Cormack–Jolly–Seber model with environmental covariates: A P‐spline approach

In capture–recapture models, survival and capture probabilities can be modelled as functions of time‐varying covariates, such as temperature or rainfall. The Cormack–Jolly–Seber (CJS) model allows for flexible modelling of these covariates; however, the functional relationship may not be linear. We extend the CJS model by semi‐parametrically modelling capture and survival probabilities using a frequentist approach via P‐splines techniques. We investigate the performance of the estimators by conducting simulation studies. We also apply and compare these models with known semi‐parametric Bayesian approaches on simulated and real data sets.     

Structural risk minimization: a robust method for density-dependence detection and model selection

Statistically distinguishing density‐dependent from density‐independent populations and selecting the best demographic model for a given population are problems of primary importance. Traditional approaches are PBLR (parametric bootstrapping of likelihood ratios) and Information criteria (IC), such as the Schwarz information criterion (SIC), the Akaike information criterion (AIC) or the Final prediction error (FPE). While PBLR is suitable for choosing from a couple of models, ICs select the best model from among a set of candidates. In this paper, we use the Structural risk minimization (SRM) approach. SRM is the model selection criterion developed within the Statistical learning theory (SLT), a theory of great generality for modelling and learning with finite samples. SRM is almost unknown in the ecological literature and has never been used to analyze time series. First, we compare SRM with PBLR in terms of their ability to discriminate between the Malthusian and the density‐dependent Ricker model. We rigorously repeat the experiments described in a previous study and find out that SRM is equally powerful in detecting density‐independence and much more powerful in detecting density‐dependence. Then, we compare SRM against ICs in terms of their ability to select one of several candidate models; we generate, via stochastic simulation, a huge amount of artificial time series both density‐independent and dependent, with and without exogenous covariates, using different dataset sizes, noise levels and parameter values. Our findings show that SRM outperforms traditional ICs, because generally a) it recognizes the model underlying the data with higher frequency, and b) it leads to lower errors in out‐of‐samples predictions. SRM superiority is specially apparent with short time series. We finally apply SRM to the population records of Alpine ibex Capra ibex living in the Gran Paradiso National Park (Italy), already investigated by other authors via traditional statistical methods; we both analyze their models and introduce some novel ones. We show that models that are best according to SRM show also the lowest leave‐one‐out cross‐validation error.     

Estimating Treatment Effects of Longitudinal Designs using Regression Models on Propensity Scores

Summary We derive regression estimators that can compare longitudinal treatments using only the longitudinal propensity scores as regressors. These estimators, which assume knowledge of the variables used in the treatment assignment, are important for reducing the large dimension of covariates for two reasons. First, if the regression models on the longitudinal propensity scores are correct, then our estimators share advantages of correctly specified model‐based estimators, a benefit not shared by estimators based on weights alone. Second, if the models are incorrect, the misspecification can be more easily limited through model checking than with models based on the full covariates. Thus, our estimators can also be better when used in place of the regression on the full covariates. We use our methods to compare longitudinal treatments for type II diabetes mellitus.     

Comparison of Bayesian methods for flexible modeling of spatial risk surfaces in disease mapping

Bayesian hierarchical models usually model the risk surface on the same arbitrary geographical units for all data sources. Poisson/gamma random field models overcome this restriction as the underlying risk surface can be specified independently to the resolution of the data. Moreover, covariates may be considered as either excess or relative risk factors. We compare the performance of the Poisson/gamma random field model to the Markov random field (MRF)‐based ecologic regression model and the Bayesian Detection of Clusters and Discontinuities (BDCD) model, in both a simulation study and a real data example. We find the BDCD model to have advantages in situations dominated by abruptly changing risk while the Poisson/gamma random field model convinces by its flexibility in the estimation of random field structures and by its flexibility incorporating covariates. The MRF‐based ecologic regression model is inferior. WinBUGS code for Poisson/gamma random field models is provided.     

Doubly robust multiple imputation using kernel‐based techniques

We consider the problem of estimating the marginal mean of an incompletely observed variable and develop a multiple imputation approach. Using fully observed predictors, we first establish two working models: one predicts the missing outcome variable, and the other predicts the probability of missingness. The predictive scores from the two models are used to measure the similarity between the incomplete and observed cases. Based on the predictive scores, we construct a set of kernel weights for the observed cases, with higher weights indicating more similarity. Missing data are imputed by sampling from the observed cases with probability proportional to their kernel weights. The proposed approach can produce reasonable estimates for the marginal mean and has a double robustness property, provided that one of the two working models is correctly specified. It also shows some robustness against misspecification of both models. We demonstrate these patterns in a simulation study. In a real‐data example, we analyze the total helicopter response time from injury in the Arizona emergency medical service data.     

Importance of dose‐response model form in probabilistic risk assessment: A case study of health effects from methylmercury in fish

We compared the effect of uncertainty in dose‐response model form on health risk estimates to the effect of uncertainty and variability in exposure. We used three different dose‐response models to characterize neurological effects in children exposed in utero to methylmercury, and applied these models to calculate risks to a native population exposed to potentially contaminated fish from a reservoir in British Columbia. Uncertainty in model form was explicitly incorporated into the risk estimates. The selection of dose‐response model strongly influenced both mean risk estimates and distributions of risk, and had a much greater impact than altering exposure distributions. We conclude that incorporating uncertainty in dose‐response model form is at least as important as accounting for variability and uncertainty in exposure parameters in probabilistic risk assessment.     

Dose–response relationship from longitudinal data with response‐dependent dose modification using likelihood methods

In some clinical trials or clinical practice, the therapeutic agent is administered repeatedly, and doses are adjusted in each patient based on repeatedly measured continuous responses, to maintain the response levels in a target range. Because a lower dose tends to be selected for patients with a better outcome, simple summarizations may wrongly show a better outcome for the lower dose, producing an incorrect dose–response relationship. In this study, we consider the dose–response relationship under these situations. We show that maximum‐likelihood estimates are consistent without modeling the dose‐modification mechanisms when the selection of the dose as a time‐dependent covariate is based only on observed, but not on unobserved, responses, and measurements are generated based on administered doses. We confirmed this property by performing simulation studies under several dose‐modification mechanisms. We examined an autoregressive linear mixed effects model. The model represents profiles approaching each patient's asymptote when identical doses are repeatedly administered. The model takes into account the previous dose history and provides a dose–response relationship of the asymptote as a summary measure. We also examined a linear mixed effects model assuming all responses are measured at steady state. In the simulation studies, the estimates of both the models were unbiased under the dose modification based on observed responses, but biased under the dose modification based on unobserved responses. In conclusion, the maximum‐likelihood estimates of the dose–response relationship are consistent under the dose modification based only on observed responses.     

Global patterns of nitrogen limitation: confronting two global biogeochemical models with observations

Projections of future changes in land carbon (C) storage using biogeochemical models depend on accurately modeling the interactions between the C and nitrogen (N) cycles. Here, we present a framework for analyzing N limitation in global biogeochemical models to explore how C‐N interactions of current models compare to field observations, identify the processes causing model divergence, and identify future observation and experiment needs. We used a set of N‐fertilization simulations from two global biogeochemical models (CLM‐CN and O‐CN) that use different approaches to modeling C‐N interactions. On the global scale, net primary productivity (NPP) in the CLM‐CN model was substantially more responsive to N fertilization than in the O‐CN model. The most striking difference between the two models occurred for humid tropical forests, where the CLM‐CN simulated a 62% increase in NPP at high N addition levels (30 g N m^?2 yr^?1), while the O‐CN predicted a 2% decrease in NPP due to N fertilization increasing plant respiration more than photosynthesis. Across 35 temperate and boreal forest sites with field N‐fertilization experiments, we show that the CLM‐CN simulated a 46% increase in aboveground NPP in response to N, which exceeded the observed increase of 25%. In contrast, the O‐CN only simulated a 6% increase in aboveground NPP at the N‐fertilization sites. Despite the small response of NPP to N fertilization, the O‐CN model accurately simulated ecosystem retention of N and the fate of added N to vegetation when compared to empirical ¹⁵N tracer application studies. In contrast, the CLM‐CN predicted lower total ecosystem N retention and partitioned more losses to volatilization than estimated from observed N budgets of small catchments. These results point to the need for model improvements in both models in order to enhance the accuracy with which global C‐N cycle feedbacks are simulated.     

Risk‐adjusted monitoring of time to event in the presence of long‐term survivors

The use of control charts for monitoring schemes in medical context should consider adjustments to incorporate the specific risk for each individual. Some authors propose the use of a risk‐adjusted survival time cumulative sum (RAST CUSUM) control chart to monitor a time‐to‐event outcome, possibly right censored, using conventional survival models, which do not contemplate the possibility of cure of a patient. We propose to extend this approach considering a risk‐adjusted CUSUM chart, based on a cure rate model. We consider a regression model in which the covariates affect the cure fraction. The CUSUM scores are obtained for Weibull and log‐logistic promotion time model to monitor a scale parameter for nonimmune individuals. A simulation study was conducted to evaluate and compare the performance of the proposed chart (RACUF CUSUM) with RAST CUSUM, based on optimal control limits and average run length in different situations. As a result, we note that the RAST CUSUM chart is inappropriate when applied to data with a cure rate, while the proposed RACUF CUSUM chart seems to have similar performance if applied to data without a cure rate. The proposed chart is illustrated with simulated data and with a real data set of patients with heart failure treated at the Heart Institute (InCor), at the University of São Paulo, Brazil.     

Evaluating the absolute quality of a single protein model using structural features and support vector machines

Knowing the quality of a protein structure model is important for its appropriate usage. We developed a model evaluation method to assess the absolute quality of a single protein model using only structural features with support vector machine regression. The method assigns an absolute quantitative score (i.e. GDT‐TS) to a model by comparing its secondary structure, relative solvent accessibility, contact map, and beta sheet structure with their counterparts predicted from its primary sequence. We trained and tested the method on the CASP6 dataset using cross‐validation. The correlation between predicted and true scores is 0.82. On the independent CASP7 dataset, the correlation averaged over 95 protein targets is 0.76; the average correlation for template‐based and ab initio targets is 0.82 and 0.50, respectively. Furthermore, the predicted absolute quality scores can be used to rank models effectively. The average difference (or loss) between the scores of the top‐ranked models and the best models is 5.70 on the CASP7 targets. This method performs favorably when compared with the other methods used on the same dataset. Moreover, the predicted absolute quality scores are comparable across models for different proteins. These features make the method a valuable tool for model quality assurance and ranking. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Semiparametric Bayesian estimation of quantile function for breast cancer survival data with cured fraction

Existing cure‐rate survival models are generally not convenient for modeling and estimating the survival quantiles of a patient with specified covariate values. This paper proposes a novel class of cure‐rate model, the transform‐both‐sides cure‐rate model (TBSCRM), that can be used to make inferences about both the cure‐rate and the survival quantiles. We develop the Bayesian inference about the covariate effects on the cure‐rate as well as on the survival quantiles via Markov Chain Monte Carlo (MCMC) tools. We also show that the TBSCRM‐based Bayesian method outperforms existing cure‐rate models based methods in our simulation studies and in application to the breast cancer survival data from the National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) database.     

Empirical geographic modeling of switchgrass yields in the United States

Switchgrass (Panicum virgatum L.) is a perennial grass native to the United States that has been studied as a sustainable source of biomass fuel. Although many field‐scale studies have examined the potential of this grass as a bioenergy crop, these studies have not been integrated. In this study, we present an empirical model for switchgrass yield and use this model to predict yield for the conterminous United States. We added environmental covariates to assembled yield data from field trials based on geographic location. We developed empirical models based on these data. The resulting empirical models, which account for spatial autocorrelation in the field data, provide the ability to estimate yield from factors associated with climate, soils, and management for both lowland and upland varieties of switchgrass. Yields of both ecotypes showed quadratic responses to temperature, increased with precipitation and minimum winter temperature, and decreased with stand age. Only the upland ecotype showed a positive response to our index of soil wetness and only the lowland ecotype showed a positive response to fertilizer. We view this empirical modeling effort, not as an alternative to mechanistic plant‐growth modeling, but rather as a first step in the process of functional validation that will compare patterns produced by the models with those found in data. For the upland variety, the correlation between measured yields and yields predicted by empirical models was 0.62 for the training subset and 0.58 for the test subset. For the lowland variety, the correlation was 0.46 for the training subset and 0.19 for the test subset. Because considerable variation in yield remains unexplained, it will be important in the future to characterize spatial and local sources of uncertainty associated with empirical yield estimates.     

Predicting and testing functional responses: An example from a tardigrade–nematode system

Numerous studies have empirically measured consumer functional responses or theoretically developed response models, but whether these models can quantitatively predict observed data has hardly been tested. We perform such a test for the terrestrial predator–prey system Macrobiotus richtersi (Tardigrada)–Acrobeloides nanus (Nematoda). For two different size classes of A. nanus, we report a functional response as measured in the laboratory and quantitatively compare it to predictions of three models with different degrees of complexity: (1) the disc equation which does not include satiation effects; (2) the steady-state satiation (SSS) equation which assumes a constant level of predator satiation; and (3) the satiation model which accounts for prey depletion and increasing predator satiation over the course of the experiments. We parameterized these models with data that were measured independently of the functional response experiments. In both prey-size classes, the predictions of the satiation model matched the observations best, and the match came close to that of logistic regressions fitted to the observations. Thus, the parameterized satiation model seems to include the most important determinants of the functional response in our focal system. For understanding functional responses, we need more studies that compare data to independently derived model predictions.     

A Misclassification Model for the Non‐Disjunction Fraction in Meiosis I

In this paper we introduce a misclassification model for the meiosis I non‐disjunction fraction in numerical chromosomal anomalies named trisomies. We obtain posteriors, and their moments, for the probability that a non‐disjunction occurs in the first division of meiosis and for the misclassification errors. We also extend previous works by providing the exact posterior, and its moments, for the probability that a non‐disjunction occurs in the first division of meiosis assuming the model proposed in the literature which does not consider that data are subject to misclassification. We perform Monte Carlo studies in order to compare Bayes estimates obtained by using both models. An application to Down Syndrome data is also presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Should ecologists prefer model‐ over distance‐based multivariate methods?

Ecological data sets often record the abundance of species, together with a set of explanatory variables. Multivariate statistical methods are optimal to analyze such data and are thus frequently used in ecology for exploration, visualization, and inference. Most approaches are based on pairwise distance matrices instead of the sites‐by‐species matrix, which stands in stark contrast to univariate statistics, where data models, assuming specific distributions, are the norm. However, through advances in statistical theory and computational power, models for multivariate data have gained traction. Systematic simulation‐based performance evaluations of these methods are important as guides for practitioners but still lacking. Here, we compare two model‐based methods, multivariate generalized linear models (MvGLMs) and constrained quadratic ordination (CQO), with two distance‐based methods, distance‐based redundancy analysis (dbRDA) and canonical correspondence analysis (CCA). We studied the performance of the methods to discriminate between causal variables and noise variables for 190 simulated data sets covering different sample sizes and data distributions. MvGLM and dbRDA differentiated accurately between causal and noise variables. The former had the lowest false‐positive rate (0.008), while the latter had the lowest false‐negative rate (0.027). CQO and CCA had the highest false‐negative rate (0.291) and false‐positive rate (0.256), respectively, where these error rates were typically high for data sets with linear responses. Our study shows that both model‐ and distance‐based methods have their place in the ecologist's statistical toolbox. MvGLM and dbRDA are reliable for analyzing species–environment relations, whereas both CQO and CCA exhibited considerable flaws, especially with linear environmental gradients.     

Evaluation of habitat suitability index models by global sensitivity and uncertainty analyses: a case study for submerged aquatic vegetation

Habitat suitability index (HSI) models are commonly used to predict habitat quality and species distributions and are used to develop biological surveys, assess reserve and management priorities, and anticipate possible change under different management or climate change scenarios. Important management decisions may be based on model results, often without a clear understanding of the level of uncertainty associated with model outputs. We present an integrated methodology to assess the propagation of uncertainty from both inputs and structure of the HSI models on model outputs (uncertainty analysis: UA) and relative importance of uncertain model inputs and their interactions on the model output uncertainty (global sensitivity analysis: GSA). We illustrate the GSA/UA framework using simulated hydrology input data from a hydrodynamic model representing sea level changes and HSI models for two species of submerged aquatic vegetation (SAV) in southwest Everglades National Park: Vallisneria americana (tape grass) and Halodule wrightii (shoal grass). We found considerable spatial variation in uncertainty for both species, but distributions of HSI scores still allowed discrimination of sites with good versus poor conditions. Ranking of input parameter sensitivities also varied spatially for both species, with high habitat quality sites showing higher sensitivity to different parameters than low‐quality sites. HSI models may be especially useful when species distribution data are unavailable, providing means of exploiting widely available environmental datasets to model past, current, and future habitat conditions. The GSA/UA approach provides a general method for better understanding HSI model dynamics, the spatial and temporal variation in uncertainties, and the parameters that contribute most to model uncertainty. Including an uncertainty and sensitivity analysis in modeling efforts as part of the decision‐making framework will result in better‐informed, more robust decisions.     

Age,sex and beauty: methodological dependence of age‐ and sex‐dichromatism in the great tit Parus major

Carotenoid‐based colour expression is frequently involved in sexual dichromatism, particularly in bird plumage, suggesting a role in sexual selection. Despite much work on expression of the carotenoid‐based ventral plumage coloration of the great tit (Parus major), which represents a popular model in evolution and ecology, a consensus on even the most basic demographic patterns of variation (e.g. age and sex differences) is lacking. This may reflect the use of variable methods for analysing colour variation, although what is not clear, either in this case or in general, is the extent to which these alternative methods are equally effective at describing age‐ and sex‐related dichromatism. Using data obtained over 4 years from a large sample of free‐ranging great tits, we examined how colour‐scoring methodology influences estimates of age‐ and sex‐related dichromatism. We compare: (1) principal components analysis‐derived scores; (2) tristimulus colour variables; (3) a visual model‐independent, carotenoid‐focussed colour score; and (4) two colour scoring methods based on avian visual models, examining how they assess colour variation with respect to age and sex to determine how methodology may influence results. We demonstrate clear age‐ and sex‐dependent expression of this colour trait, both in our own data and in meta‐analyses of results from great tit populations across Europe, and discuss the merits of the various colour scores, which yield very different estimates of the extent of age‐ and sex‐dependent dichromatism. We show variation is likely to be visible to conspecifics and propose a novel, visual model‐derived scoring system for describing variation in carotenoid‐based colour patches, where the perceived signal is divided into independent chromatic and achromatic components, in line with current understanding of visual perception. The present study highlights the impact of colour‐scoring methodology and shows that, as novel measures continue to be developed, researchers should consider carefully how they quantify colour expression. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 101 , 777–796.     

EMMLi: A maximum likelihood approach to the analysis of modularity

Identification of phenotypic modules, semiautonomous sets of highly correlated traits, can be accomplished through exploratory (e.g., cluster analysis) or confirmatory approaches (e.g., RV coefficient analysis). Although statistically more robust, confirmatory approaches are generally unable to compare across different model structures. For example, RV coefficient analysis finds support for both two‐ and six‐module models for the therian mammalian skull. Here, we present a maximum likelihood approach that takes into account model parameterization. We compare model log‐likelihoods of trait correlation matrices using the finite‐sample corrected Akaike Information Criterion, allowing for comparison of hypotheses across different model structures. Simulations varying model complexity and within‐ and between‐module contrast demonstrate that this method correctly identifies model structure and parameters across a wide range of conditions. We further analyzed a dataset of 3‐D data, consisting of 61 landmarks from 181 macaque (Macaca fuscata) skulls, distributed among five age categories, testing 31 models, including no modularity among the landmarks and various partitions of two, three, six, and eight modules. Our results clearly support a complex six‐module model, with separate within‐ and intermodule correlations. Furthermore, this model was selected for all five age categories, demonstrating that this complex pattern of integration in the macaque skull appears early and is highly conserved throughout postnatal ontogeny. Subsampling analyses demonstrate that this method is robust to relatively low sample sizes, as is commonly encountered in rare or extinct taxa. This new approach allows for the direct comparison of models with different parameterizations, providing an important tool for the analysis of modularity across diverse systems.     

The relative contribution of local habitat and landscape context to metapopulation processes: a dynamic occupancy modeling approach

Changes in site occupancy across habitat patches have often been attributed to landscape features in fragmented systems, particularly when considering metapopulations. However, failure to include habitat quality of individual patches can mask the relative importance of local scale features in determining distributional changes. We employed dynamic occupancy modeling to compare the strength of local habitat variables and metrics of landscape patterns as drivers of metapopulation dynamics for a vulnerable, high‐elevation species in a naturally fragmented landscape. Repeat surveys of Bicknell's thrush Catharus bicknelli presence/non‐detection were conducted at 88 sites across Vermont, USA in 2006 and 2007. We used an organism‐based approach, such that at each site we measured important local‐scale habitat characteristics and quantified landscape‐scale features using a predictive habitat model for this species. We performed a principal component analysis on both the local and landscape features to reduce dimensionality. We estimated site occupancy, colonization, and extinction probabilities while accounting for imperfect detection. Univariate, additive, and interaction models of local habitat and landscape context were ranked using AICc scores. Both local and landscape scales were important in determining changes in occupancy patterns. An interaction between scales was detected for occupancy dynamics indicating that the relationship of the parameters to local‐scale habitat conditions can change depending on the landscape context and vice versa. An increase in both landscape‐ and local‐scale habitat quality increased occupancy and colonization probability while decreasing extinction risk. Colonization and extinction were both more strongly influenced by local habitat quality relative to landscape patterns. We also identified clear, qualitative thresholds for landscape‐scale features. Conservation of large habitat patches in high‐cover landscapes will help ensure persistence of Bicknell's thrushes, but only if local scale habitat quality is maintained. Our results highlight the importance of incorporating information beyond landscape characteristics when investigating patch occupancy patterns in metapopulations.     

Confronting different models of community structure to species-abundance data: a Bayesian model comparison

Species abundances are undoubtedly the most widely available macroecological data, but can we use them to distinguish among several models of community structure? Here we present a Bayesian analysis of species‐abundance data that yields a full joint probability distribution of each model's parameters plus a relatively parameter‐independent criterion, the posterior Bayes factor, to compare these models. We illustrate our approach by comparing three classical distributions: the zero‐sum multinomial (ZSM) distribution, based on Hubbell's neutral model, the multivariate Poisson lognormal distribution (MPLN), based on niche arguments, and the discrete broken stick (DBS) distribution, based on MacArthur's broken stick model. We give explicit formulas for the probability of observing a particular species‐abundance data set in each model, and argue that conditioning on both sample size and species count is needed to allow comparisons between the two distributions. We apply our approach to two neotropical communities (trees, fish). We find that DBS is largely inferior to ZSM and MPLN for both communities. The tree data do not allow discrimination between ZSM and MPLN, but for the fish data ZSM (neutral model) overwhelmingly outperforms MPLN (niche model), suggesting that dispersal plays a previously underestimated role in structuring tropical freshwater fish communities. We advocate this approach for identifying the relative importance of dispersal and niche‐partitioning in determining diversity of different ecological groups of species under different environmental conditions.