Geostatistical modelling enables efficient safety assessment for mass drug administration with ivermectin in Loa loa endemic areas through a combined antibody and LoaScope testing strategy for elimination of onchocerciasis

The elimination of onchocerciasis through community-based Mass Drug Administration (MDA) of ivermectin (Mectizan) is hampered by co-endemicity of Loa loa, as individuals who are highly co-infected with Loa loa parasites can suffer serious and occasionally fatal neurological reactions from the drug. The test-and-not-treat strategy of testing all individuals participating in MDA has some operational constraints including the cost and limited availability of LoaScope diagnostic tools. As a result, a Loa loa Antibody (Ab) Rapid Test was developed to offer a complementary way of determining the prevalence of loiasis. We develop a joint geostatistical modelling framework for the analysis of Ab and Loascope data to delineate whether an area is safe for MDA. Our results support the use of a two-stage strategy, in which Ab testing is used to identify areas that, with acceptably high probability, are safe or unsafe for MDA, followed by Loascope testing in areas whose safety status is uncertain. This work therefore contributes to the global effort towards the elimination of onchocerciasis as a public health problem by potentially reducing the time and cost required to establish whether an area is safe for MDA.     

Characterising spatial patterns of neglected tropical disease transmission using integrated sero-surveillance in Northern Ghana

BackgroundAs prevalence decreases in pre-elimination settings, identifying the spatial distribution of remaining infections to target control measures becomes increasingly challenging. By measuring multiple antibody responses indicative of past exposure to different pathogens, integrated serological surveys enable simultaneous characterisation of residual transmission of multiple pathogens.Methodology/Principal findingsHere, we combine integrated serological surveys with geostatistical modelling and remote sensing-derived environmental data to estimate the spatial distribution of exposure to multiple diseases in children in Northern Ghana. The study utilised the trachoma surveillance survey platform (cross-sectional two-stage cluster-sampled surveys) to collect information on additional identified diseases at different stages of elimination with minimal additional cost. Geostatistical modelling of serological data allowed identification of areas with high probabilities of recent exposure to diseases of interest, including areas previously unknown to control programmes. We additionally demonstrate how serological surveys can be used to identify areas with exposure to multiple diseases and to prioritise areas with high uncertainty for future surveys. Modelled estimates of cluster-level prevalence were strongly correlated with more operationally feasible metrics of antibody responses.Conclusions/SignificanceThis study demonstrates the potential of integrated serological surveillance to characterise spatial distributions of exposure to multiple pathogens in low transmission and elimination settings when the probability of detecting infections is low.     

Accounting for multi‐scale spatial autocorrelation improves performance of invasive species distribution modelling (iSDM)

Aim Analyses of species distributions are complicated by various origins of spatial autocorrelation (SAC) in biogeographical data. SAC may be particularly important for invasive species distribution models (iSDMs) because biological invasions are strongly influenced by dispersal and colonization processes that typically create highly structured distribution patterns. We examined the efficacy of using a multi‐scale framework to account for different origins of SAC, and compared non‐spatial models with models that accounted for SAC at multiple levels. Location We modelled the spatial distribution of an invasive forest pathogen, Phytophthora ramorum, in western USA. Methods We applied one conventional statistical method (generalized linear model, GLM) and one nonparametric technique (maximum entropy, Maxent) to a large dataset on P. ramorum occurrence (n = 3787) to develop four types of model that included environmental variables and that either ignored spatial context or incorporated it at a broad scale using trend surface analysis, a local scale using autocovariates, or multiple scales using spatial eigenvector mapping. We evaluated model accuracies and amounts of explained spatial structure, and examined the changes in predictive power of the environmental and spatial variables. Results Accounting for different scales of SAC significantly enhanced the predictive capability of iSDMs. Dramatic improvements were observed when fine‐scale SAC was included, suggesting that local range‐confining processes are important in P. ramorum spread. The importance of environmental variables was relatively consistent across all models, but the explanatory power decreased in spatial models for factors with strong spatial structure. While accounting for SAC reduced the amount of residual autocorrelation for GLM but not for Maxent, it still improved the performance of both approaches, supporting our hypothesis that dispersal and colonization processes are important factors to consider in distribution models of biological invasions. Main conclusions Spatial autocorrelation has become a paradigm in biogeography and ecological modelling. In addition to avoiding the violation of statistical assumptions, accounting for spatial patterns at multiple scales can enhance our understanding of dynamic processes that explain ecological mechanisms of invasion and improve the predictive performance of static iSDMs.     

Geostatistical modelling on stream networks: developing valid covariance matrices based on hydrologic distance and stream flow

1. Geostatistical models based on Euclidean distance fail to represent the spatial configuration, connectivity, and directionality of sites in a stream network and may not be ecologically relevant for many chemical, physical and biological studies of freshwater streams. Functional distance measures, such as symmetric and asymmetric hydrologic distance, more accurately represent the transfer of organisms, material and energy through stream networks. However, calculating the hydrologic distances for a large study area remains challenging and substituting hydrologic distance for Euclidean distance may violate geostatistical modelling assumptions. 2. We provide a review of geostatistical modelling assumptions and discuss the statistical and ecological consequences of substituting hydrologic distance measures for Euclidean distance. We also describe a new family of autocovariance models that we developed for stream networks, which are based on hydrologic distance measures. 3. We describe the geographical information system (GIS) methodology used to generate spatial data necessary for geostatistical modelling in stream networks. We also provide an example that illustrates the methodology used to create a valid covariance matrix based on asymmetric hydrologic distance and weighted by discharge volume, which can be incorporated into common geostatistical models. 4. The methodology and tools described supply ecologically meaningful and statistically valid geostatistical models for stream networks. They also provide stream ecologists with the opportunity to develop their own functional measures of distance and connectivity, which will improve geostatistical models developed for stream networks in the future. 5. The GIS tools presented here are being made available in order to facilitate the application of valid geostatistical modelling in freshwater ecology.     

Updating bird species distribution at large spatial scales: applications of habitat modelling to data from long-term monitoring programs

Mapping of species distributions at large spatial scales has been often based on the representation of gathered observations in a general grid atlas framework. More recently, subsampling and subsequent interpolation or habitat spatial modelling techniques have been incorporated in these projects to allow more detailed species mapping. Here, we explore the usefulness of data from long-term monitoring (LTM) projects, primarily aimed at estimating trends in species abundance and collected at shorter time intervals (usually yearly) than atlas data, to develop predictive habitat models. We modelled habitat occupancy for 99 species using a bird LTM program and evaluated the predictive accuracy of these models using independent data from a contemporary and comprehensive breeding bird atlas project from the same region. Habitat models from LTM data using generalized linear modelling were significant for all the species and generally showed a high predictive power, albeit lower than that from atlas models. Sample size and species range size and niche breadth were the most important factors behind variability in model predictive accuracy, whereas the spatial distribution of sampling units at a given sample size had minor effects. Although predictive accuracy of habitat modelling was strongly species dependent, increases in sample size and, secondarily, a better spatial distribution of sampling units should lead to more powerful predictive distribution models. We suggest that data from LTM programs, now established in a large number of countries, has the potential for being a major source of good quality data suitable for the estimation and regularly update of distributions at large spatial scales for a number of species.     

Mapping landscape services,spatial synergies and trade-offs. A case study using variogram models and geostatistical simulations in an agrarian landscape in North-East Germany

This paper presents a probabilistic approach for mapping and assessment of services provided by landscapes, based on variogram modelling and geostatistical simulations. Of operational value is that several services can be treated and mapped simultaneously, providing an efficient tool to model the heterogeneity of different landscape components. The methodology was adopted to depict spatial heterogeneity of five landscape services in the case study area of Märkische Schweiz in North East Germany: habitat for species, crop production, visual appreciation, water supply, and water regulation. Results, displayed in terms of single and joint probability maps, provide new insights about the composition and interrelation of multiple services in a region. It is shown that each landscape service is characterised by a specific spatial pattern, described in terms of heterogeneity and spatial range. Setting a probability threshold of service occurrence >0.50, 10% of the area under agricultural land uses provides no landscape services, 35% delivers one service while 25% and 19% supply two and three services, respectively. The share of agricultural area with a potential joint provision of four services equals 10%, while only 1.4% of the area has a potential to deliver five joint landscape services. The highest mean join probability is that observed for the common supply of production and habitat services (30%), highlighting the occurrence of hotspots of services provision with possible conflicts due to the on-going intensification of agricultural management.     

Two-stage lot quality assurance sampling framework for monitoring and evaluation of neglected tropical diseases,allowing for imperfect diagnostics and spatial heterogeneity

BackgroundMonitoring and evaluation (M&E) is a key component of large-scale neglected tropical diseases (NTD) control programs. Diagnostic tests deployed in these M&E surveys are often imperfect, and it remains unclear how this affects the population-based program decision-making.MethodologyWe developed a 2-stage lot quality assurance sampling (LQAS) framework for decision-making that allows for both imperfect diagnostics and spatial heterogeneity of infections. We applied the framework to M&E of soil-transmitted helminth control programs as a case study. For this, we explored the impact of the diagnostic performance (sensitivity and specificity), spatial heterogeneity (intra-cluster correlation), and survey design on program decision-making around the prevalence decisions thresholds recommended by WHO (2%, 10%, 20% and 50%) and the associated total survey costs.Principal findingsThe survey design currently recommended by WHO (5 clusters and 50 subjects per cluster) may lead to incorrect program decisions around the 2% and 10% prevalence thresholds, even when perfect diagnostic tests are deployed. To reduce the risk of incorrect decisions around the 2% prevalence threshold, including more clusters (≥10) and deploying highly specific diagnostic methods (≥98%) are the most-cost saving strategies when spatial heterogeneity is moderate-to-high (intra-cluster correlation >0.017). The higher cost and lower throughput of improved diagnostic tests are compensated by lower required sample sizes, though only when the cost per test is <6.50 US$ and sample throughput is ≥3 per hour.Conclusion/SignificanceOur framework provides a means to assess and update M&E guidelines and guide product development choices for NTD. Using soil-transmitted helminths as a case study, we show that current M&E guidelines may severely fall short, particularly in low-endemic and post-control settings. Furthermore, specificity rather than sensitivity is a critical parameter to consider. When the geographical distribution of an NTD within a district is highly heterogeneous, sampling more clusters (≥10) may be required.     

Spatial prediction of malaria prevalence in an endemic area of Bangladesh

Background

Malaria is a major public health burden in Southeastern Bangladesh, particularly in the Chittagong Hill Tracts region. Malaria is endemic in 13 districts of Bangladesh and the highest prevalence occurs in Khagrachari (15.47%).

Methods

A risk map was developed and geographic risk factors identified using a Bayesian approach. The Bayesian geostatistical model was developed from previously identified individual and environmental covariates (p < 0.2; age, different forest types, elevation and economic status) for malaria prevalence using WinBUGS 1.4. Spatial correlation was estimated within a Bayesian framework based on a geostatistical model. The infection status (positives and negatives) was modeled using a Bernoulli distribution. Maps of the posterior distributions of predicted prevalence were developed in geographic information system (GIS).

Results

Predicted high prevalence areas were located along the north-eastern areas, and central part of the study area. Low to moderate prevalence areas were predicted in the southwestern, southeastern and central regions. Individual age and nearness to fragmented forest were associated with malaria prevalence after adjusting the spatial auto-correlation.

Conclusion

A Bayesian analytical approach using multiple enabling technologies (geographic information systems, global positioning systems, and remote sensing) provide a strategy to characterize spatial heterogeneity in malaria risk at a fine scale. Even in the most hyper endemic region of Bangladesh there is substantial spatial heterogeneity in risk. Areas that are predicted to be at high risk, based on the environment but that have not been reached by surveys are identified.

     

Precision gain versus effort with joint models using detection/non‐detection and banding data

Capture–recapture techniques provide valuable information, but are often more cost‐prohibitive at large spatial and temporal scales than less‐intensive sampling techniques. Model development combining multiple data sources to leverage data source strengths and for improved parameter precision has increased, but with limited discussion on precision gain versus effort. We present a general framework for evaluating trade‐offs between precision gained and costs associated with acquiring multiple data sources, useful for designing future or new phases of current studies.We illustrated how Bayesian hierarchical joint models using detection/non‐detection and banding data can improve abundance, survival, and recruitment inference, and quantified data source costs in a northern Arizona, USA, western bluebird (Sialia mexicana) population. We used an 8‐year detection/non‐detection (distributed across the landscape) and banding (subset of locations within landscape) data set to estimate parameters. We constructed separate models using detection/non‐detection and banding data, and a joint model using both data types to evaluate parameter precision gain relative to effort.Joint model parameter estimates were more precise than single data model estimates, but parameter precision varied (apparent survival > abundance > recruitment). Banding provided greater apparent survival precision than detection/non‐detection data. Therefore, little precision was gained when detection/non‐detection data were added to banding data. Additional costs were minimal; however, additional spatial coverage and ability to estimate abundance and recruitment improved inference. Conversely, more precision was gained when adding banding to detection/non‐detection data at higher cost. Spatial coverage was identical, yet survival and abundance estimates were more precise. Justification of increased costs associated with additional data types depends on project objectives.We illustrate a general framework for evaluating precision gain relative to effort, applicable to joint data models with any data type combination. This framework evaluates costs and benefits from and effort levels between multiple data types, thus improving population monitoring designs.     

Bayesian case influence diagnostics for survival models

We propose Bayesian case influence diagnostics for complex survival models. We develop case deletion influence diagnostics for both the joint and marginal posterior distributions based on the Kullback-Leibler divergence (K-L divergence). We present a simplified expression for computing the K-L divergence between the posterior with the full data and the posterior based on single case deletion, as well as investigate its relationships to the conditional predictive ordinate. All the computations for the proposed diagnostic measures can be easily done using Markov chain Monte Carlo samples from the full data posterior distribution. We consider the Cox model with a gamma process prior on the cumulative baseline hazard. We also present a theoretical relationship between our case-deletion diagnostics and diagnostics based on Cox's partial likelihood. A simulated data example and two real data examples are given to demonstrate the methodology.     

Variogram analysis of the spatial genetic structure of continuous populations using multilocus microsatellite data

A geostatistical perspective on spatial genetic structure may explain methodological issues of quantifying spatial genetic structure and suggest new approaches to addressing them. We use a variogram approach to (i) derive a spatial partitioning of molecular variance, gene diversity, and genotypic diversity for microsatellite data under the infinite allele model (IAM) and the stepwise mutation model (SMM), (ii) develop a weighting of sampling units to reflect ploidy levels or multiple sampling of genets, and (iii) show how variograms summarize the spatial genetic structure within a population under isolation-by-distance. The methods are illustrated with data from a population of the epiphytic lichen Lobaria pulmonaria, using six microsatellite markers. Variogram-based analysis not only avoids bias due to the underestimation of population variance in the presence of spatial autocorrelation, but also provides estimates of population genetic diversity and the degree and extent of spatial genetic structure accounting for autocorrelation.     

An approach to multiscale modelling with graph grammars

Background and Aims

Functional–structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs.

Methods

A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL.

Key Results

Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas.

Conclusions

The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.     

Incorporating DEM Uncertainty in Coastal Inundation Mapping

Coastal managers require reliable spatial data on the extent and timing of potential coastal inundation, particularly in a changing climate. Most sea level rise (SLR) vulnerability assessments are undertaken using the easily implemented bathtub approach, where areas adjacent to the sea and below a given elevation are mapped using a deterministic line dividing potentially inundated from dry areas. This method only requires elevation data usually in the form of a digital elevation model (DEM). However, inherent errors in the DEM and spatial analysis of the bathtub model propagate into the inundation mapping. The aim of this study was to assess the impacts of spatially variable and spatially correlated elevation errors in high-spatial resolution DEMs for mapping coastal inundation. Elevation errors were best modelled using regression-kriging. This geostatistical model takes the spatial correlation in elevation errors into account, which has a significant impact on analyses that include spatial interactions, such as inundation modelling. The spatial variability of elevation errors was partially explained by land cover and terrain variables. Elevation errors were simulated using sequential Gaussian simulation, a Monte Carlo probabilistic approach. 1,000 error simulations were added to the original DEM and reclassified using a hydrologically correct bathtub method. The probability of inundation to a scenario combining a 1 in 100 year storm event over a 1 m SLR was calculated by counting the proportion of times from the 1,000 simulations that a location was inundated. This probabilistic approach can be used in a risk-aversive decision making process by planning for scenarios with different probabilities of occurrence. For example, results showed that when considering a 1% probability exceedance, the inundated area was approximately 11% larger than mapped using the deterministic bathtub approach. The probabilistic approach provides visually intuitive maps that convey uncertainties inherent to spatial data and analysis.     

Multiple-Imputation-Based Residuals and Diagnostic Plots for Joint Models of Longitudinal and Survival Outcomes

Summary .  The majority of the statistical literature for the joint modeling of longitudinal and time-to-event data has focused on the development of models that aim at capturing specific aspects of the motivating case studies. However, little attention has been given to the development of diagnostic and model-assessment tools. The main difficulty in using standard model diagnostics in joint models is the nonrandom dropout in the longitudinal outcome caused by the occurrence of events. In particular, the reference distribution of statistics, such as the residuals, in missing data settings is not directly available and complex calculations are required to derive it. In this article, we propose a multiple-imputation-based approach for creating multiple versions of the completed data set under the assumed joint model. Residuals and diagnostic plots for the complete data model can then be calculated based on these imputed data sets. Our proposals are exemplified using two real data sets.     

Ecological genomics meets community‐level modelling of biodiversity: mapping the genomic landscape of current and future environmental adaptation

Local adaptation is a central feature of most species occupying spatially heterogeneous environments, and may factor critically in responses to environmental change. However, most efforts to model the response of species to climate change ignore intraspecific variation due to local adaptation. Here, we present a new perspective on spatial modelling of organism–environment relationships that combines genomic data and community‐level modelling to develop scenarios regarding the geographic distribution of genomic variation in response to environmental change. Rather than modelling species within communities, we use these techniques to model large numbers of loci across genomes. Using balsam poplar (Populus balsamifera) as a case study, we demonstrate how our framework can accommodate nonlinear responses of loci to environmental gradients. We identify a threshold response to temperature in the circadian clock gene GIGANTEA‐5 (GI5), suggesting that this gene has experienced strong local adaptation to temperature. We also demonstrate how these methods can map ecological adaptation from genomic data, including the identification of predicted differences in the genetic composition of populations under current and future climates. Community‐level modelling of genomic variation represents an important advance in landscape genomics and spatial modelling of biodiversity that moves beyond species‐level assessments of climate change vulnerability.     

Auditing reforested watersheds on the loess plateau: Fangshan Shanxi

Mapping watershed ecosystems, evaluating their ecological status and modelling land use futures are the aims of a project undertaken by an interdisciplinary team from Shanxi Forestry Academy and Watershed Systems Living Water Foundation. The project introduces geospatial methodologies and iGiS technologies for (a) mapping and modelling watersheds and (b) monitoring and evaluating rangeland restoration after reassigning collective forest lands to local farmers in accordance with land reform policies.Two contemporary geospatial technologies were instrumental in the Fangshan project. These technologies are driving a paradigm shift in the way primary industries like mining, farming and forestry utilize GIS, engage in land evaluations, resource mapping, environmental assessments and product certification.

• •Firstly, high resolution, true image 3D orthophoto mapping was produced as the iGiS map platform for the Fangshan project. The true colour orthophoto maps produced by the team proved very suitable, with the high resolution imagery achieving cartographic standards allowing draft mapping at 1:2000. Because unique x,y,z geocentroid coordinates are generated for each and every pixel in the orthophoto mapping process, detailed iGiS data bases with multiple attributes ranked parametrically were readily captured and recorded for every habitat and regolith.
• •Secondly, the Shanxi Forest Academy team were trained in geospatial methodologies for mapping watershed ecosystems and modelling their habitat/regolith/energy relationships. Using GiS imaging technologies, these cartographic simulation methodologies enable ecological modelling of watersheds and their subterranean water systems, while providing a framework for monitoring and evaluating the environmental health of watersheds using permanent benchmarks and ecological indicators.

Habitat mapping and modelling of Fangshan watersheds revealed how ecological restoration is gradually occurring through strategic combinations of planned reforestation, traditional terrace farming systems and natural regeneration. These ecological strategies are shown to be beneficial land use partners in restoring the mountain rangelands, riparian ecostructures and ecosystem functions of degraded loess plateau watersheds.     

Hierarchical Bayesian geostatistics for C stock prediction in disturbed plantation forest in Zimbabwe

We develop and present a novel Bayesian hierarchical geostatistical model for the prediction of plantation forest carbon stock (C stock) in the eastern highlands of Zimbabwe using multispectral Landsat-8 and Sentinel-2 remotely sensed data. Specifically, we adopt a Bayesian hierarchical methodology encompassing a model-based inferential framework making use of efficient Markov Chain Monte Carlo (MCMC) techniques for assessing model input parameters. Our proposed hierarchical modelling framework evaluates the influence of two but related covariate information sources in C stock prediction in order to build sustainable capacity on carbon reporting and monitoring. The perceived improvements in the spectral and spatial properties of Landsat-8 and Sentinel-2 data and their potential to predict C stock with shorter uncertainty bounds is tested in the developed hierarchical Bayesian models. We utilized the Mean Squared Shortest Distance (MSSD) as the objective function for optimization of sampling locations for equal area coverage. Specifically, we evaluated the models using four selected remotely sensed vegetation indices namely, the normalised difference vegetation index (NDVI), soil adjusted vegetation index (SAVI), enhanced vegetation index (EVI) and an additional distance to settlements anthropogenic variable that justifies from the history of the studied plantation forest in the eastern highlands of Zimbabwe. We evaluated two models making use of Landsat-8 and Sentinel-2 derived predictors using the Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Coverage (CVG) and Deviance Information Criteria (DIC). The Sentinel-2 based C stock model resulted in RMSE of 1.16 MgCha⁻¹, MAE of 1.11 MgCha⁻¹, CVG of 94.7% and a DIC of −554.7 whilst its Landsat-8 based C stock counterpart yielded a RMSE, MAE, CVG and DIC of 2.69 MgCha⁻¹, 1.77 MgCha⁻¹, 85.4% and 43.1 respectively. Although predictive models from both sensors show great improvement in predictive accuracy when modelling the spatial random effects, the Sentinel-2 based C stock predictive model substantially outperforms its Landsat-8 based C stock counterpart. The Sentinel-2 based C stock predictive hierarchical model therefore adequately addresses multiple sources of uncertainty inherent in the spatial prediction of C stock in disturbed plantation ecosystems. It is evident from the results of this study that carbon reporting and monitoring can always be improved by scouting for improved and easily accessible remote sensing data and allow forest practitioners to keep track of error across space in resource environments of interest.     

Identifying spatial relationships at multiple scales: principal coordinates of neighbour matrices (PCNM) and geostatistical approaches

We compared two methodological approaches – principal coordinate analysis of neighbour matrices (PCNM) and geostatistics – that both aim at extracting several spatial scales in order to identify spatial relationships between organisms and environmental variables at multiple scales. From a statistical point of view, PCNM analysis and geostatistics come from "two different worlds"– PCNM is based on classical "data analysis" while geostatistical modelling is developed in a probabilistic context. These two methods were used to investigate the spatial relationships between defoliation caused by spruce budworm Choristoneura fumiferana and bioclimatic conditions in Ontario since 1941 through a wide range of scales. On the one hand, PCNM variables related to defoliation frequency were partitioned into four spatial submodels representing respectively four spatial scales: very broad scale (ca>300 km), broad scale (ca 180 km), fine (ca 100 km), and very fine (<80 km). On the other hand, nested variogram modelling was used to identify the relevant scales. The nested variogram model was composed of four variograms with different characteristic scales close to those of the PCNM spatial submodels. Maps of PCNM submodels and kriging components revealed similar spatial patterns of defoliation frequency at very broad and broad scales while spatial patterns at fine and very fine scales looked quite different. Both methods showed that defoliation by spruce budworm occurs at the broader spatial scales but may be explained by fluctuations at the smaller scales. Finally, results based on geostatistics using a Linear Model of Coregionalisation suggested that climatic conditions can be considered to act at the level of outbreak dynamics while the tree community of spruce budworm's principal hosts controls local population dynamics.     

Bayesian mapping of quantitative trait loci for multiple complex traits with the use of variance components

Complex traits important for humans are often correlated phenotypically and genetically. Joint mapping of quantitative-trait loci (QTLs) for multiple correlated traits plays an important role in unraveling the genetic architecture of complex traits. Compared with single-trait analysis, joint mapping addresses more questions and has advantages for power of QTL detection and precision of parameter estimation. Some statistical methods have been developed to map QTLs underlying multiple traits, most of which are based on maximum-likelihood methods. We develop here a multivariate version of the Bayes methodology for joint mapping of QTLs, using the Markov chain-Monte Carlo (MCMC) algorithm. We adopt a variance-components method to model complex traits in outbred populations (e.g., humans). The method is robust, can deal with an arbitrary number of alleles with arbitrary patterns of gene actions (such as additive and dominant), and allows for multiple phenotype data of various types in the joint analysis (e.g., multiple continuous traits and mixtures of continuous traits and discrete traits). Under a Bayesian framework, parameters--including the number of QTLs--are estimated on the basis of their marginal posterior samples, which are generated through two samplers, the Gibbs sampler and the reversible-jump MCMC. In addition, we calculate the Bayes factor related to each identified QTL, to test coincident linkage versus pleiotropy. The performance of our method is evaluated in simulations with full-sib families. The results show that our proposed Bayesian joint-mapping method performs well for mapping multiple QTLs in situations of either bivariate continuous traits or mixed data types. Compared with the analysis for each trait separately, Bayesian joint mapping improves statistical power, provides stronger evidence of QTL detection, and increases precision in estimation of parameter and QTL position. We also applied the proposed method to a set of real data and detected a coincident linkage responsible for determining bone mineral density and areal bone size of wrist in humans.     

Spatial analysis of gypsy moth populations in Sardinia using geostatistical and climate models

• 1 Spatial fluctuations of the Sardinian population of the gypsy moth Lymantria dispar (L.) (Lepidoptera: Lymantriidae) were characterized using geostatistical and climate models. Data on gypsy moth egg mass abundance recorded at 282 permanent monitoring sites from 1980 to 2004 were incorporated in a geographic information system with the vegetational, geomorphological and pedological features of the sites.
• 2 Statistical analyses revealed that the relative outbreak frequency was related to the predominant host tree, slope and elevation of the monitoring sites, whereas there was no correlation between outbreak frequency and exposure and soil type.
• 3 By using bioclimatic modelling, probability maps of gypsy moth outbreaks were generated. The model identified a probability surface with climatic conditions favourable to gypsy moth outbreaks and thus potentially subject to defoliation. The maps included 92 sites where outbreaks never occurred, suggesting that the Sardinian climate may not be a determinant factor for gypsy moth outbreaks.
• 4 The geostatistical method cokriging with outbreak frequency as a covariate was found to be the most suitable technique to estimate gypsy moth egg mass abundance. Semivariograms showed spatial correlation of egg mass abundance within the range 18.5–53 km. The results obtained were used to create regional gypsy moth distribution maps by cokriging, which demonstrated the outbreak foci and different infestation levels at each monitoring area. These results can help to delimit the treatment areas and develop rational gypsy moth management programmes.