White-nose syndrome (WNS) is a fungal disease caused by Pseudogymnoascus destructans that is devastating to Nearctic bat populations but tolerated by Palearctic bats. Temperature is a factor known to be important for fungal growth and bat choice of hibernation. Here we investigated the effect of temperature on the pathogenic fungal growth in the wild across the Palearctic. We modelled body surface temperature of bats with respect to fungal infection intensity and disease severity and were able to relate this to the mean annual surface temperature at the site. Bats that hibernated at lower temperatures had less fungal growth and fewer skin lesions on their wings. Contrary to expectation derived from laboratory P. destructans culture experiments, natural infection intensity peaked between 5 and 6°C and decreased at warmer hibernating temperature. We made predictive maps based on bat species distributions, temperature and infection intensity and disease severity data to determine not only where P. destructans will be found but also where the infection will be invasive to bats across the Palearctic. Together these data highlight the mechanistic model of the interplay between environmental and biological factors, which determine progression in a wildlife disease. Graphical Abstract

Semi‐permeable barriers to geneflow in principle allow distantly related organisms to capture and exchange pre‐adapted genes potentially speeding adaptation. However, describing barriers to geneflow on a genomic scale is non‐trivial. We extend classic diagnostic allele counting measures of geneflow across a barrier to the case of genome‐scale data. Diagnostic index expectation maximisation (diem) polarises the labelling of bistate markers with respect to the sides of a barrier. An initial state of ignorance is enforced by starting with randomly generated marker polarisations. This means there is no prior on population or taxon membership of the genomes concerned. Using a deterministic data labelling, small numbers of classic diagnostic markers can be replaced by large numbers of markers, each with a diagnostic index. Individuals' hybrid indices (genome admixture proportions) are then calculated genome wide conditioned on marker diagnosticity; within diploid, haplodiploid and/or haploid genome compartments; or indeed over any subset of markers, allowing classical cline width/barrier strength comparisons along genomes. Along‐genome barrier strength heterogeneity allows for barrier regions to be identified. Furthermore, blocks of genetic material that have introgressed across a barrier are easily identified with high power. diem indicates panmixis among Myotis myotis bat genomes, with a barrier separating low data quality outliers. In a Mus musculus domesticus/Mus spretus system, diem adds multiple introgressions of olfactory (and vomeronasal) gene clusters in one direction to previous demonstrations of a pesticide resistance gene introgressing in the opposite direction across a strong species barrier. diem is a genome analysis solution, which scales over reduced representation genomics of thousands of markers to treatment of all variant sites in large genomes. While the method lends itself to visualisation, its output of markers with barrier‐informative annotation will fuel research in population genetics, phylogenetics and association studies. diem can equip such downstream applications with millions of informative markers.

Fuzzy regression provides an alternative to statistical regression when the model is indefinite, the relationships between model parameters are vague, the sample size is low, or the data are hierarchically structured. Such cases allow to consider the choice of a regression model based on the fuzzy set theory. In fuzzyreg, we implement fuzzy linear regression methods that differ in the expectations of observational data types, outlier handling, and parameter estimation method. We provide a wrapper function that prepares data for fitting fuzzy linear models with the respective methods from a syntax established in R for fitting regression models. The function fuzzylm thus provides a novel functionality for R through standardized operations with fuzzy numbers. Additional functions allow for conversion of real-value variables to be fuzzy numbers, printing, summarizing, model plotting, and calculation of model predictions from new data using supporting functions that perform arithmetic operations with triangular fuzzy numbers. Goodness of fit and total error of the fit measures allow model comparisons. The package contains a dataset named bats with measurements of temperatures of hibernating bats and the mean annual surface temperature reflecting the climate at the sampling sites. The predictions from fuzzy linear models fitted to this dataset correspond well to the observed biological phenomenon. Fuzzy linear regression has great potential in predictive modeling where the data structure prevents statistical analysis and the modeled process exhibits inherent fuzziness.