A robust procedure for comparing multiple means under heteroscedasticity in unbalanced designs.

Investigating differences between means of more than two groups or experimental conditions is a routine research question addressed in biology. In order to assess differences statistically, multiple comparison procedures are applied. The most prominent procedures of this type, the Dunnett and Tukey-Kramer test, control the probability of reporting at least one false positive result when the data are normally distributed and when the sample sizes and variances do not differ between groups. All three assumptions are non-realistic in biological research and any violation leads to an increased number of reported false positive results. Based on a general statistical framework for simultaneous inference and robust covariance estimators we propose a new statistical multiple comparison procedure for assessing multiple means. In contrast to the Dunnett or Tukey-Kramer tests, no assumptions regarding the distribution, sample sizes or variance homogeneity are necessary. The performance of the new procedure is assessed by means of its familywise error rate and power under different distributions. The practical merits are demonstrated by a reanalysis of fatty acid phenotypes of the bacterium Bacillus simplex from the "Evolution Canyons" I and II in Israel. The simulation results show that even under severely varying variances, the procedure controls the number of false positive findings very well. Thus, the here presented procedure works well under biologically realistic scenarios of unbalanced group sizes, non-normality and heteroscedasticity

On the behavior of multiple comparison procedures in complex parametric designs

The framework for simultaneous inference by Hothorn, Bretz, and Westfall (2008) allows for a unified treatment of multiple comparisons in general parametric models where the study questions are specified as linear combinations of elemental model parameters. However, due to the asymptotic nature of the reference distribution the procedure controls the error rate across all comparisons only for sufficiently large samples. This thesis evaluates the small samples properties of simultaneous inference in complex parametric designs. These designs are necessary to address questions from applied research and include nonstandard parametric models or data in which the assumptions of classical procedures for multiple comparisons are not met. This thesis first treats multiple comparisons of samples with heterogeneous variances. Usage of a heteroscedastic consistent covariance estimation prevents an increase in the probability of false positive findings for reasonable sample sizes whereas the classical procedures show liberal or conservative behavior which persists even with increasing sample size. The focus of the second part are multiple comparisons in survival models. Multiple comparisons to a control can be performed in correlated survival data modeled by a frailty Cox model under control of the familywise error rate in sample sizes applicable for clinical trials. As a further application, multiple comparisons in survival models can be performed to investigate trends. The procedure achieves good power to detect different dose-response shapes and controls the error probability to falsely detect any trend. The third part addresses multiple comparisons in semiparametric mixed models. Simultaneous inference in the linear mixed model representation of these models yields an approach for multiple comparisons of curves of arbitrary shape. The sections on which curves differ can also be identified. For reasonably large samples the overall error rate to detect any non-existent difference is controlled. An extension allows for multiple comparisons of areas under the curve. However the resulting procedure achieves an overall error control only for sample sizes considerably larger than available in studies in which multiple AUC comparisons are usually performed. The usage of the evaluated procedures is illustrated by examples from applied research including comparisons of fatty acid contents between Bacillus simplex lineages, comparisons of experimental drugs with a control for prolongation in survival of chronic myelogeneous leukemia patients, and comparisons of curves describing a morphological structure along the spinal cord between variants of the EphA4 gene in mice

Global maps of soil temperature

Research in global change ecology relies heavily on global climatic grids derived from estimates of air temperature in open areas at around 2 m above the ground. These climatic grids do not reflect conditions below vegetation canopies and near the ground surface, where critical ecosystem functions occur and most terrestrial species reside. Here, we provide global maps of soil temperature and bioclimatic variables at a 1-km2 resolution for 0–5 and 5–15 cm soil depth. These maps were created by calculating the difference (i.e. offset) between in situ soil temperature measurements, based on time series from over 1200 1-km2 pixels (summarized from 8519 unique temperature sensors) across all the world\u27s major terrestrial biomes, and coarse-grained air temperature estimates from ERA5-Land (an atmospheric reanalysis by the European Centre for Medium-Range Weather Forecasts). We show that mean annual soil temperature differs markedly from the corresponding gridded air temperature, by up to 10°C (mean = 3.0 ± 2.1°C), with substantial variation across biomes and seasons. Over the year, soils in cold and/or dry biomes are substantially warmer (+3.6 ± 2.3°C) than gridded air temperature, whereas soils in warm and humid environments are on average slightly cooler (−0.7 ± 2.3°C). The observed substantial and biome-specific offsets emphasize that the projected impacts of climate and climate change on near-surface biodiversity and ecosystem functioning are inaccurately assessed when air rather than soil temperature is used, especially in cold environments. The global soil-related bioclimatic variables provided here are an important step forward for any application in ecology and related disciplines. Nevertheless, we highlight the need to fill remaining geographic gaps by collecting more in situ measurements of microclimate conditions to further enhance the spatiotemporal resolution of global soil temperature products for ecological applications

Global maps of soil temperature

Research in global change ecology relies heavily on global climatic grids derived from estimates of air temperature in open areas at around 2 m above the ground. These climatic grids do not reflect conditions below vegetation canopies and near the ground surface, where critical ecosystem functions occur and most terrestrial species reside. Here, we provide global maps of soil temperature and bioclimatic variables at a 1-km² resolution for 0–5 and 5–15 cm soil depth. These maps were created by calculating the difference (i.e., offset) between in-situ soil temperature measurements, based on time series from over 1200 1-km² pixels (summarized from 8500 unique temperature sensors) across all the world’s major terrestrial biomes, and coarse-grained air temperature estimates from ERA5-Land (an atmospheric reanalysis by the European Centre for Medium-Range Weather Forecasts). We show that mean annual soil temperature differs markedly from the corresponding gridded air temperature, by up to 10°C (mean = 3.0 ± 2.1°C), with substantial variation across biomes and seasons. Over the year, soils in cold and/or dry biomes are substantially warmer (+3.6 ± 2.3°C) than gridded air temperature, whereas soils in warm and humid environments are on average slightly cooler (-0.7 ± 2.3°C). The observed substantial and biome-specific offsets emphasize that the projected impacts of climate and climate change on near-surface biodiversity and ecosystem functioning are inaccurately assessed when air rather than soil temperature is used, especially in cold environments. The global soil-related bioclimatic variables provided here are an important step forward for any application in ecology and related disciplines. Nevertheless, we highlight the need to fill remaining geographic gaps by collecting more in-situ measurements of microclimate conditions to further enhance the spatiotemporal resolution of global soil temperature products for ecological applications

Global maps of soil temperature.

Research in global change ecology relies heavily on global climatic grids derived from estimates of air temperature in open areas at around 2 m above the ground. These climatic grids do not reflect conditions below vegetation canopies and near the ground surface, where critical ecosystem functions occur and most terrestrial species reside. Here, we provide global maps of soil temperature and bioclimatic variables at a 1-km2 resolution for 0-5 and 5-15 cm soil depth. These maps were created by calculating the difference (i.e. offset) between in situ soil temperature measurements, based on time series from over 1200 1-km2 pixels (summarized from 8519 unique temperature sensors) across all the world's major terrestrial biomes, and coarse-grained air temperature estimates from ERA5-Land (an atmospheric reanalysis by the European Centre for Medium-Range Weather Forecasts). We show that mean annual soil temperature differs markedly from the corresponding gridded air temperature, by up to 10°C (mean = 3.0 ± 2.1°C), with substantial variation across biomes and seasons. Over the year, soils in cold and/or dry biomes are substantially warmer (+3.6 ± 2.3°C) than gridded air temperature, whereas soils in warm and humid environments are on average slightly cooler (-0.7 ± 2.3°C). The observed substantial and biome-specific offsets emphasize that the projected impacts of climate and climate change on near-surface biodiversity and ecosystem functioning are inaccurately assessed when air rather than soil temperature is used, especially in cold environments. The global soil-related bioclimatic variables provided here are an important step forward for any application in ecology and related disciplines. Nevertheless, we highlight the need to fill remaining geographic gaps by collecting more in situ measurements of microclimate conditions to further enhance the spatiotemporal resolution of global soil temperature products for ecological applications

Multiple curve comparisons with an application to the formation of the dorsal funiculus of mutant mice

Much biological experimental data are represented as curves, including measurements of growth, hormone, or enzyme levels, and physical structures. Here we consider the multiple testing problem of comparing two or more nonlinear curves. We model smooth curves of unknown form nonparametrically using penalized splines. We use random effects to model subject-specific deviations from the group-level curve. We present an approach that allows examination of overall differences between the curves of multiple groups and detection of sections in which the curves differ. Adjusted p-values for each single comparison can be obtained by exploiting the connection between semiparametric mixed models and linear mixed models and employing an approach for multiple testing in general parametric models. In simulations, we show that the probability of false-positive findings of differences between any two curves in at least one position can be controlled by a pre-specified error level. We apply our method to compare curves describing the form of the mouse dorsal funiculus - a morphological curved structure in the spinal cord - in mice wild-type for the gene encoding EphA4 or heterozygous with one of two mutations in the gene