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Geometric Constraints (geometric + constraint)
Selected AbstractsReX: a computer program for structural analysis using powder diffraction dataJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2009Mauro Bortolotti Multi-platform software has been developed for the analysis of powder diffraction data, with particular focus on structure solution. The program provides a Rietveld optimization engine, with the possibility of refining parameters describing both the sample and the instrument model. Geometric constraints such as rigid fragments and torsion angles can be defined for the atomic structure, to reduce the number of degrees of freedom of the model. An innovative hierarchical description of the asymmetric unit has been adopted, which allows, in principle, the definition of arbitrarily complex geometric relationships. Additionally, global optimization algorithms may be used in place of the standard nonlinear least squares, when particularly challenging problems are being faced. [source] Patterns in diversity of anurans along an elevational gradient in the Western Ghats, South IndiaJOURNAL OF BIOGEOGRAPHY, Issue 5 2007Rohit Naniwadekar Abstract Aim, To examine patterns in anuran species richness along an elevation gradient and identify factors that govern anuran species richness on a tropical elevational gradient. Location, Sampling for anurans was carried out in Kalakad Mundanthurai Tiger Reserve (KMTR) in the southern Western Ghats, India. Methods, Night-time sampling for anuran species richness was carried out from 20 November 2004 to 20 April 2005, during the north-east monsoon and dry seasons, using transects (50 × 2 m) and visual encounter surveys along the streams. The entire gradient was classified into thirteen 100-m elevation zones. Sampling at the alpha (single drainage basin) level was carried out in the Chinnapul River drainage basin (40,1260 m a.s.l.) and at the gamma (landscape) level in four drainage basins. Additionally, published records were used to arrive at an empirical species richness (S) for the entire landscape. Mid-Domain Null software was used to test for the possible influence of geometric constraints on anuran species at both the alpha and gamma levels. The influence of area under each elevation zone on empirical S was tested. The pattern in anuran species richness along the elevational gradient was investigated using: (1) species boundaries in each elevation zone and their habitat correlates, (2) abiotic factors as predictor variables, (3) mean snout vent lengths of anurans, and (4) correlation between the matrices of distance in the elevation zones based on microhabitat parameters and species composition. Cluster analysis on species presence,absence in the elevation zones was used to categorize the entire gradient into high, middle and low elevations. In these three elevation categories, pattern in composition of species was examined for endemism in Western Ghats,Sri Lanka biodiversity hotspot, uniqueness to an elevation zone, adaptations of adults and modes of breeding. Results, Species richness at the alpha level increased linearly with elevation, while at the gamma level there were three peaks. Maximum species richness was observed at the highest elevation (1200 m) at both the alpha and the gamma levels. The observed patterns differed significantly from mid-domain null predictions. The multi-modal pattern in species richness was a consequence of overlapping species range boundaries. Soil temperature was the best single measure in explaining the majority of variation in species richness at the alpha level (r2 = 0.846, P < 0.01). However, soil moisture was the best predictor when both the alpha and the gamma sites were pooled (r2 = 0.774, P < 0.01). Anuran body size decreased with an increase in elevation. The highest proportions of endemic and unique species were found at high elevations (> 700 m). The proportion of arboreal anurans increased from low to high elevation. Anurans exhibiting direct development were predominantly found at high elevations. Main conclusions, Geometric constraints did not influence anuran species richness along the elevational gradient. Overlapping range boundaries influenced species richness at the gamma level. Abiotic factors such as soil temperature and moisture influenced anuran species richness in the mountain range. The ,Massenerhebung effect' could be responsible for range restriction and endemism of anurans, differences in guilds and mode of reproduction. These findings highlight the importance of cloud forests for endemic anurans. [source] Mid-domain models as predictors of species diversity patterns: bathymetric diversity gradients in the deep seaOIKOS, Issue 3 2005Craig R. McClain Geometric constraints represent a class of null models that describe how species diversity may vary between hard boundaries that limit geographic distributions. Recent studies have suggested that a number of large scale biogeographic patterns of diversity (e.g. latitude, altitude, depth) may reflect boundary constraints. However, few studies have rigorously tested the degree to which mid-domain null predictions match empirical patterns or how sensitive the null models are to various assumptions. We explore how variation in the assumptions of these models alter null depth ranges and consequently bathymetric variation in diversity, and test the extent to which bathymetric patterns of species diversity in deep sea gastropods, bivalves, and polychaetes match null predictions based on geometric constraints. Range,size distributions and geographic patterns of diversity produced by these null models are sensitive to the relative position of the hard boundaries, the specific algorithms used to generate range sizes, and whether species are continuously or patchily distributed between range end points. How well empirical patterns support null expectations is highly dependent on these assumptions. Bathymetric patterns of species diversity for gastropods, bivalves and polychaetes differ substantially from null expectations suggesting that geometric constraints do not account for diversity,depth patterns in the deep sea benthos. [source] Keto-enol tautomerism in linear and cyclic ,-diketones: A DFT study in vacuo and in solutionINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 10 2008Giuliano Alagona Abstract DFT geometry optimizations have been performed at the B3LYP/6-31G* level in the gas phase and at the IEF-PCM/B3LYP/6-31G* level in tetrahydrofuran (THF) and aqueous solutions using scaled radii for the diketo and ketoenol forms of acetylacetone and cyclohexanedione. To evaluate basis set effects, starting from the aforementioned minima, the 6-311++G** optimized structures have been obtained. A number of complexes of both systems including one explicit water molecule have been considered up to the B3LYP/6-311++G** level, for cyclohexanedione taking into account the B3LYP/6-31G* basis set superposition errors as well. The diketo,ketoenol interconversion mechanisms have been investigated at the B3LYP/6-31G* level in vacuo. Interestingly, the geometric constraint due to the presence of the ring facilitates the description of the reaction mechanism in cyclohexanedione. Despite the very different flexibility of the two systems that in the case of acetylacetone prevents a straightforward interconversion of the diketo to the most stable of its ketoenol forms, both reactions occur with a very high barrier (about 62,63 kcal/mol), unaffected by continuum solvents, that decreases by 2.5,3.5 kcal/mol after the inclusion of thermal corrections. The barriers are almost halved, becoming ,31,35 kcal/mol, for the addition of a single water molecule according to various model reaction paths. Thermal corrections are limited (0.8,1.6 kcal/mol) for those adducts. The formation of a 1,1-diol, explored in the case of acetylacetone, might facilitate the obtainment of the most stable diketo conformation, featuring the carbonyl groups in distinct orientations. Inclusion of dispersion and basis set effects via the G2MP2 protocol does not alter the relative stability of both system tautomers. In contrast, the G2MP2 interconversion barriers for the isolated systems in vacuo are close to the B3LYP ones, whereas they turn out to be somewhat higher than the free energy-based B3LYP barriers in the presence of a catalytic water molecule. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Low-curvature image simplifiers: Global regularity of smooth solutions and Laplacian limiting schemesCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2004Andrea L. Bertozzi We consider a class of fourth-order nonlinear diffusion equations motivated by Tumblin and Turk's "low-curvature image simplifiers" for image denoising and segmentation. The PDE for the image intensity u is of the form where g(s) = k2/(k2 + s2) is a "curvature" threshold and , denotes a fidelity-matching parameter. We derive a priori bounds for ,u that allow us to prove global regularity of smooth solutions in one space dimension, and a geometric constraint for finite-time singularities from smooth initial data in two space dimensions. This is in sharp contrast to the second-order Perona-Malik equation (an ill-posed problem), on which the original LCIS method is modeled. The estimates also allow us to design a finite difference scheme that satisfies discrete versions of the estimates, in particular, a priori bounds on the smoothness estimator in both one and two space dimensions. We present computational results that show the effectiveness of such algorithms. Our results are connected to recent results for fourth-order lubrication-type equations and the design of positivity-preserving schemes for such equations. This connection also has relevance for other related fourth-order imaging equations. © 2004 Wiley Periodicals, Inc. [source] A grasp-based motion planning algorithm for character animationCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 3 2001Maciej Kalisiak The design of autonomous characters capable of planning their own motions continues to be a challenge for computer animation. We present a novel kinematic motion-planning algorithm for character animation which addresses some of the outstanding problems. The problem domain for our algorithm is as follows: given a constrained environment with designated handholds and footholds, plan a motion through this space towards some desired goal. Our algorithm is based on a stochastic search procedure which is guided by a combination of geometric constraints, posture heuristics, and distance-to-goal metrics. The method provides a single framework for the use of multiple modes of locomotion in planning motions through these constrained, unstructured environments. We illustrate our results with demonstrations of a human character using walking, swinging, climbing, and crawling in order to navigate through various obstacle courses. Copyright © 2001 John Wiley & Sons, Ltd. [source] CAD-Based Photogrammetry for Reverse Engineering of Industrial InstallationsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 4 2003Johan W. H. Tangelder For instance, in the case of a servicing plant, such a library contains descriptions of simple components such as straight pipes, elbows, and T-junctions. A new installation is constructed by selecting and connecting the appropriate components from the library. This article demonstrates that one can use the same approach for reverse engineering by photogrammetry. In our technique, the operator interprets images and selects the appropriate CAD component from a library. By aligning the edges of the component's wire frame to the visible edges in the images, we implicitly determine the position, orientation, and shape of the real component. For a fast object reconstruction the alignment process has been split in two parts. Initially, the operator approximately aligns a component to the images. In a second step a fitting algorithm is invoked for an automatic and precise alignment. Further improvement in the efficiency of the reconstruction is obtained by imposing geometric constraints on the CAD components of adjacent object parts. [source] An in vitro model system for cytoskeletal confinementCYTOSKELETON, Issue 10 2009Sarah Köster Abstract The motility, shape, and functionality of the cell depend sensitively on cytoskeletal mechanics which in turn is governed by the properties of filamentous proteins - mainly actin, microtubules, and intermediate filaments. These biopolymers are confined in the dense cytoplasm and therefore experience strong geometric constraints on their equilibrium thermal fluctuations. To obtain a better understanding of the influence of confinement on cytoskeletal filaments we study the thermal fluctuations of individual actin filaments in a microfluidic in vitro system by fluorescence microscopy and determine the persistence length of the filaments by analyzing the radial distribution function. A unique feature of this method is that we obtain the persistence length without detailed knowledge of the complete contour of the filament which makes the technique applicable to a broad range of biological polymers, including those with a persistence length smaller than the optical resolution. Cell Motil. Cytoskeleton 2009. © 2009 Wiley-Liss, Inc. [source] RangeModel: tools for exploring and assessing geometric constraints on species richness (the mid-domain effect) along transectsECOGRAPHY, Issue 1 2008Robert K. ColwellArticle first published online: 4 FEB 200 RangeModel is a computer application that offers animated demonstrations of the mechanism behind the mid-domain effect. The program also provides analytical tools for the assessment of geometric constraints in empirical datasets for one-dimensional domains (transects). The mid-domain effect (MDE) is the increasing overlap of species ranges towards the center of a shared, bounded domain due to geometric boundary constraints in relation to the distribution of range sizes, producing a peak or plateau of species richness towards the center of the domain. Domains may be spatial, temporal, or functional. RangeModel is a stand-alone, graphical-interface, freeware application for PC and Mac OS platforms. [source] Elevational patterns of frog species richness and endemic richness in the Hengduan Mountains, China: geometric constraints, area and climate effectsECOGRAPHY, Issue 6 2006Cuizhang Fu We studied frog biodiversity along an elevational gradient in the Hengduan Mountains, China. Endemic and non-endemic elevational diversity patterns were examined individually. Competing hypotheses were also tested for these patterns. Species richness of total frogs, endemics and non-endemics peaked at mid-elevations. The peak in endemic species richness was at higher elevations than the maxima of total species richness. Endemic species richness followed the mid-domain model predictions, and showed a nonlinear relationship with temperature. Water and energy were the most important variables in explaining elevational patterns of non-endemic species richness. A suite of interacting climatic and geometric factors best explained total species richness patterns along the elevational gradient. We suggest that the mid-domain effect was an important factor to explain elevational richness patterns, especially in regions with high endemism. [source] The river domain: why are there more species halfway up the river?ECOGRAPHY, Issue 2 2006Robert R. Dunn Biologists have long noted higher levels of species diversity in the longitudinal middle-courses of river systems and have proposed many explanations. As a new explanation for this widespread pattern, we suggest that many middle-course peaks in richness may be, at least in part, a consequence of geometric constraints on the location of species' ranges along river courses, considering river headwaters and mouths as boundaries for the taxa considered. We demonstrate this extension of the mid-domain effect (MDE) to river systems for riparian plants along two rivers in Sweden, where a previous study found a middle-course peak in richness of natural (non-ruderal) species. We compare patterns of empirical richness of these species to null model predictions of species richness along the two river systems and to spatial patterns for six environmental variables (channel width, substrate fineness, substrate heterogeneity, ice scour, bank height, and bank area). In addition, we examine the independent prediction of mid-domain effects models that species with large ranges, because the location of their ranges is more constrained, are more likely to produce a mid-domain peak in richness than are species with small ranges. Species richness patterns of riparian plants were best predicted by models including both null model predictions and environmental variables. When species were divided into large-ranged and small-ranged groups, the mid-domain effect was more prominent and the null model predictions were a better fit to the empirical richness patterns of large-ranged species than those of small-ranged species. Our results suggest that the peak in riparian plant species richness in the middle courses of the rivers studied can be explained by an underlying mid-domain effect (driven by geometric constraints on large-ranged species), together with environmental effects on richness patterns (particularly on small-ranged species). We suggest that the mid-domain effect may help to explain similar middle-course richness peaks along other rivers. [source] Patterns and causes of species richness: a general simulation model for macroecologyECOLOGY LETTERS, Issue 9 2009Nicholas J. Gotelli Abstract Understanding the causes of spatial variation in species richness is a major research focus of biogeography and macroecology. Gridded environmental data and species richness maps have been used in increasingly sophisticated curve-fitting analyses, but these methods have not brought us much closer to a mechanistic understanding of the patterns. During the past two decades, macroecologists have successfully addressed technical problems posed by spatial autocorrelation, intercorrelation of predictor variables and non-linearity. However, curve-fitting approaches are problematic because most theoretical models in macroecology do not make quantitative predictions, and they do not incorporate interactions among multiple forces. As an alternative, we propose a mechanistic modelling approach. We describe computer simulation models of the stochastic origin, spread, and extinction of species' geographical ranges in an environmentally heterogeneous, gridded domain and describe progress to date regarding their implementation. The output from such a general simulation model (GSM) would, at a minimum, consist of the simulated distribution of species ranges on a map, yielding the predicted number of species in each grid cell of the domain. In contrast to curve-fitting analysis, simulation modelling explicitly incorporates the processes believed to be affecting the geographical ranges of species and generates a number of quantitative predictions that can be compared to empirical patterns. We describe three of the ,control knobs' for a GSM that specify simple rules for dispersal, evolutionary origins and environmental gradients. Binary combinations of different knob settings correspond to eight distinct simulation models, five of which are already represented in the literature of macroecology. The output from such a GSM will include the predicted species richness per grid cell, the range size frequency distribution, the simulated phylogeny and simulated geographical ranges of the component species, all of which can be compared to empirical patterns. Challenges to the development of the GSM include the measurement of goodness of fit (GOF) between observed data and model predictions, as well as the estimation, optimization and interpretation of the model parameters. The simulation approach offers new insights into the origin and maintenance of species richness patterns, and may provide a common framework for investigating the effects of contemporary climate, evolutionary history and geometric constraints on global biodiversity gradients. With further development, the GSM has the potential to provide a conceptual bridge between macroecology and historical biogeography. [source] Ecological interpretations of the mid-domain effectECOLOGY LETTERS, Issue 10 2003John Arvid Grytnes Abstract The suggestion that spatial gradients in species richness are influenced by geometric constraints resulting in the mid-domain effect has been investigated by null models. The technical aspects of making such null models are well explored, but the implicit ecological assumptions behind these models are less explored. Four ecological models that all assume that species ranges are constrained by hard boundaries are made: evolutionary model, source-sink model, dynamic-environment model, and range-size model. These models give different predictions that make it possible to separate the models from each other, and from a model that assumes that hard boundaries are not important. [source] Rapid risk assessment using probability of fracture nomographsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 11 2009R. PENMETSA ABSTRACT Traditional risk-based design process involves designing the structure based on risk estimates obtained during several iterations of an optimization routine. This approach is computationally expensive for large-scale aircraft structural systems. Therefore, this paper introduces the concept of risk-based design plots that can be used for both structural sizing and risk assessment for fracture strength when maximum allowable crack length is available. In situations when crack length is defined as a probability distribution the presented approach can only be applied for various percentiles of crack lengths. These plots are obtained using normalized probability density models of load and material properties and are applicable for any arbitrary load and strength values. Risk-based design plots serve as a tool for failure probability assessment given geometry and applied load or they can determine geometric constraints to be used in sizing given allowable failure probability. This approach would transform a reliability-based optimization problem into a deterministic optimization problem with geometric constraints that implicitly incorporate risk into the design. In this paper, cracked flat plate and stiffened plate are used to demonstrate the methodology and its applicability. [source] Optimum design of stochastically excited non-linear dynamic systems without geometric constraintsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002M. M. Oblak Abstract This paper presents an efficient procedure for min,max dynamic response optimization of stochastically excited non-linear systems with multiple time-delayed inputs. This procedure employs a stochastic linearization technique to overcome system non-linearity and an auto-covariance analysis technique to represent the original stochastic mechanical model in a suitable form for optimization. Special attention is given to the sensitivity analysis, due to the complex nature of the problem. Therefore, exact expressions are obtained in a simple form for the evaluation of the required gradients, which greatly improve the stability and efficiency of the optimization algorithm. The numerical results and performance are presented by means of solving two min,max dynamic response optimization problems. Copyright © 2002 John Wiley & Sons, Ltd. [source] Improved implicit integrators for transient impact problems,geometric admissibility within the conserving frameworkINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002T. A. Laursen Abstract The value of energy and momentum conserving algorithms has been well established for the analysis of highly non-linear systems, including those characterized by the nonsmooth non-linearities of an impact event. This work proposes an improved integration scheme for frictionless dynamic contact, seeking to preserve the stability properties of exact energy and momentum conservation without the heretofore unavoidable compromise of violating geometric admissibility as established by the contact constraints. The physically motivated introduction of a discrete contact velocity provides an algorithmic framework that ensures exact conservation locally while remaining independent of the choice of constraint treatment, thus making full conservation equally possible in conjunction with a penalty regularization as with an exact Lagrange multiplier enforcement. The discrete velocity effects are incorporated as a post-convergence update to the system velocities, and thus have no direct effect on the non-linear solution of the displacement equilibrium equation. The result is a robust implicit algorithmic treatment of dynamic frictionless impact, appropriate for large deformations and fully conservative for a range of geometric constraints. Copyright © 2001 John Wiley & Sons, Ltd. [source] Optimization of tree-shaped flow distribution structures over a disc-shaped areaINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 8 2003S. Lorente Abstract In this paper, we review the fundamental problem of how to design a flow path with minimum overall resistance between one point (O) and many points situated equidistantly on a circle centred at O. This is a fundamental problem in energy engineering: the distribution of fluid, energy, electric power, etc., from points to surrounding areas. This problem is also fundamental in heat transfer and electronics cooling: how to bathe and cool with a single stream of coolant a disc-shaped area or volume that generates heat at every point. This paper outlines, first, a direct route to the construction of effective tree-shaped flow structures. The starting point is the optimization of the shape of each elemental area, such that the length of the flow path housed by the element is minimized. Proceeding towards larger and more complex structures,from elements to first constructs, second constructs, etc.,the paper develops tree-shaped flow structures between one point and a straight line, as an elemental problem, and a circle and its centre. We also consider the equivalent tree-shaped networks obtained by minimizing the pressure drop at every step of the construction, in accordance with geometric constraints. The construction method is applied to a fluid flow configuration with laminar fully developed flow. It is shown that there is little difference between the two methods. The minimal-length structures perform very close to the fully optimized designs. These results emphasize the robustness of optimized tree-shaped flows. Copyright © 2003 John Wiley & Sons, Ltd. [source] DFT study of core-modified porphyrin isomersINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2007Y. Soujanya Abstract B3LYP/6-311+G** calculations were performed systematically on 1,2 (syn) and 1,3 (anti) tautomeric forms of oxa- and thia- core-modified porphyrin isomers, which resulted in a total of 86 structures. The structural and energetic variation in all the isomers were analyzed. In corrphycene, hemiporphycene and porphycene the Z forms are more stable compared to the corresponding E forms in both the anti and syn oxa- and thiaporphyrin isomers. In contrast, in the syn isomeric forms of [3.0.1.0], [3.1.0.0] and [4.0.0.0] oxaporphyrins and in both syn and anti forms of thiaporphyrin isomers, Z forms are less stable. The HOMO and LUMO values are both negative and varied in a narrow zone, indicating no dramatic effect on the position of heteroatom substitution on the redox properties. The effect of geometric constraints due to the alteration of meso-bridge length and the hetero atom disposition in the porphyrin core on the relative stabilities of the isomers is analyzed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Patterns in diversity of anurans along an elevational gradient in the Western Ghats, South IndiaJOURNAL OF BIOGEOGRAPHY, Issue 5 2007Rohit Naniwadekar Abstract Aim, To examine patterns in anuran species richness along an elevation gradient and identify factors that govern anuran species richness on a tropical elevational gradient. Location, Sampling for anurans was carried out in Kalakad Mundanthurai Tiger Reserve (KMTR) in the southern Western Ghats, India. Methods, Night-time sampling for anuran species richness was carried out from 20 November 2004 to 20 April 2005, during the north-east monsoon and dry seasons, using transects (50 × 2 m) and visual encounter surveys along the streams. The entire gradient was classified into thirteen 100-m elevation zones. Sampling at the alpha (single drainage basin) level was carried out in the Chinnapul River drainage basin (40,1260 m a.s.l.) and at the gamma (landscape) level in four drainage basins. Additionally, published records were used to arrive at an empirical species richness (S) for the entire landscape. Mid-Domain Null software was used to test for the possible influence of geometric constraints on anuran species at both the alpha and gamma levels. The influence of area under each elevation zone on empirical S was tested. The pattern in anuran species richness along the elevational gradient was investigated using: (1) species boundaries in each elevation zone and their habitat correlates, (2) abiotic factors as predictor variables, (3) mean snout vent lengths of anurans, and (4) correlation between the matrices of distance in the elevation zones based on microhabitat parameters and species composition. Cluster analysis on species presence,absence in the elevation zones was used to categorize the entire gradient into high, middle and low elevations. In these three elevation categories, pattern in composition of species was examined for endemism in Western Ghats,Sri Lanka biodiversity hotspot, uniqueness to an elevation zone, adaptations of adults and modes of breeding. Results, Species richness at the alpha level increased linearly with elevation, while at the gamma level there were three peaks. Maximum species richness was observed at the highest elevation (1200 m) at both the alpha and the gamma levels. The observed patterns differed significantly from mid-domain null predictions. The multi-modal pattern in species richness was a consequence of overlapping species range boundaries. Soil temperature was the best single measure in explaining the majority of variation in species richness at the alpha level (r2 = 0.846, P < 0.01). However, soil moisture was the best predictor when both the alpha and the gamma sites were pooled (r2 = 0.774, P < 0.01). Anuran body size decreased with an increase in elevation. The highest proportions of endemic and unique species were found at high elevations (> 700 m). The proportion of arboreal anurans increased from low to high elevation. Anurans exhibiting direct development were predominantly found at high elevations. Main conclusions, Geometric constraints did not influence anuran species richness along the elevational gradient. Overlapping range boundaries influenced species richness at the gamma level. Abiotic factors such as soil temperature and moisture influenced anuran species richness in the mountain range. The ,Massenerhebung effect' could be responsible for range restriction and endemism of anurans, differences in guilds and mode of reproduction. These findings highlight the importance of cloud forests for endemic anurans. [source] Mid-domain models as predictors of species diversity patterns: bathymetric diversity gradients in the deep seaOIKOS, Issue 3 2005Craig R. McClain Geometric constraints represent a class of null models that describe how species diversity may vary between hard boundaries that limit geographic distributions. Recent studies have suggested that a number of large scale biogeographic patterns of diversity (e.g. latitude, altitude, depth) may reflect boundary constraints. However, few studies have rigorously tested the degree to which mid-domain null predictions match empirical patterns or how sensitive the null models are to various assumptions. We explore how variation in the assumptions of these models alter null depth ranges and consequently bathymetric variation in diversity, and test the extent to which bathymetric patterns of species diversity in deep sea gastropods, bivalves, and polychaetes match null predictions based on geometric constraints. Range,size distributions and geographic patterns of diversity produced by these null models are sensitive to the relative position of the hard boundaries, the specific algorithms used to generate range sizes, and whether species are continuously or patchily distributed between range end points. How well empirical patterns support null expectations is highly dependent on these assumptions. Bathymetric patterns of species diversity for gastropods, bivalves and polychaetes differ substantially from null expectations suggesting that geometric constraints do not account for diversity,depth patterns in the deep sea benthos. [source] | ||||||||||||||||