The Error Rate of Tests for Regression Coincidence and Parallelism Under Unknown Multiplicative Heteroscedasticity

The usual F test of regression coincidence, which is appropriate under a homoscedastic model, is examined under a multiplicatively heteroscedastic model. The departure of the test from its nominal level is slight when the sample of explanatory variables is symmetric, but may be substantially inflated when the sample has positive skew. Conversely, the nominal level may be slightly depressed when the sample has negative skew. The size of the perturbation from the nominal level depends on the degree of heteroscedasticity, however its effect is more pronounced with positively skewed samples. Similar trends are evident for the usual F test of regression parallelism. There is no apparent pattern to the discrepancy of the level of the test with regard to the data which would permit empirical researchers to adjust their results.     

Prey-Dependent Mortality Rate: A Critical Parameter in Microbial Models

Protozoa are key components of a wide range of ecosystems, but ecological models that incorporate these microbes often suffer from poor parameterisation, specifically of top-level predator loss rates. We (1) suggest that top-level predator mortality is prey-dependent, (2) provide a novel approach to assess this response, and (3) illustrate the ecological relevance of these findings. Ciliates, Paramecium caudatum (prey) and Didinium nasutum (predator), were used to evaluate predator mortality at varying prey levels. To assess mortality, multiple (>100) predators were individually examined (in 2-ml wells), daily (for 3 days), between 0 and 120 preys ml⁻¹. Data were used to determine non-linear mortality and growth responses over a range of prey abundances. The responses, plus literature data were then used to parameterise a predator–prey model, based on the Rosenzweig–MacArthur structure. The model assessed the impact of variable and three levels of constant (high, average and low) mortality rates on P. caudatum–D. nasutum population dynamics. Our method to determine variable mortality rate revealed a strong concave decline in mortality with increasing prey abundance. The model indicated: (1) high- and low-constant mortality rates yielded dynamics that deviate substantially from those obtained from a variable rate; (2) average mortality rate superficially produced dynamics similar to the variable rate, but there were differences in the period of predator–prey cycles, and the lowest abundance of prey and predators (by ~2 orders of magnitude). The differences between incorporating variable and constant mortality rate indicate that including a variable rate could substantially improve microbial-based ecological models.     

Estimating Litter Decomposition Rate in Single-Pool Models Using Nonlinear Beta Regression

Litter decomposition rate (k) is typically estimated from proportional litter mass loss data using models that assume constant, normally distributed errors. However, such data often show non-normal errors with reduced variance near bounds (0 or 1), potentially leading to biased k estimates. We compared the performance of nonlinear regression using the beta distribution, which is well-suited to bounded data and this type of heteroscedasticity, to standard nonlinear regression (normal errors) on simulated and real litter decomposition data. Although the beta model often provided better fits to the simulated data (based on the corrected Akaike Information Criterion, AIC_c), standard nonlinear regression was robust to violation of homoscedasticity and gave equally or more accurate k estimates as nonlinear beta regression. Our simulation results also suggest that k estimates will be most accurate when study length captures mid to late stage decomposition (50–80% mass loss) and the number of measurements through time is ≥5. Regression method and data transformation choices had the smallest impact on k estimates during mid and late stage decomposition. Estimates of k were more variable among methods and generally less accurate during early and end stage decomposition. With real data, neither model was predominately best; in most cases the models were indistinguishable based on AIC_c, and gave similar k estimates. However, when decomposition rates were high, normal and beta model k estimates often diverged substantially. Therefore, we recommend a pragmatic approach where both models are compared and the best is selected for a given data set. Alternatively, both models may be used via model averaging to develop weighted parameter estimates. We provide code to perform nonlinear beta regression with freely available software.     

Pseudo-isotherms for the sorption of cadmium ion onto tree fern

The kinetics of cadmium sorption on to tree fern has been investigated based on the assumption of a pseudo-second order rate law. The batch sorption model has been applied to predict the rate constant of sorption and the equilibrium capacity with the effect of initial cadmium concentration. The experimental results have been analysed by pseudo-Langmuir, pseudo-Freundlich and pseudo-Redlich–Peterson isotherms based on pseudo-second order kinetic expression constant. Both pseudo-Langmuir and pseudo-Redlich–Peterson isotherms were found to represent the measured sorption data well. According to the evaluation using the pseudo-Langmuir equation, the monolayer sorption capacity was obtained to he 16.3 mg/g. In addition, χ² analysis was also used to determine the most suitable model. Pseudo-Langmuir and pseudo-Redlich–Peterson were also the best models for the experiment data from χ² analysis.     

Normal frailty probit model for clustered interval‐censored failure time data

Clustered interval‐censored data commonly arise in many studies of biomedical research where the failure time of interest is subject to interval‐censoring and subjects are correlated for being in the same cluster. A new semiparametric frailty probit regression model is proposed to study covariate effects on the failure time by accounting for the intracluster dependence. Under the proposed normal frailty probit model, the marginal distribution of the failure time is a semiparametric probit model, the regression parameters can be interpreted as both the conditional covariate effects given frailty and the marginal covariate effects up to a multiplicative constant, and the intracluster association can be summarized by two nonparametric measures in simple and explicit form. A fully Bayesian estimation approach is developed based on the use of monotone splines for the unknown nondecreasing function and a data augmentation using normal latent variables. The proposed Gibbs sampler is straightforward to implement since all unknowns have standard form in their full conditional distributions. The proposed method performs very well in estimating the regression parameters as well as the intracluster association, and the method is robust to frailty distribution misspecifications as shown in our simulation studies. Two real‐life data sets are analyzed for illustration.     

Analyses of Developmental Rate Isomorphy in Ectotherms: Introducing the Dirichlet Regression

Temperature drives development in insects and other ectotherms because their metabolic rate and growth depends directly on thermal conditions. However, relative durations of successive ontogenetic stages often remain nearly constant across a substantial range of temperatures. This pattern, termed ‘developmental rate isomorphy’ (DRI) in insects, appears to be widespread and reported departures from DRI are generally very small. We show that these conclusions may be due to the caveats hidden in the statistical methods currently used to study DRI. Because the DRI concept is inherently based on proportional data, we propose that Dirichlet regression applied to individual-level data is an appropriate statistical method to critically assess DRI. As a case study we analyze data on five aquatic and four terrestrial insect species. We find that results obtained by Dirichlet regression are consistent with DRI violation in at least eight of the studied species, although standard analysis detects significant departure from DRI in only four of them. Moreover, the departures from DRI detected by Dirichlet regression are consistently much larger than previously reported. The proposed framework can also be used to infer whether observed departures from DRI reflect life history adaptations to size- or stage-dependent effects of varying temperature. Our results indicate that the concept of DRI in insects and other ectotherms should be critically re-evaluated and put in a wider context, including the concept of ‘equiproportional development’ developed for copepods.     

Comparison of Amplitude Recovery Dynamics of Two Limit Cycle Oscillator Models of the Human Circadian Pacemaker

At an organism level, the mammalian circadian pacemaker is a two‐dimensional system. For these two dimensions, phase (relative timing) and amplitude of the circadian pacemaker are commonly used. Both the phase and the amplitude (A) of the human circadian pacemaker can be observed within multiple physiological measures—including plasma cortisol, plasma melatonin, and core body temperature (CBT)—all of which are also used as markers of the circadian system. Although most previous work has concentrated on changes in phase of the circadian system, critically timed light exposure can significantly reduce the amplitude of the pacemaker. The rate at which the amplitude recovers to its equilibrium level after reduction can have physiological significance. Two mathematical models that describe the phase and amplitude dynamics of the pacemaker have been reported. These models are essentially equivalent in predictions of phase and in predictions of amplitude recovery for small changes from an equilibrium value (A=1), but are markedly different in the prediction of recovery rates when A<0.6. To determine which dynamic model best describes the amplitude recovery observed in experimental data; both models were fit to CBT data using a maximum likelihood procedure and compared using Akaike's Information Criterion (AIC). For all subjects, the model with the lower recovery rate provided a better fit to data in terms of AIC, supporting evidence that the amplitude recovery of the endogenous pacemaker is slow at low amplitudes. Experiments derived from model predictions are proposed to test the influence of low amplitude recovery on the physiological and neurobehavioral functions.     

A mechanistic damage model for ligaments

PurposeThe accuracy of biomechanical models is predicated on the realism by which they represent their biomechanical tissues. Unfortunately, most models use phenomenological ligament models that neglect the behaviour in the failure region. Therefore, the purpose of this investigation was to test whether a mechanistic model of ligamentous tissue portrays behaviour representative of actual ligament failure tests.ModelThe model tracks the time-evolution of a population of collagen fibres in a theoretical ligament. Each collagen fibre is treated as an independent linear cables with constant stiffness. Model equations were derived by assuming these fibres act as a continuum and applying a conservation law akin to Huxley’s muscle model. A breaking function models the rate of collagen fibre breakage at a given displacement, and was chosen to be a linear function for this preliminary analysis.MethodsThe model was fitted to experimental average curves for the cervical anterior longitudinal ligament. In addition, the model was cyclically loaded to test whether the tissue model behaves similarly.ResultsThe model agreed very well with experiment with an RMS error of 14.23 N and an R² of 0.995. Cyclic loading exhibited a reduction in force similar to experimental data.Discussion and conclusionThe proposed model showcases behaviour reminiscent of actual ligaments being strained to failure and undergoing cyclic load. Future work could incorporate viscous effects, or validate the model further by testing it in various loading conditions. Characterizing the breaking function more accurately would also lead to better results.     

Three-reaction model for the anaerobic digestion of microalgae

Coupling an anaerobic digester to a microalgal culture has received increasing attention as an alternative process for combined bioenergy production and depollution. In this article, a dynamic model for anaerobic digestion of microalgae is developed with the aim of improving the management of such a coupled system. This model describes the dynamics of inorganic nitrogen and volatile fatty acids since both can lead to inhibition and therefore process instability. Three reactions are considered: Two hydrolysis–acidogenesis steps in parallel for sugars/lipids and for proteins, followed by a methanogenesis step. The proposed model accurately reproduces experimental data for anaerobic digestion of the freshwater microalgae Chlorella vulgaris with an organic loading rate of 1 gCOD L^?1 d^?1. In particular, the three‐reaction pathway allows to adequately represent the observed decoupling between biogas production and nitrogen release. The reduced complexity of this model makes it suitable for developing advanced, model‐based control and monitoring strategies. Biotechnol. Bioeng. 2012; 109:415–425. © 2011 Wiley Periodicals, Inc.     

The Rate Constants of Valinomycin-Mediated Ion Transport through Thin Lipid Membranes

Electrical relaxation experiments have been performed with phosphatidylinositol bilayer membranes in the presence of the ion carrier valinomycin. After a sudden change of the voltage a relaxation of the membrane current with a time constant of about 20 μsec is observed. Together with previous stationary conductance data, the relaxation amplitude and the relaxation time are used to evaluate the rate constants of valinomycin-mediated potassium transport across the lipid membrane. It is found that the rate constants of translocation of the free carrier S and the carrier-ion complex MS⁺ are nearly equal (2·10⁴ sec^-1) and are of the same order as the dissociation rate constant of MS⁺ in the membrane-solution interface (5·10⁴ sec^-1). The equilibrium constant of the heterogeneous association reaction M⁺ (solution) + S (membrane) → MS⁺ (membrane) is found to be ~ 1 M^-1, about 10⁶ times smaller than the association constant in ethanolic solution.     

Bayesian Semiparametric Models for Survival Data with a Cure Fraction

We propose methods for Bayesian inference for a new class of semiparametric survival models with a cure fraction. Specifically, we propose a semiparametric cure rate model with a smoothing parameter that controls the degree of parametricity in the right tail of the survival distribution. We show that such a parameter is crucial for these kinds of models and can have an impact on the posterior estimates. Several novel properties of the proposed model are derived. In addition, we propose a class of improper noninformative priors based on this model and examine the properties of the implied posterior. Also, a class of informative priors based on historical data is proposed and its theoretical properties are investigated. A case study involving a melanoma clinical trial is discussed in detail to demonstrate the proposed methodology.     

Radiometric dating for recent lake sediments on the Tibetan Plateau

We present radiometric data from nine lakes across the Tibetan Plateau, and compare their reliability in relation to recent research. Unsupported ²¹⁰Pb profiles show, except for one particular lake, non-exponential decline of ²¹⁰Pb activity with sediment depth. Stratigraphic dates based on global atmospheric nuclear weapons maximum fallout of ¹³⁷Cs (1963) support the use of the constant rate of ²¹⁰Pb supply (CRS) model in four of the dated cores. The discrepancy in the others is likely due to recent increased input of catchment-derived ²¹⁰Pb. ²¹⁰Pb dates in this study suggest that post depositional diffusion of ¹³⁷Cs activity has been significant. The practice of assigning early 1950s dates (start of global atmospheric thermonuclear testing) to lake sediment sequences on the Tibetan Plateau should be used with caution. ¹³⁷Cs profiles from Tibetan lake sediment cores and their geographical distribution suggest that ¹³⁷Cs derived from the 1986 Chernobyl accident or atmospheric testing in China was not sufficient to form a significant peak effective for dating.     

Diurnal nitrate uptake in young tomato (Lycopersicon esculentum Mill.) plants: test of a feedback-based model

A simple model is proposed to describe diurnal net nitrate uptake rate patterns observed experimentally on young plants grown under constant non-limiting nutrition. It rests on two hypotheses: net uptake rate is under negative feedback control by internal plant nitrate content, and nitrogen metabolism occurs only during the light period. The model parameters were determined from the results of three independent experiments performed under non-disturbing conditions in a growth room at constant air and solution temperatures. Net hourly nitrate uptake rate was measured through a diurnal cycle and after an extended 28 h period of darkness. It increased continuously during the light period and decreased during the dark period. Under prolonged darkness, net uptake declined to an asymptotic positive uptake rate of about 10^-5 mol h^-1 g^-1 total plant dry weight. The measured hourly nitrate uptake rate values were consistent with independent determinations of long-term nitrate and total N accumulations in the plant. Realistic simulations of experimental data are achieved with the proposed model. Furthermore, the maintenance of a positive net uptake rate, measured in non-growing plants subjected to prolonged darkness, is explained in the model by the continuous increase of plant water content. The importance of the diurnal variations of plant water content for nitrate uptake rate is emphasized and gives consistency to the homeostasis hypothesis of the model. The diurnal changes in nitrate uptake predicted by the model are strongly dependent on the assumption made for diurnal changes in nitrate assimilation. While the purely photosynthetic assumption is convenient, a more realistic metabolism sub-model is needed.     

Theory of friction-limited DNA unwinding

The theory of friction-limited DNA unwinding is developed explicitly for moderate tind large perturbations. This extension of the earlier theory of the relaxation kinetics is necessary because of the complex nature of the rate limitation for small perturbations. The assumption of the theory that is violated under relaxation conditions is that base pairing reactions occurring at a constant local degree of twist of the strands are fast compared to the net unwinding of the molecule. However, these reactions that are slow for small perturbations have a large activation energy, and become faster than friction-limited un winding for large enough temperature jumps and sufficiently large DXA molecules. Thus only the rate for moderate and large perturbations is clearly limited by frictional resistance to turning the molecule in solution. The model used is a diffusional unwinding of the two strands, driven by the accompanying decrease in free energy. For large perturbations a numerical solution of the diffusion equation is required, since the diffusion coefficient is not constant. Two new parameters must be introduced into the equilibrium statistical theory to describe friction-limited unwinding kinetics. These are the force constant b, for winding up coil regions and the frictional coefficient per base pair β_cfor rotating coil regions in solution. We find by fitting the theory to experiment that b = 1.8 × 10^?13 ergs/ rad²- and β_c = 3.5 × 10^?21 erg see/base pair, both for DNA melted in alkali at 0.4.M Na ⁺ and ～30 °C. The latter value is in agreement with predictions based on the viscosity of single stranded DNA in alkali. The quoted value of bcan be interpreted to mean that the number of conformational states of a nucleolide is reduced by an average factor of 1.55 when it is wound around another strand to the degree of twist in a double helix, but without forming a base pair.     

Using Light-Use and Production Efficiency Models to Predict Photosynthesis and Net Carbon Exchange During Forest Canopy Disturbance

Vegetation growth models are used with remotely sensed and meteorological data to monitor terrestrial carbon dynamics at a range of spatial and temporal scales. Many of these models are based on a light-use efficiency equation and two-component model of whole-plant growth and maintenance respiration that have been parameterized for distinct vegetation types and biomes. This study was designed to assess the robustness of these parameters for predicting interannual plant growth and carbon exchange, and more specifically to address inconsistencies that may arise during forest disturbances and the loss of canopy foliage. A model based on the MODIS MOD17 algorithm was parameterized for a mature upland hardwood forest by inverting CO₂ flux tower observations during years when the canopy was not disturbed. This model was used to make predictions during a year when the canopy was 37% defoliated by forest tent caterpillars. Predictions improved after algorithms were modified to scale for the effects of diffuse radiation and loss of leaf area. Photosynthesis and respiration model parameters were found to be robust at daily and annual time scales regardless of canopy disturbance, and differences between modeled net ecosystem production and tower net ecosystem exchange were only approximately 2 g C m⁻² d⁻¹ and less than 23 g C m⁻² y⁻¹. Canopy disturbance events such as insect defoliations are common in temperate forests of North America, and failure to account for cyclical outbreaks of forest tent caterpillars in this stand could add an uncertainty of approximately 4–13% in long-term predictions of carbon sequestration.     

Visual Saliency Models for Text Detection in Real World

This paper evaluates the degree of saliency of texts in natural scenes using visual saliency models. A large scale scene image database with pixel level ground truth is created for this purpose. Using this scene image database and five state-of-the-art models, visual saliency maps that represent the degree of saliency of the objects are calculated. The receiver operating characteristic curve is employed in order to evaluate the saliency of scene texts, which is calculated by visual saliency models. A visualization of the distribution of scene texts and non-texts in the space constructed by three kinds of saliency maps, which are calculated using Itti''s visual saliency model with intensity, color and orientation features, is given. This visualization of distribution indicates that text characters are more salient than their non-text neighbors, and can be captured from the background. Therefore, scene texts can be extracted from the scene images. With this in mind, a new visual saliency architecture, named hierarchical visual saliency model, is proposed. Hierarchical visual saliency model is based on Itti''s model and consists of two stages. In the first stage, Itti''s model is used to calculate the saliency map, and Otsu''s global thresholding algorithm is applied to extract the salient region that we are interested in. In the second stage, Itti''s model is applied to the salient region to calculate the final saliency map. An experimental evaluation demonstrates that the proposed model outperforms Itti''s model in terms of captured scene texts.     

Patterns in departure phenology and mass gain on African non‐breeding territories prior to the Sahara crossing in a long‐distance migrant

Afro‐Palaearctic migrants are declining to a greater degree than other European species, suggesting that processes occurring in Africa or on migration may be driving these trends. Constraints on food availability on the wintering grounds may contribute to these declines but little is known about when and where these resource constraints may occur. Sufficient resources are particularly important prior to spring migration, when migrants must cross the Sahara Desert. We examined mass gain and departure phenology in a long‐distance Palaearctic passerine migrant to determine the degree to which pre‐migratory fattening occurs in their long‐term non‐breeding territories in the Guinea Savannah region of Africa. We monitored 75 Whinchats Saxicola rubetra for departure from their non‐breeding territories in one spring, and analysed mass data of 377 Whinchats collected over three non‐breeding seasons plus 141 migrating Whinchats caught in April over 8 years, all within the same few square kilometres of human‐modified Guinea Savannah in central Nigeria. Whinchats left their winter territories throughout April, with males departing on average 8 days earlier than females. However, there was no evidence that time of departure from territory was linked to age, body size or mass at capture. Whinchats departed their territories with a predicted mass of 16.8 ± 0.3 g, considerably less than the c. 24 g required for the average Whinchat to cross the Sahara directly. Comparing departure dates with arrival dates in southern Europe showed a discrepancy of at least 2 weeks, suggesting that many Whinchats spend considerable time on pre‐migratory fuelling outside their winter territory prior to crossing the Sahara. Overwintering birds gained mass slowly during February and March (0.03 g/day), and non‐territorial or migrating birds at a much higher rate in April (at least 0.23 g/day), with up to 20% of migrating Whinchats in April potentially having sufficient fuel loads to cross the Sahara directly from central Nigeria. Our results suggest that most Whinchats leave their winter territories to fatten up locally or, possibly, by staging further north, closer to the southern limit of the Sahara. Resource constraints are therefore likely to be particularly focused in West Africa during mid‐April and possibly at staging areas before the crossing of the Sahara Desert.     

A Bayesian Chi‐Squared Goodness‐of‐Fit Test for Censored Data Models

Summary We propose a Bayesian chi‐squared model diagnostic for analysis of data subject to censoring. The test statistic has the form of Pearson's chi‐squared test statistic and is easy to calculate from standard output of Markov chain Monte Carlo algorithms. The key innovation of this diagnostic is that it is based only on observed failure times. Because it does not rely on the imputation of failure times for observations that have been censored, we show that under heavy censoring it can have higher power for detecting model departures than a comparable test based on the complete data. In a simulation study, we show that tests based on this diagnostic exhibit comparable power and better nominal Type I error rates than a commonly used alternative test proposed by Akritas (1988, Journal of the American Statistical Association 83, 222–230). An important advantage of the proposed diagnostic is that it can be applied to a broad class of censored data models, including generalized linear models and other models with nonidentically distributed and nonadditive error structures. We illustrate the proposed model diagnostic for testing the adequacy of two parametric survival models for Space Shuttle main engine failures.     

Influence of mass transfer and surface ligand heterogeneity on quantitative BIAcoreTM binding data. Analysis of the interaction of NC10 Fab with an anti-idiotype Fab′

The interaction of monovalent Fab fragments of NC10, an antiviral neuraminidase antibody, and the anti-idiotype antibody 3-2G12 has been used as a model system to demonstrate experimentally the influence of non-ideal binding effects on BIAcore^TM binding data. Because the association rate constant for these two molecules was found to be relatively high (about 5×10⁵ M ⁻¹ s⁻¹), mass transfer was recognised as a potential source of error in the analysis of the interaction kinetics. By manipulation of the flow rate and the surface density of the immobilised ligand, however, the magnitude to this error was minimised. In addition, the application of site-specific immobilisation procedures was found to improve considerably the correlation of experimental binding data to the ideal 1:1 kinetic model such that the discrepancy between experimental and fitted curves was within the noise range of the instrument. Experiments performed to measure the equilibrium constant (K_D) in solution resulted in a value of similar magnitude to those obtained from the ratio of the kinetic rate constants, even those measured with a heterogeneous ligand or with a significant mass transfer component. For this system, the experimental complexities introduced by covalent immobilisation did not lead to large errors in the K_D values obtained using the BIAcore © 1997 John Wiley & Sons, Ltd.