Aim Soil microbes are essential for maintenance of life‐supporting ecosystem services, but projections of how these microbes will be affected by global change scenarios are lacking. Therefore, our aim was to provide projections of future soil microbial distribution using several scenarios of global change. Location Global. Time period 1950–2090. Major taxa studied Bacteria and fungi. Methods We used a global database of soil microbial communities across six continents to estimate past and future trends of the soil microbiome. To do so, we used structural equation models to include the direct and indirect effects of changes in climate and land use in our predictions, using current climate (temperature and precipitation) and land‐use projections between 1950 and 2090. Results Local bacterial richness will increase in all scenarios of change in climate and land use considered, although this increase will be followed by a generalized community homogenization process affecting > 85% of terrestrial ecosystems. Changes in the relative abundance of functional genes associated with the increases in bacterial richness are also expected. Based on an ecological cluster analysis, our results suggest that phylotypes such as Geodermatophilus spp. (typical desert bacteria), Mycobacterium sp. (which are known to include important human pathogens), Streptomyces mirabilis (major producers of antibiotic resistance genes) or potential fungal soil‐borne plant pathogens belonging to Ascomycota fungi (Venturia spp., Devriesia spp.) will become more abundant in their communities. Main conclusions Our results provide evidence that climate change has a stronger influence on soil microbial communities than change in land use (often including deforestation and agricultural expansion), although most of the effects of climate are indirect, through other environmental variables (e.g., changes in soil pH). The same was found for microbial functions such as the prevalence of phosphate transport genes. We provide reliable predictions about the changes in the global distribution of microbial communities, showing an increase in alpha diversity and a homogenization of soil microbial communities in the Anthropocene.

We study multivariate Gaussian statistical models whose maximum likelihood estimator (MLE) is a rational function of the observed data. We establish a one-to-one correspondence between such models and the solutions to a nonlinear firstorder partial differential equation (PDE). Using our correspondence, we reinterpret familiar classes of models with rational MLE, such as directed (and decomposable undirected) Gaussian graphical models. We also find new models with rational MLE. For linear concentration models with rational MLE, we show that homaloidal polynomials from birational geometry lead to solutions to the PDE. We thus shed light on the problem of classifying Gaussian models with rational MLE by relating it to the open problem in birational geometry of classifying homaloidal polynomials.

Coloured probability tree models are statistical models coding conditional independence between events depicted in a tree graph. They are more general than the very important class of contextspecific Bayesian networks. In this paper, we study the algebraic properties of their ideal of model invariants. The generators of this ideal can be easily read from the tree graph and have a straightforward interpretation in terms of the underlying model: they are differences of odds ratios coming from conditional probabilities. One of the key findings in this analysis is that the tree is a convenient tool for understanding the exact algebraic way in which the sum-to-1 conditions on the parameter space translate into the sum-to-one conditions on the joint probabilities of the statistical model. This enables us to identify necessary and sufficient graphical conditions for a staged tree model to be a toric variety intersected with a probability simplex.