A general method for controlling the genome-wide type I error rate in linkage and association mapping experiments in plants

Control of the genome-wide type I error rate (GWER) is an important issue in association mapping and linkage mapping experiments. For the latter, different approaches, such as permutation procedures or Bonferroni correction, were proposed. The permutation test, however, cannot account for population structure present in most association mapping populations. This can lead to false positive associations. The Bonferroni correction is applicable, but usually on the conservative side, because correlation of tests cannot be exploited. Therefore, a new approach is proposed, which controls the genome-wide error rate, while accounting for population structure. This approach is based on a simulation procedure that is equally applicable in a linkage and an association-mapping context. Using the parameter settings of three real data sets, it is shown that the procedure provides control of the GWER and the generalized genome-wide type I error rate (GWER(k)).     

Allelic association and disease mapping.

The application of allelic association to map genes for complex traits, particularly using high-density maps of single nucleotide polymorphisms in candidate regions, is an area of very active research. Here we present some aspects of the methodology and applications to both major gene mapping, which illustrates the effectiveness of the method, and oligogenes, where methods are still in flux and for which there have been relatively few successes to date. Several important considerations emerge, including the selection of the optimal metric for measuring association and the importance of modelling the decline in association with distance given the variability in association in a candidate region. The Malecot model of association with distance is shown to have a resolution of greater than 50 kilobases but the available evidence suggests that considerably higher resolution might be achieved with dense single nucleotide polymorphism (SNP) maps.     

Autoregressive spatial smoothing and temporal spline smoothing for mapping rates

This article proposes generalized additive mixed models for the analysis of geographic and temporal variability of mortality rates. This class of models accommodates random spatial effects and fixed and random temporal components. Spatiotemporal models that use autoregressive local smoothing across the spatial dimension and B-spline smoothing over the temporal dimension are developed. The objective is the identification of temporal treads and the production of a series of smoothed maps from which spatial patterns of mortality risks can be monitored over time. Regions with consistently high rate estimates may be followed for further investigation. The methodology is illustrated by analysis of British Columbia infant mortality data.     

Estimation in Bayesian disease mapping

Recent work on Bayesian inference of disease mapping models discusses the advantages of the fully Bayesian (FB) approach over its empirical Bayes (EB) counterpart, suggesting that FB posterior standard deviations of small-area relative risks are more reflective of the uncertainty associated with the relative risk estimation than counterparts based on EB inference, since the latter fail to account for the variability in the estimation of the hyperparameters. In this article, an EB bootstrap methodology for relative risk inference with accurate parametric EB confidence intervals is developed, illustrated, and contrasted with the hyperprior Bayes. We elucidate the close connection between the EB bootstrap methodology and hyperprior Bayes, present a comparison between FB inference via hybrid Markov chain Monte Carlo and EB inference via penalized quasi-likelihood, and illustrate the ability of parametric bootstrap procedures to adjust for the undercoverage in the "naive" EB interval estimates. We discuss the important roles that FB and EB methods play in risk inference, map interpretation, and real-life applications. The work is motivated by a recent analysis of small-area infant mortality rates in the province of British Columbia in Canada.     

At what spatial scales does resource selection vary? A case study of koalas in a semi‐arid region

The conservation of any species requires understanding and predicting the distribution of its habitat and resource use, including the effects of scale‐dependent variation in habitat and resource quality. Consequently, testing for resource selection at the appropriate scales is critical. We investigated how the resource selection process varies across scales, using koalas in a semi‐arid landscape of eastern Australia as a case study. We asked: at what scales does tree selection by koalas vary across regions? We tested the importance of the variation of our ecological predictors at the following scales: (i) the site‐scale (a stand of trees representing an individual koala's perception of local habitat); (ii) the landscape‐scale (10 × 10 km area representing a space within which a population of koalas exists); and (iii) a combination of these scales. We used a mixed‐modelling approach to quantify variation in selection of individual trees by koalas among sites and landscapes within a 1600 km² study area. We found that tree species, and tree height, were the most important factors influencing tree selection, and that their effect did not vary across scales. In contrast, preferences for trees of different condition, which is the state of tree canopy health, did vary across landscapes, indicating spatial variation in the selection of trees with respect to tree condition at the landscape‐scale, but not at the site‐scale. We conclude that resource selection processes can depend on the quality of those resources at different scales and their heterogeneous nature across landscapes, highlighting the consequence of scale‐dependent ecological processes. Designing studies that capture the heterogeneity in habitat and resources used by species that have an extensive distribution is an important prerequisite for effective conservation planning and management.     

Logistic regression when covariates are random effects from a non‐linear mixed model

In many studies, the association of longitudinal measurements of a continuous response and a binary outcome are often of interest. A convenient framework for this type of problems is the joint model, which is formulated to investigate the association between a binary outcome and features of longitudinal measurements through a common set of latent random effects. The joint model, which is the focus of this article, is a logistic regression model with covariates defined as the individual‐specific random effects in a non‐linear mixed‐effects model (NLMEM) for the longitudinal measurements. We discuss different estimation procedures, which include two‐stage, best linear unbiased predictors, and various numerical integration techniques. The proposed methods are illustrated using a real data set where the objective is to study the association between longitudinal hormone levels and the pregnancy outcome in a group of young women. The numerical performance of the estimating methods is also evaluated by means of simulation.     

Polytomous disease mapping to detect uncommon risk factors for related diseases

A statistical model for jointly analysing the spatial variation of incidences of three (or more) diseases, with common and uncommon risk factors, is introduced. Deaths for different diseases are described by a logit model for multinomial responses (multinomial logit or polytomous logit model). For each area and confounding strata population (i.e. age-class, sex, race) the probabilities of death for each cause (the response probabilities) are estimated. A specic disease, the one having a common risk factor only, acts as the baseline category. The log odds are decomposed additively into shared (common to diseases different by the reference disease) and specic structured spatial variability terms, unstructured unshared spatial terms and confounders terms (such as age, race and sex) to adjust the crude observed data for their effects. Disease specic spatially structured effects are estimated; these are considered as latent variables denoting disease-specic risk factors. The model is presented with reference to a specic application. We considered the mortality data (from 1990 to 1994) relative to oral cavity, larynx and lung cancers in 13 age groups of males, in the 287 municipalities of Region of Tuscany (Italy). All these pathologies share smoking as a common risk factor; furthermore, two of them (oral cavity and larynx cancer) share alcohol consumption as a risk factor. All studies suggest that smoking and alcohol consumption are the major known risk factors for oral cavity and larynx cancers; nevertheless, in this paper, we investigate the possibility of other different risk factors for these diseases, or even the presence of an interaction effect (between smoking and alcohol risk factors) but with different spatial patterns for oral and larynx cancer. For each municipality and age-class the probabilities of death for each cause (the response probabilities) are estimated. Lung cancer acts as the baseline category. The log odds are decomposed additively into shared (common to oral cavity and larynx diseases) and specic structured spatial variability terms, unstructured unshared spatial terms and an age-group term. It turns out that oral cavity and larynx cancer have different spatial patterns for residual risk factors which are not the typical ones such as smoking habits and alcohol consumption. But, possibly, these patterns are due to different spatial interactions between smoking habits and alcohol consumption for the first and the second disease.     

An individual level infectious disease model in the presence of uncertainty from multiple,imperfect diagnostic tests

Bayesian compartmental infectious disease models yield important inference on disease transmission by appropriately accounting for the dynamics and uncertainty of infection processes. In addition to estimating transition probabilities and reproductive numbers, these statistical models allow researchers to assess the probability of disease risk and quantify the effectiveness of interventions. These infectious disease models rely on data collected from all individuals classified as positive based on various diagnostic tests. In infectious disease testing, however, such procedures produce both false-positives and false-negatives at varying rates depending on the sensitivity and specificity of the diagnostic tests being used. We propose a novel Bayesian spatio-temporal infectious disease modeling framework that accounts for the additional uncertainty in the diagnostic testing and classification process that provides estimates of the important transmission dynamics of interest to researchers. The method is applied to data on the 2006 mumps epidemic in Iowa, in which over 6,000 suspected mumps cases were tested using a buccal or oral swab specimen, a urine specimen, and/or a blood specimen. Although all procedures are believed to have high specificities, the sensitivities can be low and vary depending on the timing of the test as well as the vaccination status of the individual being tested.     

Regional vegetation mapping in Australia: a case study in the practical use of statistical modelling

Conservation evaluation of large areas ( > 10 000 km²) in Australia requires detailed mapping of vegetation types. Predicting the original vegetation cover of extensive cleared areas in an explicit, consistent and repeatable manner necessitates the use of statistical modelling. This paper describes an integrated approach to vegetation mapping in a region of New South Wales, Australia. The approach uses separate statistical models for each tree and shrub species to predict the vegetation composition in each grid cell in a geographic information system (GIS). Allocation of these grid cells to communities allows communities that no longer exist in the remaining remnants of woodland to be defined. Examples of use of this information for management are presented. This paper addresses the practical considerations which constrain the way statistical modelling can be used for vegetation mapping in an applied project. Constraints include: (1) data availability (use of sampling to fill gaps in existing data), (2) the effects of cover abundance values, (3) availability of GIS predictors, (4) data management, (5) current generalised additive model methods and (6) prediction methods. Careful attention to the practicality of all components of a vegetation mapping study is essential if modern methods are to be applied in regional studies which must provide functional products for land managers with limited resources, skills and finances at their disposal.     

Does dispersal capacity matter for freshwater biodiversity under climate change?

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Developing approaches for linear mixed modeling in landscape genetics through landscape‐directed dispersal simulations

Dispersal can impact population dynamics and geographic variation, and thus, genetic approaches that can establish which landscape factors influence population connectivity have ecological and evolutionary importance. Mixed models that account for the error structure of pairwise datasets are increasingly used to compare models relating genetic differentiation to pairwise measures of landscape resistance. A model selection framework based on information criteria metrics or explained variance may help disentangle the ecological and landscape factors influencing genetic structure, yet there are currently no consensus for the best protocols. Here, we develop landscape‐directed simulations and test a series of replicates that emulate independent empirical datasets of two species with different life history characteristics (greater sage‐grouse; eastern foxsnake). We determined that in our simulated scenarios, AIC and BIC were the best model selection indices and that marginal R² values were biased toward more complex models. The model coefficients for landscape variables generally reflected the underlying dispersal model with confidence intervals that did not overlap with zero across the entire model set. When we controlled for geographic distance, variables not in the underlying dispersal models (i.e., nontrue) typically overlapped zero. Our study helps establish methods for using linear mixed models to identify the features underlying patterns of dispersal across a variety of landscapes.     

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.     

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.     

Estimation of Spatial Variation in Risk Using Matched Case‐control Data

A common problem in environmental epidemiology is to estimate spatial variation in disease risk after accounting for known risk factors. In this paper we consider this problem in the context of matched case‐control studies. We extend the generalised additive model approach of Kelsall and Diggle (1998) to studies in which each case has been individually matched to a set of controls. We discuss a method for fitting this model to data, apply the method to a matched study on perinatal death in the North West Thames region of England and explain why, if spatial variation is of particular scientific interest, matching is undesirable.     

On small‐sample inference in group randomized trials with binary outcomes and cluster‐level covariates

Group randomized trials (GRTs) randomize groups, or clusters, of people to intervention or control arms. To test for the effectiveness of the intervention when subject‐level outcomes are binary, and while fitting a marginal model that adjusts for cluster‐level covariates and utilizes a logistic link, we develop a pseudo‐Wald statistic to improve inference. Alternative Wald statistics could employ bias‐corrected empirical sandwich standard error estimates, which have received limited attention in the GRT literature despite their broad utility and applicability in our settings of interest. The test could also be carried out using popular approaches based upon cluster‐level summary outcomes. A simulation study covering a variety of realistic GRT settings is used to compare the accuracy of these methods in terms of producing nominal test sizes. Tests based upon the pseudo‐Wald statistic and a cluster‐level summary approach utilizing the natural log of observed cluster‐level odds worked best. Due to weighting, some popular cluster‐level summary approaches were found to lead to invalid inference in many settings. Finally, although use of bias‐corrected empirical sandwich standard error estimates did not consistently result in nominal sizes, they did work well, thus supporting the applicability of marginal models in GRT settings.     

Egg limitation and individual variation in parasitization risk among hosts in host–parasitoid dynamics

Egg limitation is known to destabilize host–parasitoid dynamics. This study reexamines the effect of egg limitation in light of the individual variation in parasitization risk among hosts (e.g., some hosts are more likely to be parasitized than others). Previous studies have considered egg limitation (predicted as a destabilizing factor) and individual variation among hosts (predicted as a stabilizing factor) in isolation; however, their interaction is not known. An individual‐based model was used to examine the effects of each factor and their interaction. The model‐based analysis shows a clear interaction between egg limitation and individual variation in risk among hosts. Egg limitation can both stabilize and destabilize host–parasitioid dynamics depending on the presence and absence of the risk variation. The result suggests that the population‐dynamic consequences of egg limitation are more complex than previously thought and emphasizes the importance of the simultaneous consideration of multiple ecological factors (with individual‐level details) to uncover potential interactions among them.     

The theoretical basis and practical application of relationships between different disease intensity measurements in plants

The literature concerning relationships among different measures of plant disease intensity is reviewed. Some previous confusion over the definition of the terms “incidence” and “severity” is noted and clarified. The review highlights the common features of relationships between incidence and severity, incidence and disease density, and incidence at pairs of scales in a spatial hierarchy. These relationships often show a similar saturation curve form that can frequently be described empirically using the complementary log‐log transformation. A catalogue of alternative functional forms is provided. Practical applications in varietal evaluation are discussed.     

Exploring spatial and temporal variations of cadmium concentrations in pacific oysters from british columbia

Oysters from the Pacific Northwest coast of British Columbia, Canada, contain high levels of cadmium, in some cases exceeding some international food safety guidelines. A primary goal of this article is the investigation of the spatial and temporal variation in cadmium concentrations for oysters sampled from coastal British Columbia. Such information is important so that recommendations can be made as to where and when oysters can be cultured such that accumulation of cadmium within these oysters is minimized. Some modern statistical methods are applied to achieve this goal, including monotone spline smoothing, functional principal component analysis, and semi-parametric additive modeling. Oyster growth rates are estimated as the first derivatives of the monotone smoothing growth curves. Some important patterns in cadmium accumulation by oysters are observed. For example, most inland regions tend to have a higher level of cadmium concentration than most coastal regions, so more caution needs to be taken for shellfish aquaculture practices occurring in the inland regions. The semi-parametric additive modeling shows that oyster cadmium concentration decreases with oyster length, and oysters sampled at 7 m have higher average cadmium concentration than those sampled at 1 m.