Spatial analysis of BSE cases in the Netherlands

<p>Abstract</p> <p>Background</p> <p>In many of the European countries affected by Bovine Spongiform Encephalopathy (BSE), case clustering patterns have been observed. Most of these patterns have been interpreted in terms of heterogeneities in exposure of cattle to the BSE agent. Here we investigate whether spatial clustering is present in the Dutch BSE case data.</p> <p>Results</p> <p>We have found three spatial case clusters in the Dutch BSE epidemic. The clusters are geographically distinct and each cluster appears in a different birth cohort. When testing all birth cohorts together, only one significant cluster was detected. The fact that we found stronger spatial clustering when using a cohort-based analysis, is consistent with the evidence that most BSE infections occur in animals less than 12 or 18 months old.</p> <p>Conclusion</p> <p>Significant spatial case clustering is present in the Dutch BSE epidemic. The spatial clusters of BSE cases are most likely due to time-dependent heterogeneities in exposure related to feed production.</p

How much would it cost to monitor farmland biodiversity in Europe?

International audienceTo evaluate progress on political biodiversity objectives, biodiversity monitoring provides information on whether intended results are being achieved. Despite scientific proof that monitoring and evaluation increase the (cost) efficiency of policy measures, cost estimates for monitoring schemes are seldom available, hampering their inclusion in policy programme budgets. Empirical data collected from 12 case studies across Europe were used in a power analysis to estimate the number of farms that would need to be sampled per major farm type to detect changes in species richness over time for four taxa (vascular plants, earthworms, spiders and bees). A sampling design was developed to allocate spatially, across Europe, the farms that should be sampled. Cost estimates are provided for nine monitoring scenarios with differing robustness for detecting temporal changes in species numbers. These cost estimates are compared with the Common Agricultural Policy (CAP) budget (2014-2020) to determine the budgetallocation required for the proposed farmland biodiversity monitoring. Results show that the bee indicator requires the highest number of farms to be sampled and the vascular plant indicator the lowest. The costs for the nine farmland biodiversity monitoring scenarios corresponded to 001%-074% of the total CAP budget and to 004%-248% of the CAP budget specifically allocated to environmental targets.Synthesis and applications. The results of the cost scenarios demonstrate that, based on the taxa and methods used in this study, a Europe-wide farmland biodiversity monitoring scheme would require a modest share of the Common Agricultural Policy budget. The monitoring scenarios are flexible and can be adapted or complemented with alternate data collection options (e.g. at national scale or voluntary efforts), data mobilization, data integration or modelling efforts. Editor's Choic

Statistical approaches for spatial sample survey : Persistent misconceptions and new developments

Several misconceptions about the design-based approach for sampling and statistical inference, based on classical sampling theory, seem to be quite persistent. These misconceptions are the result of confusion about basic statistical concepts such as independence, expectation, and bias and variance of estimators or predictors. These concepts have a different meaning in the design-based and model-based approach, because they consider different sources of randomness. Also, a population mean is still often confused with a model mean, and a population variance with a model-variance, leading to invalid formulas for the variance of an estimator of the population mean. In this paper the fundamental differences between these two approaches are illustrated with simulations, so that hopefully more pedometricians get a better understanding of this subject. An overview is presented of how in the design-based approach we can make use of knowledge of the spatial structure of the study variable. In the second part, new developments in both the design-based and model-based approach are described that try to combine the strengths of the two approaches.</p

How to compare sampling designs for mapping?

If a map is constructed through prediction with a statistical or non-statistical model, the sampling design used for selecting the sample on which the model is fitted plays a key role in the final map accuracy. Several sampling designs are available for selecting these calibration samples. Commonly, sampling designs for mapping are compared in real-world case studies by selecting just one sample for each of the sampling designs under study. In this study, we show that sampling designs for mapping are better compared on the basis of the distribution of the map quality indices over repeated selection of the calibration sample. In practice this is only feasible by subsampling a large dataset representing the population of interest, or by selecting calibration samples from a map depicting the study variable. This is illustrated with two real-world case studies. In the first case study a quantitative variable, soil organic carbon, is mapped by kriging with an external drift in France, whereas in the second case a categorical variable, land cover, is mapped by random forest in a region in France. The performance of two sampling designs for mapping are compared: simple random sampling and conditioned Latin hypercube sampling, at various sample sizes. We show that in both case studies the sampling distributions of map quality indices obtained with the two sampling design types, for a given sample size, show large variation and largely overlap. This shows that when comparing sampling designs for mapping on the basis of a single sample selected per design, there is a serious risk of an incidental result. Highlights: We provide a method to compare sampling designs for mapping. Random designs for selecting calibration samples should be compared on the basis of the sampling distribution of the map quality indices

Transferability of a soil variogram for sampling design : A case study of three grasslands in Ireland

It is commonly accepted that an estimated soil variogram can be transferred to another similar area for deriving the tolerable spacing of a sampling grid or, more generally, the sample size, given a requirement on the quality of the soil property map of the recipient area. The quality of the derived tolerable grid spacing depends on how similar the population variograms of the donor area and recipient area are. In practice we are uncertain about the variograms of both areas due to sampling errors. Ideally, the uncertainty about the variogram of the donor area is accounted for in deriving the tolerable grid spacing. To assess the transferability, we should also account for uncertainty in the estimated variogram of the recipient area. In this study the transferability of variograms of soil pH, P, Mg and K is analysed for three grassland fields in Ireland, which are similar in soil-forming factors. One field served as donor area, the other two as recipient area. For all three fields and for each soil property, 500 variograms were sampled from the posterior distribution of the variogram parameters. Results showed that the estimated variogram parameters of the recipient fields differed largely from those of the transferred variograms. The ranges of estimated mean kriging variance values for the various grid spacings, as obtained with the two sets of variograms (one set of the donor field, one set of the recipient field), did not overlap. Even after scaling the transferred variogram with an estimate of the variance of the recipient field, the transferred variogram was of no use for determining the tolerable grid spacing. The difference in the variograms can possibly be explained by the difference in historical land use. Highlights: Transferability of variograms to derive tolerable grid spacing for mapping grassland fields is assessed Transferability should be based on the uncertainty distributions of the tolerable grid spacings Due to difference in historical land use, local and transferred variograms differed largely Transferability of a variogram is very poor, even after scaling the transferred variogram

Optimization of sample patterns for universal kriging of environmental variables

Abstract The quality of maps obtained by interpolation of observations of a target environmental variable at a restricted number of locations, is partly determined by the spatial pattern of the sample locations. A method is presented for optimization of the sample pattern when the environmental variable is interpolated with the help of exhaustively known covariates, which are assumed to be linearly related to the target variable. In this method the spatially averaged universal kriging variance (MUKV), which incorporates trend estimation error as well as spatial interpolation error, is minimized. The optimal pattern is obtained using simulated annealing. The method requires that the covariance function or variogram of the regression-residuals is known. The method is tested in a case study on the Mean Highest Water table in a coversand area in The Netherlands. The patterns of 25, 50 and 100 sample locations are optimized and compared with the patterns optimized with the ordinary kriging (OK) model (assuming no trend) and with the multiple linear regression (MLR) model (assuming no spatial autocorrelation of residuals). The results show that the UK-patterns are a good compromise between spreading in geographic space and feature space. The MUKV for the UK-patterns is 19% (n = 25), 7% (n = 50) and 3% (n = 100) smaller than for the OK-patterns. Compared with the MLR-patterns the reduction is 2%, 4% and 4%, respectively

Mapping the probability of ripened subsoils using Bayesian logistic regression with informative priors

One of the first soil forming processes in marine and fluviatile clay soils is ripening, the irreversible change of physical and chemical soil properties, especially consistency, under influence of air. We used Bayesian binomial logistic regression (BBLR) to update the map showing unripened subsoils for a reclamation area in the west of The Netherlands. Similar to conventional binomial logistic regression (BLR), in BBLR the binary target variable (the subsoil is ripened or unripened) is modelled by a Bernoulli distribution. The logit transform of the `probability of success' parameter of the Bernoulli distribution was modelled as a linear combination of the covariates soil type, freeboard (the desired water level in the ditches, compared to surface level) and mean lowest groundwater table. To capture all available information, Bayesian statistics combines legacy data summarized in a ‘prior’ probability distribution for the regression coefficients with actual observations. Our research focused on quantifying the influence of priors with different information levels, in combination with different sample sizes, on the resulting parameters and maps. We combined subsamples of different size (ranging from 5% to 50% of the original dataset of 676 observations) with priors representing different levels of trust in legacy data and investigated the effect of sample size and prior distribution on map accuracy. The resulting posterior parameter distributions, calculated by Markov chain Monte Carlo simulation, vary in centrality as well as in dispersion, especially for the smaller datasets. More informative priors decreased dispersion and pushed posterior central values towards prior central values. Interestingly, the resulting probability maps were almost similar. However, the associated uncertainty maps were different: a more informative prior decreased prediction uncertainty. When using the ‘overall accuracy’ validation metric, we found an optimal value for the prior information level, indicating that the standard deviation of the legacy data regression parameters should be multiplied by 10. This effect is only detectable for smaller datasets. The Area Under Curve validation statistic did not provide a meaningful optimal multiplier for the standard deviation. Bayesian binomial logistic regression proved to be a flexible mapping tool but the accuracy gain compared to conventional logistic regression was marginal and may not outweigh the extra modelling and computing effort.</p

How serious a problem is subsoil compaction in the Netherlands? A survey based on probability sampling

Although soil compaction is widely recognized as a soil threat to soil resources, reliable estimates of the acreage of overcompacted soil and of the level of soil compaction parameters are not available. In the Netherlands data on subsoil compaction were collected at 128 locations selected by stratified random sampling. A map showing the risk of subsoil compaction in five classes was used for stratification. Measurements of bulk density, porosity, clay content and organic matter content were used to compute the relative bulk density and relative porosity, both expressed as a fraction of a threshold value. A subsoil was classified as overcompacted if either the relative bulk density exceeded 1 or the relative porosity was below 1. The sample data were used to estimate the means of the two subsoil compaction parameters and the overcompacted areal fraction. The estimated global means of relative bulk density and relative porosity were 0.946 and 1.090, respectively. The estimated areal fraction of the Netherlands with overcompacted subsoils was 43 %. The estimates per risk map unit showed two groups of map units: A "low-risk " group (units 1 and 2, covering only 4.6%of the total area) and a "high-risk" group (units 3, 4 and 5). The estimated areal fraction of overcompacted subsoil was 0% in the lowrisk unit and 47% in the high-risk unit. The map contains no information about where overcompacted subsoils occur. This was caused by the poor association of the risk map units 3, 4 and 5 with the subsoil compaction parameters and subsoil overcompaction. This can be explained by the lack of time for recuperation

Model-based geostatistics from a Bayesian perspective: investigating area-to-point kriging with small data sets

Area-to-point kriging (ATPK) is a geostatistical method for creating high-resolution raster maps using data of the variable of interest with a much lower resolution. The data set of areal means is often considerably smaller