Estimates of the number of species of bacteria per gram of soil vary between 2000 and 8.3 million (Gans et al., 2005; Schloss and Handelsman, 2006). The highest estimate suggests that the number may be so large as to be impractical to test by amplification and sequencing of the highly conserved 16S rRNA gene from soil DNA (Gans et al., 2005). Here we present the use of high throughput DNA pyrosequencing and statistical inference to assess bacterial diversity in four soils across a large transect of the western hemisphere. The number of bacterial 16S rRNA sequences obtained from each site varied from 26,140 to 53,533. The most abundant bacterial groups in all four soils were the Bacteroidetes, Betaproteobacteria and Alphaproteobacteria. Using three estimators of diversity, the maximum number of unique sequences (operational taxonomic units roughly corresponding to the species level) never exceeded 52,000 in these soils at the lowest level of dissimilarity. Furthermore, the bacterial diversity of the forest soil was phylum rich compared to the agricultural soils, which are species rich but phylum poor. The forest site also showed far less diversity of the Archaea with only 0.009% of all sequences from that site being from this group as opposed to 4%-12% of the sequences from the three agricultural sites. This work is the most comprehensive examination to date of bacterial diversity in soil and suggests that agricultural management of soil may significantly influence the diversity of bacteria and archaea.

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Pyrosequencing enumerates and contrasts soil microbial diversity

Box & Cox (1964) proposed a parametric power transformation technique in order to reduce anomalies such as non-additivity, non-normality and heteroscedasticity. Although the transformation has been extensively studied, no bibliography of the published research exists at present. An attempt is made here to review the work relating to this transformation.

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The Box-Cox transformation technique: a review

Single-index models are potentially important tools for multivariate nonparametric regression. They generalize linear regression by replacing the linear combination α0Tx with a nonparametric component, η0(α0Tx), where η0(·) is an unknown univariate link function. By reducing the dimensionality from that of a general covariate vector x to a univariate index α0Tx, single-index models avoid the so-called “curse of dimensionality.” We propose penalized spline (P-spline) estimation of η0(·) in partially linear single-index models, where the mean function has the form η0(α0Tx) + β 0Tz. The P-spline approach offers a number of advantages over other fitting methods for single-index models. All parameters in the P-spline single-index model can be estimated simultaneously by penalized nonlinear least squares. As a direct least squares fitting method, our approach is rapid and computationally stable. Standard nonlinear least squares software can be used. Moreover, joint inference for η0(·), α0, and β0 is possible by...

Penalized Spline Estimation for Partially Linear Single-Index Models

A variety of model selection criteria have been developed, of general and specific types. Most of these aim at selecting a single model with good overall properties, for example, formulated via average prediction quality or shortest estimated overall distance to the true model. The Akaike, the Bayesian, and the deviance information criteria, along with many suitable variations, are examples of such methods. These methods are not concerned, however, with the actual use of the selected model, which varies with context and application. The present article takes the view that the model selector should instead focus on the parameter singled out for interest; in particular, a model that gives good precision for one estimand may be worse when used for inference for another estimand. We develop a method that, for a given focus parameter, estimates the precision of any submodel-based estimator. The framework is that of large-sample likelihood inference. Using an unbiased estimate of limiting risk, we propose a foc...

The Focused Information Criterion

Nonlinear regression models are important tools because many crop and soil processes are better represented by nonlinear than linear models. Fitting nonlinear models is not a single-step procedure but an involved process that requires careful examination of each individual step. Depending on the objective and the application domain, different priorities are set when fitting nonlinear models; these include obtaining acceptable parameter estimates and a good model fit while meeting standard assumptions of statistical models. We propose steps in fitting nonlinear models as described by a flow diagram and discuss each step separately providing examples and updates on procedures used. The following steps are considered: (i) choose candidate models, (ii) set starting values, (iii) fit models, (iv) check convergence and parameter estimates, (v) find the "best" model among competing models, (vi) check model assumptions (residual analysis), and (vii) calculate statistical descriptors and confidence intervals. The associated feedback mechanisms are also addressed (i.e., model variance homogeneity). In particular, we emphasize the first step (choose candidate models) by providing an extensive library of nonlinear functions (77 equations with the associated parameter meanings) and examples of typical applications in agriculture. We hope that this contribution will clarify some of the difficulties and confusion with the task of using nonlinear models.

Nonlinear Regression Models and Applications in Agricultural Research

Summary In many regression applications the independent variable is measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two diVerent approaches to nonparametric regression. The first uses the simex, simulation-extrapolation, method and makes no assumption about the distribution of the unobserved error-prone predictor. For this approach we derive an asymptotic theory for kernel regression which has some surprising implications. Penalised regression splines are also considered for fixed number of known knots. The second approach assumes that the error-prone predictor has a distribution of a mixture of normals with an unknown number of components, and uses regression splines. Simulations illustrate the results.

Nonparametric regression in the presence of measurement error

: There has been considerable disagreement about how best to estimate the parameters in Michaelis-Menten models. This document points out that many fitting methods are based on different stochastic models, being weighted least squares estimates after appropriate transformation. The authors propose a flexible model which can be used to help determine the proper transformation and choice of weights. The method is illustrated by examples. Keywords: Nonlinear regression; Lineweaver Burke transformation.

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A Transformation/Weighting Model for Estimating Michaelis-Menten Parameters,

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Penalized regression splines

The following biological components concerning the population dynamics of Atlantic menhaden (Brevoortia tyrannus) were investigated: growth, natural mortality, migration, fishing mortality, and rec...

An Investigation of the Population Dynamics of Atlantic Menhaden (Brevoortia tyrannus)

A model including an age-structure, a stochastic egg-recruitment relationship, density-dependent juvenile growth, age-dependent fishing mortality, and fecundity dependent upon size as well as age w...

D. Ruppert

Papers

Nonparametric regression in the presence of measurement error

A Transformation/Weighting Model for Estimating Michaelis-Menten Parameters,

Penalized regression splines

An Investigation of the Population Dynamics of Atlantic Menhaden (Brevoortia tyrannus)

A Stochastic Population Model for Managing the Atlantic Menhaden (Brevoortia tyrannus) Fishery and Assessing Managerial Risks