Independent Data Points Research Articles

G_wham—A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates

The Weighted Histogram Analysis Method (WHAM) is a standard technique used to compute potentials of mean force (PMFs) from a set of umbrella sampling simulations. Here, we present a new WHAM implementation, termed g_wham, which is distributed freely with the GROMACS molecular simulation suite. g_wham estimates statistical errors using the technique of bootstrap analysis. Three bootstrap methods are supported: (i) bootstrapping new trajectories based on the umbrella histograms, (ii) bootstrapping of complete histograms, and (iii) Bayesian bootstrapping of complete histograms, that is, bootstrapping via the assignment of random weights to the histograms. Because methods ii and iii consider only complete histograms as independent data points, these methods do not require the accurate calculation of autocorrelation times. We demonstrate that, given sufficient sampling, bootstrapping new trajectories allows for an accurate error estimate. In the presence of long autocorrelations, however, (Bayesian) bootstrapping of complete histograms yields a more reliable error estimate, whereas bootstrapping of new trajectories may underestimate the error. In addition, we emphasize that the incorporation of autocorrelations into WHAM reduces the bias from limited sampling, in particular, when computing periodic PMFs in inhomogeneous systems such as solvated lipid membranes or protein channels.

A new approach to the 2-variable Subnormal Completion Problem

We study the Subnormal Completion Problem (SCP) for 2-variable weighted shifts. We use tools and techniques from the theory of truncated moment problems to give a general strategy to solve SCP. We then show that when all quadratic moments are known (equivalently, when the initial segment of weights consists of five independent data points), the natural necessary conditions for the existence of a subnormal completion are also sufficient. To calculate explicitly the associated Berger measure, we compute the algebraic variety of the associated truncated moment problem; it turns out that this algebraic variety is precisely the support of the Berger measure of the subnormal completion.

Optic Foramen Morphology and Activity Pattern in Birds

The optic nerve is the sole output of visual information from the ganglion cell layer of the retina to the brain in vertebrates. The size of the optic nerve is predicted to be closely associated with activity pattern, and, in many birds, the size of the optic foramen approximates the size of the optic nerve. Specifically, nocturnal species should have relatively smaller optic foramina than diurnal species because of differences in retinal pooling between activity patterns. If optic foramen morphology varies predictably with activity pattern in birds, this variable may be useful for interpreting activity pattern for birds that do not have soft tissue available for study, specifically for fossils. Across 177 families (from 27 orders), we describe four different optic foramen morphologies, only one of which corresponds well with the size of the optic nerve and is therefore appropriate for activity pattern analyses. Here, we test our hypothesis that nocturnal species will have relatively smaller optic foramina than diurnal species, across all species that we measured that have a discrete optic foramen. Regression analyses using species as independent data points and using comparative methods yielded significant differences in optic foramen size between nocturnal and diurnal species relative to three variables: head length, orbit depth, and sclerotic ring inner diameter. Nocturnal species consistently exhibit significantly smaller relative optic foramen diameters than diurnal species. Our results indicate that optic foramen diameter, in combination with either the sclerotic ring or the orbit diameter, can be used to predict activity pattern.

The Initial Freezing Temperature of Foods at High Pressure

The Pure water (P,T)-phase diagram is known in the form of empirical equations or tables from nearly a century as a result of Bridgman's work. However, few data are available on other aqueous systems probably due to the difficulty of high-pressure measurements. As an alternative, six approaches are presented here to obtain the food phase diagrams in the range of pressure 0.1–210 MPa. Both empirical and theoretical methods are described including the use of an artificial neural network (ANN). Experimental freezing points obtained at the laboratory of the authors and from literature are statistically compared to the calculated ones. About 400 independent freezing data points of aqueous solutions, gels, and foods are analysed. A polynomial equation is the most accurate and simple method to describe the entire melting curve. The ANN is the most versatile model, as only one model allows the calculation of the initial freezing point of all the aqueous systems considered. Robinson and Stokes' equation is successfully extended to the high pressures domain with an average prediction error of 0.4°C. The choice of one approach over the others depends mainly on the availability of experimental data, the accuracy required and the intended use for the calculated data.

MULTILOCUS PHYLOGEOGRAPHY OF A HOLARCTIC DUCK: COLONIZATION OF NORTH AMERICA FROM EURASIA BY GADWALL (ANAS STREPERA)

More than 100 species of birds have Holarctic distributions extending across Eurasia and North America, and many of them likely achieved these distributions by recently colonizing one continent from the other. Mitochondrial DNA (mtDNA) and five nuclear introns were sequenced to test the direction and timing of colonization for a Holarctic duck, the gadwall (Anas strepera). Three lines of evidence suggest gadwalls colonized North America from Eurasia. First, New World (NW) gadwalls had fewer alleles at every locus and 61% of the allelic richness found in Old World (OW) gadwalls. Second, NW gadwalls had lower mtDNA allelic richness than other NW ducks. Third, coalescent analysis suggested that less than 5% of the ancestral population contributed to NW gadwalls at the time of divergence. Gadwalls likely colonized North America during the Late Pleistocene (approximately 81,000 years ago), but the confidence interval on that estimate was large (8500-450,000 years ago). Intercontinental gene flow and selection also likely contributed to genetic diversity in gadwalls. This study illustrates the use of multiple loci and coalescent analyses for critically testing a priori hypotheses regarding dispersal and colonization and provides an independent datapoint supporting an OW to NW bias in the direction of colonization.

Phylogenetic analysis of the scaling of wet and dry biological fibrillar adhesives

Fibrillar, or "hairy," adhesives have evolved multiple times independently within arthropods and reptiles. These adhesives exhibit highly desirable properties for dynamic attachment, including orientation dependence, wear resistance, and self-cleaning. Our understanding of how these properties are related to their fibrillar structure is limited, although theoretical models from the literature have generated useful hypotheses. We survey the morphology of 81 species with fibrillar adhesives to test the hypothesis that packing density of contact elements should increase with body size, whereas the size of the contact elements should decrease. We test this hypothesis in a phylogenetic context to avoid treating historically related species as statistically independent data points. We find that fiber morphology is better predicted by evolutionary history and adhesive mechanism than by body size. As we attempt to identify which morphological parameters are most responsible for the performance of fibrillar adhesives, it will be important to take advantage of the natural variation in morphology and the potentially suboptimal outcomes it encompasses, rather than assuming evolution to be an inherently optimizing process.

Experience-dependence of neural responses to social versus isolate conspecific songs in the forebrain of female Zebra Finches

Early exposure to conspecific song influences the ontogeny of behavioural discrimination between social and isolate songs of males in non-singing female Zebra Finches (Taeniopygia guttata). We explored the potential neural basis of this behavioural plasticity in song preference of female Zebra Finches, reared by both parents in a conspecific colony (controls) or by mothers only in sound-attenuation chambers (father-absent treatment). Comparing extracellular recordings of auditory neurons in the primary auditory forebrain area Field L showed that single units consistently responded with greater response strengths to male songs, over the synthetic stimuli of both frequency-matched pure tone assemblages and reversed conspecific songs, irrespective of females’ ontogenetic treatment. Contrary to expectations, consistent response selectivity for social versus isolate Zebra Finch songs was detected from neurons only in father-absent females and not in control subjects. These results based on statistical analyses of data from single neurons were confirmed by a contingency analysis that used female subjects as independent datapoints. Our findings suggest that differences in the early social and/or auditory experience affect the neurophysiological responses to specific classes of male songs in auditory forebrain neurons of female Zebra Finches. Contrary to expectations, patterns of neuronal discrimination in the Field L complex do not parallel patterns of experience-dependent behavioural discrimination between social and isolate conspecific songs.

Beyond Gaussian averages: redirecting international business and management research toward extreme events and power laws

Practicing managers live in a world of ‘extremes’, but international business and management research is based on Gaussian statistics that rule out such extremes. On occasion, positive feedback processes among interactive data points cause extreme events characterized by power laws. They seem ubiquitous; we list 80 kinds of them – half each among natural and social phenomena. We use imposed tension and Per Bak's ‘self-organized criticality’ to argue that Pareto-based science and statistics (based on interdependence, positive feedback, scalability, (nearly) infinite variance, and emphasizing extremes) should parallel the traditional dominance of Gaussian statistics (based on independent data points, finite variance and emphasizing averages). We question quantitative journal publications depending on Gaussian statistics. The cost is inaccurate science and irrelevance to practitioners. In conclusion, no statistical findings should be accepted into business studies if they gain significance via some assumption device by which extreme events and (nearly) infinite variance are ignored. Accordingly, we suggest redirecting international business studies, and management research in general.

The Frequency of Large‐Radius Hot and Very Hot Jupiters in ω Centauri

We present the results of a deep, wide-field search for transiting hot Jupiter (HJ) planets in the globular cluster ? Centauri. As a result of a 25 night observing run with the ANU 40 inch (1 m) telescope at Siding Spring Observatory, a total of 109,726 stellar time series composed of 787 independent data points were produced with differential photometry in a 52' ? 52' (0.75 deg2) field centered on the cluster core, but extending well beyond. Taking into account the size of transit signals as a function of stellar radius, 45,406 stars have suitable photometric accuracy (?0.045 mag to -->V = 19.5) to search for transits. Of this sample, 31,000 stars are expected to be main-sequence cluster members. All stars, both cluster and foreground, were subjected to a rigorous search for transit signatures; none were found. Extensive Monte Carlo simulations based on our actual data set allow us to determine the sensitivity of our survey to planets with radii ~1.5 RJup and thus place statistical upper limits on their occurrence frequency F. Smaller planets are undetectable in our data. At 95% confidence, the frequency of very hot Jupiters (VHJs) with periods P satisfying -->1 day FVHJ 1 day . Our limits on large, short-period planets are comparable to those recently reported for other Galactic fields, despite being derived with less telescope time.

Wing‐bone length allometry in birds

A comparative analysis using both independent contrasts (CAIC) and a species level analysis was used to investigate the allometric scaling of avian wing‐bone lengths. Total arm (ta=humerus+ulna+manus) scaled with positive allometry as body mass (M)0.37–0.39. Similarly, and in accordance with previous studies, wing‐span (b) was positively allometric, but CAIC suggested a lower allometric exponent (M0.35) than found using species as independent data points (M0.39). Contrary to previous studies, individual wing‐bones appear to scale with similar exponents against M and scale isometrically with ta. In addition to a general trend for larger birds to have longer wings, wing‐bones and ta, their ta was a larger proportion of their b. A detailed study of primary feather length and elbow joint angle across a wide range of bird species and bird size, however, is required before a conclusive explanation for this increase in ta relative to b in larger birds can be established. Scaling equations are presented that can be used to predict M, ta and b from individual wing‐bone lengths, which may be of use to palaeontologists wishing to reconstruct whole animals from single bones.

REEXAMINING THE RELATIONSHIP BETWEEN BODY SIZE AND TONAL SIGNALS FREQUENCY IN WHALES: A COMPARATIVE APPROACH USING A NOVEL PHYLOGENY

AbstractA negative relationship between cetacean body size and tonal sound minimum and maximum frequencies has been demonstrated in several studies using standard statistical approaches where species are considered independent data points. Such studies, however, fail to account for known dependencies among related species—shared similarity due to common ancestry. Here we test these hypotheses by generating the most complete species level cetacean phylogeny to date, which we then use to reconstruct the evolutionary history of body size and standard tonal sounds parameters (minimum, maximum, and center frequency). Our results show that when phylogenetic relationships are considered the correlation between body size (length or mass) and minimum frequency is corroborated with approximately 27% of the variation in tonal sound frequency being explained by body size compared to 86% to 93% explained when phylogenetic relationships are not considered. Central frequency also correlates with body size in toothed whales, but for other tonal sound frequency parameters, including maximum frequency, this hypothesized correlation disappears. Therefore, constraints imposed by body size seem to have played a role in the evolution of minimum frequency but alternative hypotheses are required to explain variation in maximum frequency.

Beyond Gaussian Averages: Redirecting Management Research Toward Extreme Events and Power Laws

Practicing managers live in a world of ‘extremes’ but management research is based on Gaussian statistics that rule out those extremes. On occasion, deviation amplifying mutual causal processes among interdependent data points cause extreme events characterized by power laws. They seem ubiquitous; we lis t80 kinds of them – half each among natural and social phenomena. We draw a ‘line in the sand’ between Gaussian (based on independent data points, finite variance and emphasizing averages) and Paretian statistics(based on interdependence, positive feedback, infinite variance, and emphasizing extremes). Quantitative journal publication depends almost entirely on Gaussian statistics. We draw on complexity and earthquake sciences to propose redirecting Management Studies. No statistical findings should be accepted into Management Studies if they gain significance via some assumption-device by which extreme events and infinite variance are ignored. The cost is inaccurate science and irrelevance to practitioners.

The Iron-Sulfur Cluster-free Hydrogenase (Hmd) Is a Metalloenzyme with a Novel Iron Binding Motif

The iron-sulfur cluster-free hydrogenase (Hmd) from methanogenic archaea harbors an iron-containing cofactor of yet unknown structure. X-ray absorption spectroscopy of the active, as isolated enzyme from Methanothermobacter marburgensis (mHmd) and of the active, reconstituted enzyme from Methanocaldococcus jannaschii (jHmd) revealed the presence of mononuclear iron with two CO, one sulfur and one or two N/O in coordination distance. In jHmd, the single sulfur ligand is most probably provided by Cys176, as deduced from a comparison of the activity and of the x-ray absorption and Mössbauer spectra of the enzyme mutated in any of the three conserved cysteines. In the isolated Hmd cofactor, two CO, one sulfur, and two nitrogen/oxygen atoms coordinate the iron, the sulfur ligand being most probably provided by mercaptoethanol, which is absolutely required for the extraction of the iron-containing cofactor from the holoenzyme and for the stabilization of the extracted cofactor. In active mHmd holoenzyme, the number of iron ligands increased by one when one of the Hmd inhibitors (CO or KCN) were present, indicating that in active Hmd, the iron contains an open coordination site, which is proposed to be the site of H2 interaction.

Derivation of statistical properties of wave-induced offshore structural response by principal component technique

According to linear random wave theory, water particle kinematics at different nodes of an offshore structure form a set of correlated jointly Gaussian random variables. Thus, using principal component analysis, all the foregoing kinematics can be expressed as linear combinations of a few independent Gaussian random variables. This technique can be used to generate statistically independent hydrodynamic load and response values, as opposed to time simulation technique that leads to correlated response values. The sampling variability of the statistics generated from a set of independent data points is considerably smaller than that of a set (of the same size) of correlated values. Therefore, a much smaller number of simulated data points are necessary for accurate prediction of the statistical properties of response. Furthermore, simulating N data points by principal component technique (PCT) has proved to be at least two times faster than simulating the same number of data points by the time simulation technique (TST). As a result, PCT is considerably more efficient (about 25 times) than TST. The forgoing conclusions have been verified by applying both techniques to two test structures under different environmental conditions.

In the deep end: pooling data and other statistical challenges of zoo and aquarium research

Zoo and aquarium research presents many logistic challenges, including extremely small sample sizes and lack of independent data points, which lend themselves to the misuse of statistics. Pseudoreplication and pooling of data are two statistical problems common in research in the biological sciences. Although the prevalence of these and other statistical miscues have been documented in other fields, little attention has been paid to the practice of statistics in the field of zoo biology. A review of articles published in the journal Zoo Biology between 1999–2004 showed that approximately 40% of the 146 articles utilizing inferential statistics during that span contained some evidence of pseudoreplication or pooling of data. Nearly 75% of studies did not provide degrees of freedom for all statistics and approximately 20% did not report test statistic values. Although the level of pseudoreplication in this dataset is not outside the levels found in other branches of biology, it does indicate the challenges of dealing with appropriate data analysis in zoo and aquarium studies. The standardization of statistical techniques to deal with the methodological challenges of zoo and aquarium populations can help advance zoo research by guiding the production and analysis of applied studies. This study recommends techniques for dealing with these issues, including complete disclosure of data manipulation and reporting of statistical values, checking and control for institutional effects in statistical models, and avoidance of pseudoreplicated observations. Additionally, zoo biologists should seek out other models such as hierarchical or factorial models or randomization tests to supplement their repertoire of t-tests and ANOVA. These suggestions are intended to stimulate conversation and examination of the current use of statistics in zoo biology in an effort to develop more consistent requirements for publication. Zoo Biol 0:1–14, 2006. © 2006 Wiley-Liss, Inc.

Metabolic correlates of leg length in breeding arctic shorebirds: the cost of getting high

AbstractAim We test the hypothesis that tarsus length in all shorebirds breeding in the Canadian arctic shows an evolutionary response to average metabolic stress encountered across the breeding range, such that birds nesting in metabolically stressful environments have relatively shorter legs. Longer‐legged birds living in colder environments will experience greater metabolic costs because their torsos are elevated farther away from the ground's wind‐dampening boundary layer.Methods We use weather data (temperature, wind speed, global solar radiation) from 27 arctic weather stations measured over 37 years, and a previously published model of heat transfer, to characterize the metabolic harshness over the breeding season of the ranges of each of the 17 shorebirds of the family Charadriidae nesting in the Canadian arctic.Results After controlling for the lengths of two other body extremities (wing and bill), there was a significant negative relationship between tarsus length and mean metabolic harshness. This result was obtained whether species were treated as independent data points, or in a comparative analysis using standardized independent contrasts.Main conclusions We support a unique extension of Allen's rule: body‐supporting appendages of homeotherms may be shorter in colder environments so as to take advantage of a boundary layer effect, thereby reducing metabolic costs.

Horse dung germinable seed content in relation to plant species abundance, diet composition and seed characteristics

Abstract The abundance and species richness of the germinable seed content of dung of free ranging horses was quantified and related to seven variables: plant species abundance in the field (cover) and in the horse diet, seed sizes (length, width and mass), seed longevity index and seed shape which was expressed as variance in seed dimensions. Analyses were run both across species, with species treated as independent data points, and for 40 ‘phylogenetically independent contrasts’. From 56 dung samples, 2.5 l each, 53,493 seedlings emerged, representing 106 different plant species, i.e. 21.4% of all species recorded in the established vegetation of the study sites. A majority of plant species (50%) was only found in less than 10% of the dung samples while 68% of the germinating species emerged with on average less than 1 seedling per dung sample. Overall dung seed density ranged on average between 280.4 and 525.2 seedlings per litre. Mean species richness of dung samples varied between 19 and 34 plant species. Urtica dioica , Veronica spp. and several graminoid species were among the most abundant and frequently out of dung emerging plant taxa. Dung seed content was positively correlated with plant species abundance in the field and in the diet. Relative dung seed density (i.e. per unit cover) was positively correlated with seed longevity index and negatively correlated with all three seed size variables. There was no significant relationship with seed shape. These relationships were not affected by phylogenetic constraints. As far as the possible role of endozoochory for conservation of plant diversity in grassland is concerned, the results emphasise the importance of large herbivores as potentially strong seed dispersal vectors.

Reply [to “Cosmic rays, carbon dioxide, and climate”

In our analysis [Rahmstorf et al., 2004], we arrived at two main conclusions: the data of Shaviv and Veizer [2003] do not show a significant correlation of cosmic ray flux (CRF) and climate, and the authors' estimate of climate sensitivity to CO2 based on a simple regression analysis is questionable. After careful consideration of Shaviv and Veizer's comment, we want to uphold and reaffirm these conclusions.Concerning the question of correlation, we pointed out that a correlation arose only after several adjustments to the data, including shifting one of the four CRF peaks and stretching the time scale. To calculate statistical significance, we first need to compute the number of independent data points in the CRF and temperature curves being correlated, accounting for their autocorrelation. A standard estimate [Quenouille, 1952] of the number of effective data points is urn:x-wiley:00963941:media:eost14930:eost14930-math-0001 where N is the total number of data points and r1, r2 are the autocorrelations of the two series. For the curves of Shaviv and Veizer [2003], the result is NEFF = 4.8. This is consistent with the fact that these are smooth curves with four humps, and with the fact that for CRF the position of the four peaks is determined by four spiral arm crossings or four meteorite clusters, respectively; that is, by four independent data points. The number of points that enter the calculation of statistical significance of a linear correlation is (NEFF− 2), since any curves based on only two points show perfect correlation; at least three independent points are needed for a meaningful result.

Origin of Madagascar's extant fauna: A perspective from amphibians, reptiles and other non‐flying vertebrates

The origins of the highly endemic and partly very diverse fauna and flora of Madagascar were longtime unsolved and are still strongly disputed, although dispersalists are recently prevailing over advocates of Gondwanan vicariance. Madagascar has been separated from other continents and continental fragments since the Mesozoic, and the assumption of vicariance origins requires very old ages of the lineages involved. Herein I review the recent progress of knowledge on the molecular phylogenetic relationships of the amphibians, reptiles, and other non‐flying vertebrates of Madagascar. Of 17 Malagasy clades for which relationships seem to be resolved with sufficient and unanimous support, the largest proportion have their sister‐group in Africa, and very few show a general area cladogram consistent with the succession of events in the fragmentation of the supercontinent Gondwana. A survey of pairwise sequence divergences between 25 Malagasy lineages and their non‐Malagasy relatives in the 16S and 12S rRNA genes resulted in values that in most cases were distinctly below the saturation plateaus of these genes. Multiple calibrations based on 34 largely independent data points indicate that such saturation would be strongly expected in the case of ages corresponding to the geographical isolation of Madagascar in the Jurassic and Cretaceous. A Cenozoic age for most Malagasy lineages is therefore most likely. Analysis of phylogenetic patterns of some taxa provides indications for a scenario in which the ancestors of the Malagasy clades first arrived by transmarine dispersal from Africa at the Malagasy west coast, and in a second step a subset of them underwent species‐rich radiations into the rainforests.

PROTOCOL: The Effectiveness of Neighbourhood Watch

PROTOCOL: The Effectiveness of Neighbourhood Watch