Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

Land use intensification alters ecosystem multifunctionality via loss of biodiversity and changes to functional composition

Global change, especially land-use intensification, affects human well-being by impacting the deliv-ery of multiple ecosystem services (multifunctionality). However, whether biodiversity loss is amajor component of global change effects on multifunctionality in real-world ecosystems, as inexperimental ones, remains unclear. Therefore, we assessed biodiversity, functional compositionand 14 ecosystem services on 150 agricultural grasslands differing in land-use intensity. We alsointroduce five multifunctionality measures in which ecosystem services were weighted according torealistic land-use objectives. We found that indirect land-use effects, i.e. those mediated by biodi-versity loss and by changes to functional composition, were as strong as direct effects on average.Their strength varied with land-use objectives and regional context. Biodiversity loss explainedindirect effects in a region of intermediate productivity and was most damaging when land-useobjectives favoured supporting and cultural services. In contrast, functional composition shifts,towards fast-growing plant species, strongly increased provisioning services in more inherentlyunproductive grasslands.