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.

In this paper we give a complete characterization of the statistical equivalence classes of CEGs and of staged trees. We are able to show that all graphical representations of the same model share a common polynomial description. Then, simple transformations on that polynomial enable us to traverse the corresponding class of graphs. We illustrate our results with a real analysis of the implicit dependence relationships within a previously studied dataset.MSC 2010 subject classifications: Primary 60E05, 60K35; secondary 62E99.

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Sensitivity methods for the analysis of the outputs of discrete Bayesian networks have been extensively studied and implemented in different software packages. These methods usually focus on the study of sensitivity functions and on the impact of a parameter change to the Chan-Darwiche distance. Although not fully recognized, the majority of these results rely heavily on the multilinear structure of atomic probabilities in terms of the conditional probability parameters associated with this type of network. By defining a statistical model through the polynomial expression of its associated defining conditional probabilities, we develop here a unifying approach to sensitivity methods applicable to a large suite of models including extensions of Bayesian networks, for instance context-specific ones. Our algebraic approach enables us to prove that for models whose defining polynomial is multilinear both the Chan-Darwiche distance and any divergence in the family of φ-divergences are minimized for a certain class of multi-parameter contemporaneous variations when parameters are proportionally covaried.

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.

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Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the primary decomposition of monomial ideals associated with an interpolating polynomial to quickly compute all nested representations of that polynomial. It hereby determines an important subclass of all trees representing the same statistical model. To illustrate this method we analyze the full polynomial equivalence class of a staged tree representing the best fitting model inferred from a real-world dataset.1 We should say more precisely: when the symbols θ(e) are evaluated in (0, 1) for all e ∈ E.