Cumulative Damage Survival Models for the Randomized Complete Block Design

A continuous time discrete state cumulative damage process {X(t), t ≥ 0} is considered, based on a non‐homogeneous Poisson hit‐count process and discrete distribution of damage per hit, which can be negative binomial, Neyman type A, Polya‐Aeppli or Lagrangian Poisson. Intensity functions considered for the Poisson process comprise a flexible three‐parameter family. The survival function is S(t) = P(X(t) ≤ L) where L is fixed. Individual variation is accounted for within the construction for the initial damage distribution {P(X(0) = x) | x = 0, 1, …,}. This distribution has an essential cut‐off before x = L and the distribution of L – X(0) may be considered a tolerance distribution. A multivariate extension appropriate for the randomized complete block design is developed by constructing dependence in the initial damage distributions. Our multivariate model is applied (via maximum likelihood) to litter‐matched tumorigenesis data for rats. The litter effect accounts for 5.9 percent of the variance of the individual effect. Cumulative damage hazard functions are compared to nonparametric hazard functions and to hazard functions obtained from the PVF‐Weibull frailty model. The cumulative damage model has greater dimensionality for interpretation compared to other models, owing principally to the intensity function part of the model.     

The Concordance Index C and the Mann–Whitney Parameter Pr(X>Y) with Randomly Censored Data

Harrell's c‐index or concordance C has been widely used as a measure of separation of two survival distributions. In the absence of censored data, the c‐index estimates the Mann–Whitney parameter Pr(X>Y), which has been repeatedly utilized in various statistical contexts. In the presence of randomly censored data, the c‐index no longer estimates Pr(X>Y); rather, a parameter that involves the underlying censoring distributions. This is in contrast to Efron's maximum likelihood estimator of the Mann–Whitney parameter, which is recommended in the setting of random censorship.     

Simulating tick distributions over sub-Saharan Africa: the use of observed and simulated climate surfaces

Aim A broad suit of climate data sets is becoming available for use in predictive species modelling. We compare the efficacy of using interpolated climate surfaces [Center for Resource and Environmental Studies (CRES) and Climate Research Unit (CRU)] or high‐resolution model‐derived climate data [Division of Atmospheric Research limited‐area model (DARLAM)] for predictive species modelling, using tick distributions from sub‐Saharan Africa. Location The analysis is restricted to sub‐Saharan Africa. The study area was subdivided into 3000 grids cells with a resolution of 60 × 60 km. Methods Species distributions were predicted using an established multivariate climate envelope modelling approach and three very different climate data sets. The recorded variance in the climate data sets was quantified by employing omnidirectional variograms. To further compare the interpolated tick distributions that flowed from using three climate data sets, we calculated true positive (TP) predictions, false negative (FN) predictions as well as the proportional overlaps between observed and modelled tick distributions. In addition, the effect of tick data set size on the performance of the climate data sets was evaluated by performing random draws of known tick distribution records without replacement. Results The predicted distributions were consistently wider ranging than the known records when using any of the three climate data sets. However, the proportional overlap between predicted and known distributions varied as follows: for Rhipicephalus appendiculatus Neumann (Acari: Ixodidae), these were 60%, 60% and 70%; for Rhipicephalus longus Neumann (Acari: Ixodidae) 60%, 57% and 75%; for Rhipicephalus zambeziensis Walker, Norval & Corwin (Acari: Ixodidae) 57%, 51% and 62%, and for Rhipicephalus capensis Koch (Acari: Ixodidae) 70%, 60% and 60% using the CRES, CRU and DARLAM climate data sets, respectively. All data sets were sensitive to data size but DARLAM performed better when using smaller species data sets. At a 20% data subsample level, DARLAM was able to capture more than 50% of the known records and captured more than 60% of known records at higher subsample levels. Main conclusions The use of data derived from high‐resolution nested climate models (e.g. DARLAM) provided equal or even better species distribution modelling performance. As the model is dynamic and process based, the output data are available at the modelled resolution, and are not hamstrung by the sampling intensity of observed climate data sets (c. one sample per 30,000 km² for Africa). In addition, when exploring the biodiversity consequences of climate change, these modelled outputs form a more useful basis for comparison with modelled future climate scenarios.     

Unraveling the habitat preferences of two closely related bumble bee species in Eastern Europe

Co‐occurrence of closely related species is often explained through resource partitioning, where key morphological or life‐history traits evolve under strong divergent selection. In bumble bees (genus Bombus), differences in tongue lengths, nest sites, and several life‐history traits are the principal factors in resource partitioning. However, the buff‐tailed and white‐tailed bumble bee (Bombus terrestris and B. lucorum respectively) are very similar in morphology and life history, but their ranges nevertheless partly overlap, raising the question how they are ecologically divergent. What little is known about the environmental factors determining their distributions stems from studies in Central and Western Europe, but even less information is available about their distributions in Eastern Europe, where different subspecies occur. Here, we aimed to disentangle the broad habitat requirements and associated distributions of these species in Romania and Bulgaria. First, we genetically identified sampled individuals from many sites across the study area. We then not only computed species distributions based on presence‐only data, but also expanded on these models using relative abundance data. We found that B. terrestris is a more generalist species than previously thought, but that B. lucorum is restricted to forested areas with colder and wetter climates, which in our study area are primarily found at higher elevations. Both vegetation parameters such as annual mean Leaf Area Index and canopy height, as well as climatic conditions, were important in explaining their distributions. Although our models based on presence‐only data suggest a large overlap in their respective distributions, results on their relative abundance suggest that the two species replace one another across an environmental gradient correlated to elevation. The inclusion of abundance enhances our understanding of the distribution of these species, supporting the emerging recognition of the importance of abundance data in species distribution modeling.     

Improved power of familywise error rate procedures for discrete data under dependency

In many applications where it is necessary to test multiple hypotheses simultaneously, the data encountered are discrete. In such cases, it is important for multiplicity adjustment to take into account the discreteness of the distributions of the p‐values, to assure that the procedure is not overly conservative. In this paper, we review some known multiple testing procedures for discrete data that control the familywise error rate, the probability of making any false rejection. Taking advantage of the fact that the exact permutation or exact pairwise permutation distributions of the p‐values can often be determined when the sample size is small, we investigate procedures that incorporate the dependence structure through the exact permutation distribution and propose two new procedures that incorporate the exact pairwise permutation distributions. A step‐up procedure is also proposed that accounts for the discreteness of the data. The performance of the proposed procedures is investigated through simulation studies and two applications. The results show that by incorporating both discreteness and dependency of p‐value distributions, gains in power can be achieved.     

Model Diagnostic Plots for Repeated Measures Data

In the analysis of repeated measurements, multivariate regression models that account for the correlations among the observations from the same subject are widely used. Like the usual univariate regression models, these multivariate regression models also need some model diagnostic procedures. Though these models have been widely used, not many studies have been performed in model diagnostic areas. In this paper, we propose simple residual plots to investigate the goodness of model fit for repeated measures data. Here, we mainly focus on the mean model diagnostics. The proposed residual plots are based on the quantile‐quantile(Q–Q) plots of a χ² distribution and a normal distribution. In particular, the proposed model is useful in comparing several models simultaneously. The proposed method is illustrated using two examples. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical interpretation of dose-response curves

The dose-response of an individual organism can be described by a step functions if the organism survives when the dose is below a certain lethal level and dies when this level is exceeded. If, in a population of organism, the lethal dose for an individual has a unimodal distribution, the latter's properties will determine the shape of the population's response in the following manner. If the distribution is symmetric the dose-response curve has a symmetric sigmoid shape when plotted on linear coordinates. The location of the inflection point and the curve's slope around it are determined by the distribution's mode and variance. When the distribution is skewed, the dose-response curve has an asymmetric sigmoid shape which becomes reminiscent of an exponential decay when the distribution is strongly skewed to the right. The population's dose-response curve can be constructed by integration of the step changes over the distribution range. The step function representing the dose-response of an individual organism can be approximate by a Fermi function, and the distribution of an lethal doses can be represented by the Weibull distribution function. When the two functions are combined, the resulting dose-response of the populationS(X)), which is the fraction of survivors after exposure to a doseX, is given by:S(X)=∫ ₀ ¹ [1/{+exp{(X-X _c (φ))/a _i ]}]dω whereX _c (ω)={(1/b)[-ln(1-ω)]}^(1/n),n andb being the constants of the Weibull distribution anda _i an arbitrarily small number, i.e.a _i ≪[X−X _c (ϕ)], whose actual magnitude is of little significance. This model can be used to determine the underlying distributions of experimental dose-response relationship. It was applied to published survival data of microorganisms exposed to pulsed electric field, X-ray radiation and ozone to show that the different observed shapes of the dose-response curve, and shifts between them, can be expressed in terms of the correponding distribution parameters, namely the mode, variance and skewness.     

On the distribution of developmental errors: comparing the normal, gamma, and log-normal distribution

The amount of between‐individual variation in the unobservable developmental instability (DI) has been the subject of intense recent debates. The unexpectedly high estimates of between‐individual variation in DI based on distributional characteristics of observable asymmetry values (of on average bilaterally symmetric traits) rely on statistical models that assume an underlying normal distribution of developmental errors. This prompted doubts on the assumption of the Gaussian nature of developmental errors. However, when applying other candidate distributions [log‐normal and gamma (γ)], recent analyses of empirical datasets have indicated that estimates remain generally high. Yet, all estimates were based on bilaterally symmetric traits, which did not allow for a formal comparison of the alternative distributions. In the present study, we extend a recent statistical model to allow statistical comparison of the different distributions based on traits that developed repeatedly under the same conditions, such as flower traits and regrown feathers. We analyse simulated and empirical data and show that: (1) it is statistically difficult to differentiate among the three alternatives when variances are small relative to the mean, as is often the case with DI; (2) the normal distribution fits the log‐normal or γ relatively well under those circumstances; (3) the deviance information criterion (DIC) is able to pick up differences in model fit among the three alternative distributions, yet more strongly so when levels of DI were high; (4) empirical datasets show a better fit of the normal over the log‐normal and γ‐distributions as judged by the DIC; and (5) estimates of between‐individual variation in DI in the three empirical datasets were relatively high (> 50%) under each distributional assumption. In conclusion, and based on our three datasets, the normal approximation appears to be a reasonable choice for statistical models of DI and the remarkably high estimates of variation in DI cannot be attributed to non‐normal developmental noise. Nevertheless, our method should be applied to a broad range of traits and organisms to evaluate the generality of this result. We argue that there is an urgent need for studies that reveal the underlying mechanisms of developmental noise and stability, as well as the role of developmental selection, in order to be able to determine the biological importance of the highly skewed distributions of developmental instability often observed. © 2007 The Linnean Society of London, Biological Journal of the Linnean Society, 2007, 92 , 197–210.     

Using niche‐based GIS modeling to test geographic predictions of competitive exclusion and competitive release in South American pocket mice

Geographic studies addressing the role of competition in determining species’ macrodistributions have been limited by only simple or subjective means of identifying regions of suitable habitat. Now, ecological‐niche models of species’ potential distributions present a possible approach to testing for the geographic patterns predicted under competitive exclusion and competitive release. Previously, we modeled the potential distributions of two spiny pocket mice (Heteromys australis and H. anomalus) in northwestern South America using specimen localities, environmental data, and the Genetic Algorithm for Rule‐Set Prediction (GARP). Here we superimpose the models to examine known distributional records in areas of potential sympatry between the two species, thus testing the geographic predictions of competitive exclusion. In addition, we examine environmental characteristics of known localities, testing for data consistent with competitive release. Areas of potential sympatry are minimal, lying in regions of intermediate water balance. Only records of H. australis are known from areas of potential sympatry in regions where the species’ ranges meet, consistent with exclusion of H. anomalus by H. australis. Heteromys anomalus inhabits areas ecologically suitable for both species only in the isolated Sierra Nevada de Santa Marta, in which H. australis is not present (most likely for historical reasons). Furthermore, environmental characteristics of localities of H. anomalus in biogeographic regions where H. australis is absent fit the pattern predicted under competitive release. In contrast, localities of H. australis show no indication of competitive release. Although the results of present analyses do not conclusively demonstrate competitive exclusion or release, they provide directional hypotheses that can now be tested in experimental field and laboratory studies.     

Modeling stream fish distributions using interval‐censored detection times

Controlling for imperfect detection is important for developing species distribution models (SDMs). Occupancy‐detection models based on the time needed to detect a species can be used to address this problem, but this is hindered when times to detection are not known precisely. Here, we extend the time‐to‐detection model to deal with detections recorded in time intervals and illustrate the method using a case study on stream fish distribution modeling. We collected electrofishing samples of six fish species across a Mediterranean watershed in Northeast Portugal. Based on a Bayesian hierarchical framework, we modeled the probability of water presence in stream channels, and the probability of species occupancy conditional on water presence, in relation to environmental and spatial variables. We also modeled time‐to‐first detection conditional on occupancy in relation to local factors, using modified interval‐censored exponential survival models. Posterior distributions of occupancy probabilities derived from the models were used to produce species distribution maps. Simulations indicated that the modified time‐to‐detection model provided unbiased parameter estimates despite interval‐censoring. There was a tendency for spatial variation in detection rates to be primarily influenced by depth and, to a lesser extent, stream width. Species occupancies were consistently affected by stream order, elevation, and annual precipitation. Bayesian P‐values and AUCs indicated that all models had adequate fit and high discrimination ability, respectively. Mapping of predicted occupancy probabilities showed widespread distribution by most species, but uncertainty was generally higher in tributaries and upper reaches. The interval‐censored time‐to‐detection model provides a practical solution to model occupancy‐detection when detections are recorded in time intervals. This modeling framework is useful for developing SDMs while controlling for variation in detection rates, as it uses simple data that can be readily collected by field ecologists.     

Envelope: interactive software for modeling and fitting complex isotope distributions

Background  

An important aspect of proteomic mass spectrometry involves quantifying and interpreting the isotope distributions arising from mixtures of macromolecules with different isotope labeling patterns. These patterns can be quite complex, in particular with in vivo metabolic labeling experiments producing fractional atomic labeling or fractional residue labeling of peptides or other macromolecules. In general, it can be difficult to distinguish the contributions of species with different labeling patterns to an experimental spectrum and difficult to calculate a theoretical isotope distribution to fit such data. There is a need for interactive and user-friendly software that can calculate and fit the entire isotope distribution of a complex mixture while comparing these calculations with experimental data and extracting the contributions from the differently labeled species.     

Multiple Comparisons of Polynomial Distributions

Asymptotically correct 90 and 95 percentage points are given for multiple comparisons with control and for all pair comparisons of several independent samples of equal size from polynomial distributions. Test statistics are the maxima of the X²-statistics for single comparisons. For only two categories the asymptotic distributions of these test statistics result from DUNNETT'S many-one tests and TUKEY'S range test (cf. MILLER, 1981). The percentage points for comparisons with control are computed from the limit distribution of the test statistic under the overall hypothesis H₀. To some extent the applicability of these bounds is investigated by simulation. The bounds can also be used to improve Holm's sequentially rejective Bonferroni test procedure (cf. HOLM, 1979). The percentage points for all pair comparisons are obtained by large simulations. Especially for 3×3-tables the limit distribution of the test statistic under H₀ is derived also for samples of unequal size. Also these bounds can improve the corresponding Bonferroni-Holm procedure. Finally from SKIDÁK's probability inequality for normal random vectors (cf. SKIDÁK, 1967) a similar inequality is derived for dependent X²-variables applicable to simultaneous X²-tests.     

Ciliate diversity and distribution across an environmental and depth gradient in Long Island Sound,USA

The nature and extent of microbial biodiversity remain controversial with persistent debates over patterns of distributions (i.e. cosmopolitanism versus endemism) and the processes that structure these patterns (neutrality versus selection). We used culture‐independent approaches to address these issues focusing on two groups of ciliates, the Oligotrichia (Spirotrichea) and Choreotrichia (Spirotrichea) across an environmental gradient. We assessed SSU rDNA diversity in ciliate communities at six stations in Long Island Sound spanning the frontal region that separates the fresher Connecticut River outflow plume from the open Sound. As in previous studies, we find one abundant cosmopolitan species (Strombidium biarmatum), a few moderately abundant sequences, and a long list of rare sequences. Furthermore, neither ciliate diversity nor species composition showed any clear relationship to measured environmental parameters (temperature, salinity, accessory pigment composition and chorophyll). Overall, we observed that diversity decreased moving from nearshore to offshore. We also conducted analyses to detect clustering among the sampled communities using the software Unifrac. This approach revealed three significant clusters grouping samples from nearshore, surface and deep/well mixed stations. We find no strong fit of our communities to log series, geometric or log normal distributions, though one of the 3 clusters is most consistent with a log series distribution. However, when we remove the abundant cosmopolitan species S. biarmatum, all three clusters fit to a log series distribution. These analyses suggest that, with the exception of one cosmopolitan species, the oligotrich and choreotrich communities at these stations may be distributed in a neutral manner.     

Partitioning global change: Assessing the relative importance of changes in climate and land cover for changes in avian distribution

Understanding the relative impact of climate change and land cover change on changes in avian distribution has implications for the future course of avian distributions and appropriate management strategies. Due to the dynamic nature of climate change, our goal was to investigate the processes that shape species distributions, rather than the current distributional patterns. To this end, we analyzed changes in the distribution of Eastern Wood Pewees (Contopus virens) and Red‐eyed Vireos (Vireo olivaceus) from 1997 to 2012 using Breeding Bird Survey data and dynamic correlated‐detection occupancy models. We estimated the local colonization and extinction rates of these species in relation to changes in climate (hours of extreme temperature) and changes in land cover (amount of nesting habitat). We fit six nested models to partition the deviance explained by spatial and temporal components of land cover and climate. We isolated the temporal components of environmental variables because this is the essence of global change. For both species, model fit was significantly improved when we modeled vital rates as a function of spatial variation in climate and land cover. Model fit improved only marginally when we added temporal variation in climate and land cover to the model. Temporal variation in climate explained more deviance than temporal variation in land cover, although both combined only explained 20% (Eastern Wood Pewee) and 6% (Red‐eyed Vireo) of temporal variation in vital rates. Our results showing a significant correlation between initial occupancy and environmental covariates are consistent with biological expectation and previous studies. The weak correlation between vital rates and temporal changes in covariates indicated that we have yet to identify the most relevant components of global change influencing the distributions of these species and, more importantly, that spatially significant covariates are not necessarily driving temporal shifts in avian distributions.     

Effect of chronological addition of records to species distribution maps: The case of Tonatia saurophila maresi (Chiroptera,Phyllostomidae) in South America

Ecological niche models have become very popular for analysing the potential distribution of species. Nevertheless, models are strongly influenced by many factors, such as spatial resolution, environmental variables and the quality of distribution records. In this paper, we evaluated how ecological niche models changed with the addition of records accumulated over four decades. Our model species was the stripe‐headed round‐eared bat (Tonatia saurophila). Thus, with data organized in chronological order, we could observe how the models changed in predicting distributions over time in comparison with all known point locations. We tested if partial models could predict the occurrence of new unpublished records for savannah areas in central Brazil, considering that the species is typically associated with forest environments. Our results indicate a high omission rate for models built with point localities from the 1970s and 1980s (58.5% and 50.0% of all known points respectively), and predicted that the species could occur in central Brazil. Although T. saurophila has indeed been recorded recently in central Brazil, it was found in places different from those predicted by the models using these restricted earlier data. Nevertheless, the environmental suitability of such areas is significantly different from sites largely described in earlier records from the Amazonia region, as shown by principal components analysis. We argue that populations of T. saurophila that occupy open habitats in central South America (including Caatinga, Cerrado, Chaco and semi‐deciduous interior forests) deserve further study at the genetic level to determine if bats in these very different habitats are taxonomically distinct from Amazonian populations. Our results also suggest that models based on very limited datasets for species occurrence can lead conservationists or decision makers to wrong conclusions.     

A computationally inspired investigation of the solid forms of (R)‐1‐phenylethylammonium‐(S)‐2‐phenylbutyrate

Following the computation of a lattice energy landscape which predicted that there should be more stable, denser forms of (R)‐1‐phenylethylammonium‐(S)‐2‐phenylbutyrate, crystallizations from a range of solvents were performed to search for other polymorphs and investigate the possibility that the known P4₁ structure could be a hydrate. Extensive crystallization experiments from a wide range of solvents gave fine needles or microcrystalline samples. A redetermination of the P4₁ structure by powder X‐ray diffraction located all protons, and in conjunction with other experimental and computational evidence showed that the structure was anhydrous. Evidence for two additional forms was found as mixtures with form I. These include an orthorhombic form, possibly a Z′ = 3 polymorph, and another as yet unidentified form obtained as a minor component from dichloromethane solution. However, both these forms appear to be metastable with respect to form I (P4₁), which is therefore probably the most thermodynamically stable form that can be crystallized from solution under ambient conditions. This determination of the solid state behavior of the less readily crystallized member of the diastereomeric salt system (R)‐1‐phenylethylammonium‐(R/S)‐2‐phenylbutyrate provides a challenge to the theoretical modeling to explain its ideal resolution behavior. Chirality 2010. © 2009 Wiley‐Liss, Inc.     

Generalized Exponential Distribution in Flood Frequency Analysis for Polish Rivers

Many distributions have been used in flood frequency analysis (FFA) for fitting the flood extremes data. However, as shown in the paper, the scatter of Polish data plotted on the moment ratio diagram shows that there is still room for a new model. In the paper, we study the usefulness of the generalized exponential (GE) distribution in flood frequency analysis for Polish Rivers. We investigate the fit of GE distribution to the Polish data of the maximum flows in comparison with the inverse Gaussian (IG) distribution, which in our previous studies showed the best fitting among several models commonly used in FFA. Since the use of a discrimination procedure without the knowledge of its performance for the considered probability density functions may lead to erroneous conclusions, we compare the probability of correct selection for the GE and IG distributions along with the analysis of the asymptotic model error in respect to the upper quantile values. As an application, both GE and IG distributions are alternatively assumed for describing the annual peak flows for several gauging stations of Polish Rivers. To find the best fitting model, four discrimination procedures are used. In turn, they are based on the maximized logarithm of the likelihood function (K procedure), on the density function of the scale transformation maximal invariant (QK procedure), on the Kolmogorov-Smirnov statistics (KS procedure) and the fourth procedure based on the differences between the ML estimate of 1% quantile and its value assessed by the method of moments and linear moments, in sequence (R procedure). Due to the uncertainty of choosing the best model, the method of aggregation is applied to estimate of the maximum flow quantiles.     

Identification of novel Xanthomonas euvesicatoria type III effector proteins by a machine‐learning approach

The Gram‐negative bacterium Xanthomonas euvesicatoria (Xcv) is the causal agent of bacterial spot disease in pepper and tomato. Xcv pathogenicity depends on a type III secretion (T3S) system that delivers effector proteins into host cells to suppress plant immunity and promote disease. The pool of known Xcv effectors includes approximately 30 proteins, most identified in the 85‐10 strain by various experimental and computational techniques. To identify additional Xcv 85‐10 effectors, we applied a genome‐wide machine‐learning approach, in which all open reading frames (ORFs) were scored according to their propensity to encode effectors. Scoring was based on a large set of features, including genomic organization, taxonomic dispersion, hypersensitive response and pathogenicity (hrp)‐dependent expression, 5′ regulatory sequences, amino acid composition bias and GC content. Thirty‐six predicted effectors were tested for translocation into plant cells using the hypersensitive response (HR)‐inducing domain of AvrBs2 as a reporter. Seven proteins (XopAU, XopAV, XopAW, XopAP, XopAX, XopAK and XopAD) harboured a functional translocation signal and their translocation relied on the HrpF translocon, indicating that they are bona fide T3S effectors. Remarkably, four belong to novel effector families. Inactivation of the xopAP gene reduced the severity of disease symptoms in infected plants. A decrease in cell death and chlorophyll content was observed in pepper leaves inoculated with the xopAP mutant when compared with the wild‐type strain. However, populations of the xopAP mutant in infected leaves were similar in size to those of wild‐type bacteria, suggesting that the reduction in virulence was not caused by impaired bacterial growth.     

Modified GEE and Goodness of the Marginal Fit (GOMF) Test with Correlated Binary Responses for Contingency Tables

This paper addresses testing the goodness of fit of models for marginal probabilities estimated by generalized estimating equations. We develop a modified version of generalized estimating equation and a goodness‐of‐fit test based on the fitted marginal means. The test statistic is easy to compute and has a simple reference distribution. Its performance is evaluated asymptotically and in small samples. It is also compared to the deviance and Pearson X² statistics. Example applications are given. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)