Introducing a Mechanistic Model in Digital Soil Mapping to Predict Soil Organic Matter Stocks in the Cantabrian Region (Spain)

ABSTRACT: Digital soil mapping (DSM) is an effective mapping technique that supports the increased need for quantitative soil data. In DSM, soil properties are correlated with environmental characteristics using statistical models such as regression. However, many of these relationships are explicitly described in mechanistic simulation models. Therefore, the mechanistic relationships can, in theory, replace the statistical relationships in DSM. This study aims to develop a mechanistic model to predict soil organic matter (SOM) stocks in Natura2000 areas of the Cantabria region (Spain). The mechanistic model is established in four steps: (a) identify major processes that influence SOM stocks, (b) review existing models describing the major processes and the respective environmental data that they require, (c) establish a database with the required input data, and (d) calibrate the model with field observations. The SOM stocks map resulting from the mechanistic model had a mean error (ME) of -2 t SOM ha−1 and a root mean square error (RMSE) of 66t SOM ha-1. The Lin's concordance correlation coefficient was 0.47 and the amount of variance explained (AVE) was 0.21. The results of the mechanistic model were compared to the results of a statistical model. It turned out that the correlation coefficient between the two SOM stock maps was 0.8. This study illustrated that mechanistic soil models can be used for DSM, which brings new opportunities. Mechanistic models for DSM should be considered for mapping soil characteristics that are difficult to predict by statistical models, and for extrapolation purposes.This research was financially supported by the Environmental Hydraulics Institute ‘IH Cantabria of Universidad de Cantabria’ and the CGIAR Research Programme on Climate Change, Agriculture and Food Security (CCAFS). The CCAFS project is carried out with support from CGIAR Fund Donors and through bilateral funding agreements. Besides the financial support, we would like to thank Sara Alcalde Aparicio for collaboration in the collection and analyses of soil samples

The Many-to-Many Mapping Between the Concordance Correlation Coefficient and the Mean Square Error

We derive the mapping between two of the most pervasive utility functions, the mean square error ($MSE$) and the concordance correlation coefficient (CCC, $\rho_c$). Despite its drawbacks, $MSE$ is one of the most popular performance metrics (and a loss function); along with lately $\rho_c$ in many of the sequence prediction challenges. Despite the ever-growing simultaneous usage, e.g., inter-rater agreement, assay validation, a mapping between the two metrics is missing, till date. While minimisation of $L_p$ norm of the errors or of its positive powers (e.g., $MSE$) is aimed at $\rho_c$ maximisation, we reason the often-witnessed ineffectiveness of this popular loss function with graphical illustrations. The discovered formula uncovers not only the counterintuitive revelation that `$MSE_1<MSE_2$' does not imply `$\rho_{c_1}>\rho_{c_2}$', but also provides the precise range for the $\rho_c$ metric for a given $MSE$. We discover the conditions for $\rho_c$ optimisation for a given $MSE$; and as a logical next step, for a given set of errors. We generalise and discover the conditions for any given $L_p$ norm, for an even p. We present newly discovered, albeit apparent, mathematical paradoxes. The study inspires and anticipates a growing use of $\rho_c$-inspired loss functions e.g., $\left|\frac{MSE}{\sigma_{XY}}\right|$, replacing the traditional $L_p$-norm loss functions in multivariate regressions.Comment: Why this discovery, or the mapping formulation is important: MSE1CCC2. In other words, MSE minimisation does not necessarily guarantee CCC maximisatio

Entry and Patenting in the Software Industry

To what extent are firms kept out of a market by patents covering related technologies? Do patents held by potential entrants make it easier to enter markets? We estimate the empirical relationship between market entry and patents for 27 narrowly defined categories of software products during the period 1990-2004. Controlling for demand, market structure, average patent quality, and other factors, we find that a 10% increase in the number of patents relevant to market reduces the rate of entry by 3-8%, and this relationship intensified following expansions in the patentability of software in the mid-1990s. However, potential entrants with patent applications relevant to a market are more likely to enter it. Finally, patents appear to substitute for complementary assets in the entry process, as patents have both greater entry-deterring and entry-promoting effects for firms without prior experience in other markets.

Does linear equating improve prediction in mapping? Crosswalking MacNew onto EQ‑5D‑5L value sets

Purpose: Preference-based measures are essential for producing quality-adjusted life years (QALYs) that are widely used for economic evaluations. In the absence of such measures, mapping algorithms can be applied to estimate utilities from disease-specific measures. This paper aims to develop mapping algorithms between the MacNew Heart Disease Quality of Life Questionnaire (MacNew) instrument and the English and the US-based EQ-5D-5L value sets. Methods: Individuals with heart disease were recruited from six countries: Australia, Canada, Germany, Norway, UK and the US in 2011/12. Both parametric and non-parametric statistical techniques were applied to estimate mapping algorithms that predict utilities for MacNew scores from EQ-5D-5L value sets. The optimal algorithm for each country-specific value set was primarily selected based on root mean square error (RMSE), mean absolute error (MAE), concordance correlation coefficient (CCC), and r-squared. Leave-one-out cross-validation was conducted to test the generalizability of each model. Results: For both the English and the US value sets, the one-inflated beta regression model consistently performed best in terms of all criteria. Similar results were observed for the cross-validation results. The preferred model explained 59 and 60% for the English and the US value set, respectively. Linear equating provided predicted values that were equivalent to observed values. Conclusions: The preferred mapping function enables to predict utilities for MacNew data from the EQ-5D-5L value sets recently developed in England and the US with better accuracy. This allows studies, which have included the MacNew to be used in cost-utility analyses and thus, the comparison of services with interventions across the health system.publishedVersio

Comparison of measures of marker informativeness for ancestry and admixture mapping

<p>Abstract</p> <p>Background</p> <p>Admixture mapping is a powerful gene mapping approach for an admixed population formed from ancestral populations with different allele frequencies. The power of this method relies on the ability of ancestry informative markers (AIMs) to infer ancestry along the chromosomes of admixed individuals. In this study, more than one million SNPs from HapMap databases and simulated data have been interrogated in admixed populations using various measures of ancestry informativeness: Fisher Information Content (FIC), Shannon Information Content (SIC), F statistics (F_ST), Informativeness for Assignment Measure (I_n), and the Absolute Allele Frequency Differences (delta, δ). The objectives are to compare these measures of informativeness to select SNP markers for ancestry inference, and to determine the accuracy of AIM panels selected by each measure in estimating the contributions of the ancestors to the admixed population.</p> <p>Results</p> <p>F_STand I_nhad the highest Spearman correlation and the best agreement as measured by Kappa statistics based on deciles. Although the different measures of marker informativeness performed comparably well, analyses based on the top 1 to 10% ranked informative markers of simulated data showed that I_nwas better in estimating ancestry for an admixed population.</p> <p>Conclusions</p> <p>Although millions of SNPs have been identified, only a small subset needs to be genotyped in order to accurately predict ancestry with a minimal error rate in a cost-effective manner. In this article, we compared various methods for selecting ancestry informative SNPs using simulations as well as SNP genotype data from samples of admixed populations and showed that the I_nmeasure estimates ancestry proportion (in an admixed population) with lower bias and mean square error.</p

Attention-dependent modulation of cortical taste circuits revealed by granger causality with signal-dependent noise

We show, for the first time, that in cortical areas, for example the insular, orbitofrontal, and lateral prefrontal cortex, there is signal-dependent noise in the fMRI blood-oxygen level dependent (BOLD) time series, with the variance of the noise increasing approximately linearly with the square of the signal. Classical Granger causal models are based on autoregressive models with time invariant covariance structure, and thus do not take this signal-dependent noise into account. To address this limitation, here we describe a Granger causal model with signal-dependent noise, and a novel, likelihood ratio test for causal inferences. We apply this approach to the data from an fMRI study to investigate the source of the top-down attentional control of taste intensity and taste pleasantness processing. The Granger causality with signal-dependent noise analysis reveals effects not identified by classical Granger causal analysis. In particular, there is a top-down effect from the posterior lateral prefrontal cortex to the insular taste cortex during attention to intensity but not to pleasantness, and there is a top-down effect from the anterior and posterior lateral prefrontal cortex to the orbitofrontal cortex during attention to pleasantness but not to intensity. In addition, there is stronger forward effective connectivity from the insular taste cortex to the orbitofrontal cortex during attention to pleasantness than during attention to intensity. These findings indicate the importance of explicitly modeling signal-dependent noise in functional neuroimaging, and reveal some of the processes involved in a biased activation theory of selective attention

Relationships in soil distribution from digital soil modelling and mapping over eastern Australia under past, present and future conditions

This research project applied digital soil modelling and mapping (DSMM) techniques to elucidate relationships between key soil properties and the main soil-forming factors. It attempted to address several broad research issues relating to quantifying the factors that control soil distribution and identifying how these combine together to control soil distribution and their change due to alteration in land use and climate over New South Wales and eastern Australia.«br /» «br /» These broad issues were examined through a number of more specific research issues that were progressively addressed over five chapters, each intended as publishable journal papers. These chapters/journal papers relate to (i) the influence of lithology in soil formation and its application in DSMM (ii) relationships of soil-forming factors to key soil properties and their use in digital soil mapping; (iii) factors controlling the distribution of soil organic carbon stocks (SOC), spatially and with depth; (iv) change in SOC stocks following historic clearing of native vegetation, and (v) change in SOC stocks with projected climate change.«br /» «br /» The strong influence of lithology in controlling soil distribution was demonstrated. Following its classification into 12 classes based on mineral and chemical composition, it was shown to have the highest influence of all soil-forming factors for six key soil properties (SOC, pH, cation exchange capacity (CEC), sum-of-bases, total phosphorous and clay content) examined over NSW. Lithology had similar influence at the scale of eastern Australia; however climate variables were of equivalent or slightly stronger influence for SOC and pH. It was shown to have two to five times more influence than the next highest ranked geophysical covariate such as gamma radiometrics in the models. A marked improvement in the statistical quality of digital models and maps was demonstrated when lithology was applied together with other geophysical covariates.«br /» «br /» Quantitative relationships that are readily interpreted were developed with eight key properties (those listed above plus sand and silt contents) over eastern Australia. These relationships at least partially solve Jenny’s fundamental soil equation in a manner that is more universally applicable and readily interpreted than appears to have been reported previously. Using these relationships, the quantitative influence of the different factors on each soil property is determined, including the unit change per unit variation in the factor, for example a decrease of 0.11 pH units for each 100 mm increase in annual rainfall for the 0-10 cm interval (other factors remaining constant). These relationships were applied together with readily available covariate grids to prepare digital soil maps (DSMs) with 100-m resolution for the eight soil properties over NSW. The predictive ability demonstrated by the maps was broadly moderate, with Lin’s concordance generally between 0.4 and 0.7. They compared well with maps prepared using more sophisticated modelling methods and covariate data. They have the ability to be readily prepared and interpreted and thus have the potential to serve as a useful introduction to the more sophisticated DSMM approaches.«br /» «br /» Systematic patterns of SOC stock levels were graphically demonstrated over 45 different climate-parent material-vegetation cover regimes for upper soils (0-30 cm) and lower soils (30-100 cm) over eastern Australia. There are generally uniform trends of increasing SOC stocks with increasingly moist climate, increasing mafic character of parent material and increasing vegetation cover. Average SOC stocks in the 0-30 cm depth interval range from 16.3 Mg ha-1 (t/ha) in dry, highly siliceous parent material and low vegetation cover environments, up to over 145.0 Mg ha-1 in wet, mafic parent material and high vegetation cover environments. It was demonstrated that the proportion of SOC stored in the subsoil (30-100 cm) relative to the top 100 cm varies systematically from an average of 43% in moist climates to an average of 54% in dry climates.«br /» «br /» Digital soil maps of pre-clearing (pre-European) SOC stocks (100-m resolution) were prepared over NSW. These maps may be used to provide baseline soil carbon levels for carbon turnover models and carbon accounting and trading schemes. They were demonstrated to outperform the existing equivalent maps produced by conventional soil survey methods, with independent validation RMSE values being 33% lower. Comparison of these maps with current SOC stock maps allowed an examination of the change in SOC over NSW following native vegetation clearing. A total SOC loss of approximately 0.53 Gt (530 million Mg or tonnes), or 12.6% over the entire State was revealed. It was demonstrated that the change in SOC stocks following clearing increases (in both absolute and relative terms) with increasingly cool (moist) climate, more mafic parent material and more intensive land use. In the 56 different climate-parent material – land use regimes, the loss varied from less than 1 Mg ha-1 (or 4%) in warmer climates over highly siliceous parent materials under grazing land uses to 44.3 Mg ha-1 (or 50.0%) in cooler (moist) conditions over mafic parent materials under intensive cropping land use.«br /» «br /» Digital soil mapping techniques involving Cubist piecewise linear decision trees, in combination with a space-for-time substitution process (DSM-SFTS), were demonstrated to be effective in mapping the potential change in SOC stocks due to projected climate change over NSW until approximately 2070. Considerable variation in both direction and magnitude of change was demonstrated with application of the 12 different climate change models with their differing climate trajectories. For the mean state-wide change there were some climate models that predicted an increase but others that predicted a decrease over the two depth intervals studied (0-30 and 30-100 cm). Greater consistency between climate change models is required. The predicted SOC changes are primarily controlled by the balance between changing temperatures and rainfall. However, the extent of change is also shown to be dependent on the precise environmental regime, with systematically differing changes demonstrated over 36 current climate-parent material-land use combinations. For example, the projected mean decline of SOC is less than 1 Mg ha-1 for dry-highly siliceous-cropping regimes but over 15 Mg ha-1 for wet-mafic-native vegetation regimes.«br /» «br /» The study has provided quantitative data on the influence of the main soil-forming factors. The necessity of considering the combined influence of multiple soil-forming factors to make meaningful quantitative estimates of current and potential future soil properties is demonstrated. Clear patterns of soil property distribution and change under changing land use and climate conditions are identified, particularly for the vital soil property of SOC. The presentation of relationships that are readily interpreted can assist in their application in natural resource planning and management activities and also in other environment modelling programs. They may thus potentially help to address a range of environmental challenges facing eastern Australia and beyond