The Gaussian process is an indispensable tool for spatial data analysts. The onset of the “big data” era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low-rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics. Supplementary materials regarding implementation details of the methods and code are available for this article online.

Continuous, consistent, and long time-series from remote sensing are essential to monitoring changes on Earth's surface. However, analyzing such data sets is often challenging due to missing values introduced by cloud cover, missing orbits, sensor geometry artifacts, and so on. We propose a new and accurate spatio-temporal prediction method to replace missing values in remote sensing data sets. The method exploits the spatial coherence and temporal seasonal regularity that are inherent in many data sets. The key parts of the method are: 1) the adaptively chosen spatio-temporal subsets around missing values; 2) the ranking of images within the subsets based on a scoring algorithm; 3) the estimation of empirical quantiles characterizing the missing values; and 4) the prediction of missing values through quantile regression. One advantage of quantile regression is the robustness to outliers, which enables more accurate parameter retrieval in the analysis of remote sensing data sets. In addition, we provide bootstrap-based quantification of prediction uncertainties. The proposed prediction method was applied to a Normalized Difference Vegetation Index data set from the Moderate Resolution Imaging Spectroradiometer and assessed with realistic test data sets featuring between 20% and 50% missing values. Validation against established methods showed that the proposed method has a good performance in terms of the root-mean-squared prediction error and significantly outperforms its competitors. This paper is accompanied by the open-source R package gapfill, which provides a flexible, fast, and ready-to-use implementation of the method.

How biological systems such as proteins achieve robustness to ubiquitous perturbations is a fundamental biological question. Such perturbations include errors that introduce phenotypic mutations into nascent proteins during the translation of mRNA. These errors are remarkably frequent. They are also costly, because they reduce protein stability and help create toxic misfolded proteins. Adaptive evolution might reduce these costs of protein mistranslation by two principal mechanisms. The first increases the accuracy of translation via synonymous “high fidelity” codons at especially sensitive sites. The second increases the robustness of proteins to phenotypic errors via amino acids that increase protein stability. To study how these mechanisms are exploited by populations evolving in the laboratory, we evolved the antibiotic resistance gene TEM-1 in Escherichia coli hosts with either normal or high rates of mistranslation. We analyzed TEM-1 populations that evolved under relaxed and stringent selection for antibiotic resistance by single molecule real-time sequencing. Under relaxed selection, mistranslating populations reduce mistranslation costs by reducing TEM-1 expression. Under stringent selection, they efficiently purge destabilizing amino acid changes. More importantly, they accumulate stabilizing amino acid changes rather than synonymous changes that increase translational accuracy. In the large populations we study, and on short evolutionary timescales, the path of least resistance in TEM-1 evolution consists of reducing the consequences of translation errors rather than the errors themselves.

To study the effect of short N-acetylglucosamine (GlcNAc) oligosaccharides on the physiology of plants, N-ACETYLGLUCOSAMINYLTRANSFERASE (NodC) of Azorhizobium caulinodans was expressed in Arabidopsis (Arabidopsis thaliana). The corresponding enzyme catalyzes the polymerization of GlcNAc and, accordingly, β-1,4-GlcNAc oligomers accumulated in the plant. A phenotype characterized by difficulties in developing an inflorescence stem was visible when plants were grown for several weeks under short-day conditions before transfer to long-day conditions. In addition, a positive correlation between the oligomer concentration and the penetrance of the phenotype was demonstrated. Although NodC overexpression lines produced less cell wall compared with wild-type plants under nonpermissive conditions, no indications were found for changes in the amount of the major cell wall polymers. The effect on the cell wall was reflected at the transcriptome level. In addition to genes encoding cell wall-modifying enzymes, a whole set of genes encoding membrane-coupled receptor-like kinases were differentially expressed upon GlcNAc accumulation, many of which encoded proteins with an extracellular Domain of Unknown Function26. Although stress-related genes were also differentially expressed, the observed response differed from that of a classical chitin response. This is in line with the fact that the produced chitin oligomers were too small to activate the chitin receptor-mediated signal cascade. Based on our observations, we propose a model in which the oligosaccharides modify the architecture of the cell wall by acting as competitors in carbohydrate-carbohydrate or carbohydrate-protein interactions, thereby affecting noncovalent interactions in the cell wall or at the interface between the cell wall and the plasma membrane.