Abstract. The spatial assessment of soil functions requires maps of basic soil properties. Unfortunately, these are either missing for many regions or are not available at the desired spatial resolution or down to the required soil depth. The field-based generation of large soil datasets and conventional soil maps remains costly. Meanwhile, legacy soil data and comprehensive sets of spatial environmental data are available for many regions.Digital soil mapping (DSM) approaches relating soil data (responses) to environmental data (covariates) face the challenge of building statistical models from large sets of covariates originating, for example, from airborne imaging spectroscopy or multi-scale terrain analysis. We evaluated six approaches for DSM in three study regions in Switzerland (Berne, Greifensee, ZH forest) by mapping the effective soil depth available to plants (SD), pH, soil organic matter (SOM), effective cation exchange capacity (ECEC), clay, silt, gravel content and fine fraction bulk density for four soil depths (totalling 48 responses). Models were built from 300-500 environmental covariates by selecting linear models through (1) grouped lasso and (2) an ad hoc stepwise procedure for robust external-drift kriging (georob). For (3) geoadditive models we selected penalized smoothing spline terms by component-wise gradient boosting (geoGAM). We further used two tree-based methods: (4) boosted regression trees (BRTs) and (5) random forest (RF). Lastly, we computed (6) weighted model averages (MAs) from the predictions obtained from methods 1-5.Lasso, georob and geoGAM successfully selected strongly reduced sets of covariates (subsets of 3-6 % of all covariates). Differences in predictive performance, tested on independent validation data, were mostly small and did not reveal a single best method for 48 responses. Nevertheless, RF was often the best among methods 1-5 (28 of 48 responses), but was outcompeted by MA for 14 of these 28 responses. RF tended to over-fit the data. The performance of BRT was slightly worse than RF. GeoGAM performed poorly on some responses and was the best only for 7 of 48 responses. The prediction accuracy of lasso was intermediate. All models generally had small bias. Only the computationally very efficient lasso had slightly larger bias because it tended to under-fit the data. Summarizing, although differences were small, the frequencies of the best and worst performance clearly favoured RF if a single method is applied and MA if multiple prediction models can be developed.Published by Copernicus Publications on behalf of the European Geosciences Union.

Abstract. Spatial assessment of soil functions requires maps of basic soil properties. Unfortunately, these are either missing for many regions or are not available at the desired spatial resolution or down to required soil depth. Conventional soil map generation remains costly. Field based generation of large soil data sets and of conventional soil maps remains costly. Meanwhile, soil legacy data and comprehensive sets of spatial environmental data are available for many regions. Digital soil mapping (DSM) approaches – relating soil data (responses) to environmental data (covariates) – are facing the challenge to build statistical models from large sets of covariates originating for example from airborne imaging spectroscopy or multi-scale terrain analysis. We evaluated six approaches for DSM in three study regions in Switzerland (Berne, Greifensee, ZH forest) by mapping effective soil depth available to plants (SD), pH, soil organic matter (SOM), effective cation exchange capacity (ECEC), clay, silt, gravel content and bulk density for four soil layers (totalling 48 responses). Models were built from 300–500 environmental covariates by selecting linear models by (1) grouped lasso and by an ad-hoc stepwise procedure for (2) robust external-drift kriging (EDK). For (3) geoadditive models we selected penalized smoothing spline terms by componentwise gradient boosting (geoGAM). We further used two tree-based methods: (4) boosted regression trees (BRT) and (5) Random Forest (RF). Lastly, we computed (6) weighted model averages (MA) from predictions obtained from methods 1–5. Lasso, georob and geoGAM successfully selected strongly reduced sets of covariates (subsets of 3–6 % of all covariates). To automatically select a sparse trend model for EDK was however difficult, and the applied ad hoc procedure was computationally inefficient and over-fitted the data. Differences in predictive performance, tested on independent validation data, were mostly small and did not reveal a single best method for 48 responses. Nevertheless, RF was on average often best among methods 1–5 (28 of 48 responses), but was outcompeted by MA for 14 of these 28 responses. RF tended to over-fit the data. Performance of BRT was slightly worse than RF. GeoGAM performed poorly on some responses and was only best for 7 of 48 responses. Predictive precision of lasso was intermediate. All models generally had small bias. Only the computationally very efficient lasso had slightly larger bias likely because it tended to under-fit the data. Summarizing, although differences were small, the frequencies of best and worst performance clearly favoured RF if a single method is applied MA if multiple prediction models can be developed.

The study of pattern formation has benefited from reverse-engineering gene regulatory network (GRN) structure from spatio-temporal quantitative gene expression data. Traditional approaches omit tissue morphogenesis, hence focusing on systems where the timescales of pattern formation and morphogenesis can be separated. In such systems, pattern forms as an emergent property of the underlying GRN. This is not the case in many animal patterning systems, where patterning and morphogenesis are simultaneous. To address pattern formation in these systems we need to adapt our methodologies to explicitly accommodate cell movements and tissue shape changes. In this work we present a novel framework to reverse-engineer GRNs underlying pattern formation in tissues experiencing morphogenetic changes and cell rearrangements. By combination of quantitative data from live and fixed embryos we approximate gene expression trajectories (AGETs) in single cells and use a subset to reverse-engineer candidate GRNs using a Markov Chain Monte Carlo approach. GRN fit is assessed by simulating on cell tracks (live-modelling) and comparing the output to quantitative data-sets. This framework outputs candidate GRNs that recapitulate pattern formation at the level of the tissue and the single cell. To our knowledge, this inference methodology is the first to integrate cell movements and gene expression data, making it possible to reverse-engineer GRNs patterning tissues undergoing morphogenetic changes.

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