In data analysis, we often ask the following questions:Which is the best model to describe our data? Which is the best statistical index to judge the goodness of fit? How do we choose among competing models? There are no simple answers to these questions. Here we attempt to provide agronomists with a general framework on how to approach these questions appropriately. Our specific objectives are: (i) to provide a succinct overview of nonlinear models and to develop a guideline to understand the family of functions used in agricultural applications; (ii) to indicate techniques to modify nonlinear models and how to cope with multiple nonlinear models; (iii) to discuss key methodological issues on parameter estimation, model performance, and comparison; and (iv) to demonstrate step-by-step analysis of experimental data using a nonlinear regression model. The structure follows the flow diagram in Fig. 1. We start with the definition of nonlinear regression models and discuss their main advantages and disadvantages. Then we present 77 nonlinear functions (including those in supplemental tables) with references to applications in agriculture. We offer an updated overview of methodologies to fit models, choose starting values, assess goodness of fit, select the best models, and evaluate residuals. Finally, we reanalyze experimental data on biomass growth with time (Danalatos et al., 2009). NONLINEAR REGRESSION MODELS DefinitionIn general, statistical models used in agricultural applications can be described with the following notation:where y is the response variable, f is the function or model, x are the inputs, q denotes the parameters to be estimated, and e is the error. Each parameter can be evaluated for whether it is linear or not: if the second derivative of the function with respect to a parameter is not equal to zero, then the parameter is nonlinear. Thus a given function ( f ) can have a mix of linear and nonlinear parameters. Why Should We Use Nonlinear Models?The main advantages of nonlinear models are parsimony, interpretability, and prediction (Bates and Watts, 2007). In general, nonlinear models are capable of accommodating a vast variety of mean functions, although each individual nonlinear model can be less flexible than linear models (i.e., polynomials) in terms of the variety of data they can describe; however, nonlinear models appropriate for a given application can be more parsimonious (i.e., there will be fewer parameters involved) and more easily interpretable. Interpretability comes from the fact that the parameters can be associated with a biologically meaningful process. For example, one of the most widely used nonlinear models is the logistic equation (Eq. [2.1] in Table 1). This model describes the pervasive S-shaped growth curve. The ABSTRACT 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 examinati...

There are many environmental benefits to incorporating cover crops into crop rotations, such as their potential to decrease soil erosion, reduce nitrate (NO 3 ) leaching, and increase soil organic matter. Some of these benefits impact other agroecosystem processes, such as greenhouse gas emissions. In particular, there is not a consensus in the literature regarding the effect of cover crops on nitrous oxide (N 2 O) emissions. Compared to site-specific studies, meta-analysis can provide a more general investigation into these effects. Twenty-six peer-reviewed articles including 106 observations of cover crop effects on N 2 O emissions from the soil surface were analyzed according to their response ratio, the natural log of the N 2 O flux with a cover crop divided by the N 2 O flux without a cover crop (LRR). Forty percent of the observations had negative LRRs, indicating a cover crop treatment which decreased N 2 O, while 60% had positive LRRs indicating a cover crop treatment which increased N 2 O. There was a significant interaction between N rate and the type of cover crop where legumes had higher LRRs at lower N rates than nonlegume species. When cover crop residues were incorporated into the soil, LRRs were significantly higher than those where residue was not incorporated. Geographies with higher total precipitation and variability in precipitation tended to produce higher LRRs. Finally, data points measured during cover crop decomposition had large positive LRRs and were larger than those measured when the cover crop was alive. In contrast, those data points measuring for a full year had LRRs close to zero, indicating that there was a balance between periods when cover crops increased N 2 O and periods when cover crops decreased emissions. Therefore, N 2 O measurements over the entire year may be needed to determine the net effect of cover crops on N 2 O. The data included in this meta-analysis indicate some overarching crop management practices that reduce direct N 2 O emissions from the soil surface, such as no soil incorporation of residues and use of nonlegume cover crop species. However, our results demonstrate that cover crops do not always reduce direct N 2 O emissions from the soil surface in the short term and that more work is needed to understand the full global warming potential of cover crop management. Key words: cover crops-global warming potential-meta-analysis-nitrous oxideAgricultural soils account for 69% of nitrous oxide (N 2 O) emissions in the United States (USEPA 2013). This occurs because nitrogen (N) is an essential nutrient for agricultural production; N is added to soil as N fertilizer and manure, released from soil organic matter, and has high reactivity and mobility in terrestrial ecosystems (Robertson and Vitousek 2009). Fertilizer N recovery efficiency for major cereal production is less than 50% and even as low as 20% (Cassman et al. 2002), which potentially makes large quantities of N available for the biological processes that release N 2 O. Nitrous oxide, which ...

Increasing the water-holding capacity of sandy soils will help improve efficiency of water use in agricultural production, and may be critical for providing enough energy and food for an increasing global population. We hypothesized that addition of biochar will increase the water-holding capacity of a sandy loam soil, and that the depth of biochar incorporation will influence the rate of biochar surface oxidation in the amended soils. Hardwood fast pyrolysis biochar was mixed with soil (0%, 3%, and 6% w/w) and placed into columns in either the bottom 11.4 cm or the top 11.4 cm to simulate deep banding in rows (DBR) and uniform topsoil mixing (UTM) applications, respectively. Four sets of 18 columns were incubated at 30 °C and 80% RH. Every 7 days, 150 mL of 0.001 M calcium chloride solution was added to the columns to produce leaching. Sets of columns were harvested after 1, 15, 29, and 91 days. Addition of biochar increased the gravity-drained water content 23% relative to the control. Bulk density of the control soils increased with incubation time (from 1.41 to 1.45 g cm−3), whereas bulk density of biochar-treated soils was up to 9% less than the control and remained constant throughout the incubation period. Biochar did not affect the CEC of the soil. The results suggest that biochar added to sandy loam soil increases water-holding capacity and might increase water available for crop use. Assessing potential of biochar for increasing waterholding capacity of sandy soils A N D R E S S . B A S S O , F E R N A N D O E . M I G U E Z , D A V I D A . L A I R D , R O B E R T H O R T O N and M A R K W E S T G A T EDepartment of Agronomy, Iowa State University, Ames, Iowa, USA AbstractIncreasing the water-holding capacity of sandy soils will help improve efficiency of water use in agricultural production, and may be critical for providing enough energy and food for an increasing global population. We hypothesized that addition of biochar will increase the water-holding capacity of a sandy loam soil, and that the depth of biochar incorporation will influence the rate of biochar surface oxidation in the amended soils. Hardwood fast pyrolysis biochar was mixed with soil (0%, 3%, and 6% w/w) and placed into columns in either the bottom 11.4 cm or the top 11.4 cm to simulate deep banding in rows (DBR) and uniform topsoil mixing (UTM) applications, respectively. Four sets of 18 columns were incubated at 30°C and 80% RH. Every 7 days, 150 mL of 0.001 M calcium chloride solution was added to the columns to produce leaching. Sets of columns were harvested after 1, 15, 29, and 91 days. Addition of biochar increased the gravity-drained water content 23% relative to the control. Bulk density of the control soils increased with incubation time (from 1.41 to 1.45 g cm À3), whereas bulk density of biochar-treated soils was up to 9% less than the control and remained constant throughout the incubation period. Biochar did not affect the CEC of the soil. The results suggest that biochar added to sandy loam soil increases wate...

The presence of workers that forgo reproduction and care for their siblings is a defining feature of eusociality and a major challenge for evolutionary theory. It has been proposed that worker behavior evolved from maternal care behavior. We explored this idea by studying gene expression in the primitively eusocial wasp Polistes metricus. Because little genomic information existed for this species, we used 454 sequencing to generate 391,157 brain complementary DNA reads, resulting in robust hits to 3017 genes from the honey bee genome, from which we identified and assayed orthologs of 32 honey bee behaviorally related genes. Wasp brain gene expression in workers was more similar to that in foundresses, which show maternal care, than to that in queens and gynes, which do not. Insulin-related genes were among the differentially regulated genes, suggesting that the evolution of eusociality involved major nutritional and reproductive pathways.