SPH. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT The subtitle of this article could be 'Modern engineer meets the masters of mathematical physics.' While there is no way to know how the masters would use our modern technology, we can educate ourselves in their way of thinking and adapt their mathematical methods to our computational capabilities. This article attempts to do just that and illustrates the findings with examples from dynamics, electro-magnetics, and quantum mechanics. It does this from the engineer's viewpoint and in keeping with the mission of the Computer Applications in Engineering Education publication. © 2011 Wiley Periodicals, Inc. Comput Appl Eng Educ 22:238-251, 2014; View this article online at ; DOI [ABSTRACT FROM AUTHOR]

ABSTRACT Aim Scaly tree ferns, Cyatheaceae, are a well-supported group of mostly tree-forming ferns found throughout the tropics, the subtropics and the south-temperate zone. Fossil evidence shows that the lineage originated in the Late Jurassic period. We reconstructed large-scale historical biogeographical patterns of Cyatheaceae and tested the hypothesis that some of the observed distribution patterns are in fact compatible, in time and space, with a vicariance scenario related to the break-up of Gondwana. Location Tropics, subtropics and south-temperate areas of the world. Methods The historical biogeography of Cyatheaceae was analysed in a maximum likelihood framework using Lagrange. The 78 ingroup taxa are representative of the geographical distribution of the entire family. The phylogenies that served as a basis for the analyses were obtained by Bayesian inference analyses of mainly previously published DNA sequence data using MrBayes. Lineage divergence dates were estimated in a Bayesian Markov chain Monte Carlo framework using beast. Results Cyatheaceae originated in the Late Jurassic in either South America or Australasia. Following a range expansion, the ancestral distribution of the marginate-scaled clade included both these areas, whereas Sphaeropteris is reconstructed as having its origin only in Australasia. Within the marginate-scaled clade, reconstructions of early divergences are hampered by the unresolved relationships among the Alsophila, Cyathea and Gymnosphaera lineages. Nevertheless, it is clear that the occurrence of the Cyathea and Sphaeropteris lineages in South America may be related to vicariance, whereas transoceanic dispersal needs to be inferred for the range shifts seen in Alsophila and Gymnosphaera. Main conclusions The evolutionary history of Cyatheaceae involves both Gondwanan vicariance scenarios as well as long-distance dispersal events. The number of transoceanic dispersals reconstructed for the family is rather few when compared with other fern lineages. We suggest that a causal relationship between reproductive mode (outcrossing) and dispersal limitations is the most plausible explanation for the pattern observed. [ABSTRACT FROM AUTHOR]

Aim To use recently published phylogenies of three major reef fish families to explore global patterns of species origin and dispersal over the past 65 million years. The key questions are: when and where did reef fishes arise, and how has this shaped current biodiversity patterns? Location Biogeographic reconstructions were performed on globally distributed reef fish lineages. Patterns of lineage origination and dispersal were explored in five major biogeographic regions: the East Pacific, the Atlantic, the Indian Ocean, the Indo- Australian Archipelago hotspot, and the Central Pacific. Methods A dispersal, extinction and cladogenesis ( DEC) model implemented in Lagrange was used to infer the most likely biogeographic scenarios at nodes on chronograms of three diverse reef fish families ( Labridae, Pomacentridae, Chaetodontidae). For the terminal branches ANOVA was used to compare patterns of origination on a regional and global scale. Patterns of origination and dispersal were examined within discrete time periods for the five biogeographic regions. Results Temporal examination of hypothetical ancestral lineages reveal a pattern of increasing isolation of the East Pacific and Atlantic regions from the Eocene, and the changing role of the Indo- Australian Archipelago from a location of accumulating ranges in the Palaeo/ Eocene, a centre of origination in the Miocene, to extensive expansion of lineages into adjacent regions from the Pliocene to Recent. Main conclusions While the East Pacific and Atlantic have a history of isolation, the Indo- Australian Archipelago has a history of connectivity. It has sequentially and then simultaneously acted as a centre of accumulation ( Palaeocene/ Eocene onwards), survival ( Eocene/ Oligocene onwards), origin ( Miocene onwards), and export ( Pliocene/Recent) for reef fishes. The model suggests that it was the proliferation and expansion of lineages in the Indo- Australian Archipelago (the Coral Triangle) during the Miocene that underpinned the current biodiversity in the Indian and Pacific Oceans. [ABSTRACT FROM AUTHOR]

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This study uses phylogenetic analysis of the Sclerodermatineae to reconstruct the evolution of ectomycorrhizal host associations in the group using divergence dating, ancestral range and ancestral state reconstructions., Supermatrix and supertree analysis were used to create the most inclusive phylogeny for the Sclerodermatineae. Divergence dates were estimated in BEAST. Lagrange was used to reconstruct ancestral ranges. B ayesT raits was used to reconstruct ectomycorrhizal host associations using extant host associations with data derived from literature sources., The supermatrix data set was combined with internal transcribed spacer (ITS) data sets for Astraeus, Calostoma, and Pisolithus to produce a 168 operational taxonomic unit (OTU) supertree. The ensuing analysis estimated that basal Sclerodermatineae originated in the late Cretaceous while major genera diversified near the mid Cenozoic. Asia and North America are the most probable ancestral areas for all Sclerodermatineae, and angiosperms, primarily rosids, are the most probable ancestral hosts., Evolution in the Sclerodermatineae follows the biogeographic history of disjunct plant communities associated with early Cenozoic mesophytic forests and a boreotropical history. Broad geographic distributions are observed in the most promiscuous Sclerodermatineae (those with broad host ranges), while those with relatively limited distribution have fewer documented ectomycorrhizal associations. This suggests that ectomycorrhizal generalists have greater dispersal capabilities than specialists. [ABSTRACT FROM AUTHOR]

We infer the biogeography and colonization history of a dispersal-limited terrestrial vertebrate, the Japanese four-lined ratsnake ( Elaphe quadrivirgata), to reveal the number of times mainland populations have invaded the Izu Archipelago of Japan, the mainland sources of these colonists, and the time-scale of colonization. We compare these results with those of past studies in an attempt to uncover general biogeographical patterns. Moreover, we briefly examine the significance of colonization history when evaluating the evolution of body size and melanism of the Izu Island E. quadrivirgata populations. The Izu Islands (Oshima, Toshima, Niijima, Shikine, Kozu, Tadanae and Mikura), a volcanic archipelago off the Pacific coast of central Japan. We obtained DNA sequences of the mitochondrial cytochrome b gene (1117 base pairs) from 373 individual snakes sampled from seven of the Izu Islands and 25 mainland localities. We employed partitioned Bayesian phylogenetic analyses assuming a relaxed molecular clock to estimate phylogenetic relationships among extant haplotypes and to give an explicit temporal scale to the timing of clade divergence, colonization history and tempo of body-size evolution. Moreover, we employed model-based biogeographical analysis to calculate the minimum number of times E. quadrivirgata colonized the Izu Islands. We found evidence that three separate regions of the Izu Archipelago have been colonized independently from mainland ancestors within the past 0.58-0.20 Ma. The Izu Peninsula plus Oshima and Mikura were both colonized independently from lineages inhabiting eastern mainland Japan. The Toshima, Niijima, Shikine, Kozu and Tadanae populations all derive from a single colonization from western mainland Japan. Oshima has been subject to three or possibly four colonizations. These results support the hypothesis that the extreme body-size disparity among island populations of this ratsnake evolved in situ. Moreover, the fact that the dwarf, melanistic population inhabiting Oshima descends from multiple mainland colonization events is evidence of an extremely strong natural selection pressure resulting in the rapid evolution of this unique morphology. These results contrast with theoretical predictions that natural selection pressures should play a decreased role on islands close to the mainland and/or subject to frequent or recent immigration. [ABSTRACT FROM AUTHOR]