Reproductive Allometry in Soybean, Maize and Sunflower

Vega, Claudia Rosa Cecilia; Sadras, Víctor O.; Andrade, Fernando H.; Uhart, Sergio Adolfo

doi:10.1006/anbo.1999.1084

Cited by 139 publications

(120 citation statements)

References 37 publications

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“…[3.1]). For application examples, see Vega et al (2000), Vega and Sadras (2003), and Archontoulis et al (2010). The Michaelis-Menten equation (Eq.…”

Section: Group Vi-othersmentioning

confidence: 99%

Nonlinear Regression Models and Applications in Agricultural Research

2015

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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...

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“…[3.1]). For application examples, see Vega et al (2000), Vega and Sadras (2003), and Archontoulis et al (2010). The Michaelis-Menten equation (Eq.…”

Section: Group Vi-othersmentioning

confidence: 99%

Nonlinear Regression Models and Applications in Agricultural Research

2015

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“…The increase of stover yield with the increase of plant densities may be due to increasing numbers of plants and dry matter yield. Vega et al (2000) reported that maize grain yield is affected to a greater extent by variations in plant density than in other members of the grass family due to its tillering capacity. Tollenaar et al (1997) also reported that maize grain yield declines when plant density is increased beyond an optimum, primarily because of the decline in harvest index (HI) and increased stem lodging.…”

Section: Effect On Yield Stover Yield Harvest Index and Grain: Stovmentioning

confidence: 99%

Growth and Yield of Hybrid Maize (<i>Zea mays</i> L.) in Relation to Planting Density and Nitrogen Levels during Winter Season in Nepal

Dawadi¹,

Sah

2012

Trop. Agric. Res.

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“…Vega et al (2000) highlighted that maize has limited capacity to adjust the number of ears in response to resource availability, and low stability in HI. Improvement of yield potential of single plants is expected to be associated with improved HI and prolificacy at lower populations.…”

Section: Environmental Yield Index (Eyi) and Crop Yield Potential (Cyp)mentioning

confidence: 99%

Adapting maize crop to climate change

Tokatlidis

2012

Agron. Sustain. Dev.

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Global weather changes compel agriculture to be adequately productive under diverse and marginal conditions. In maize, modern hybrids fail to meet this requirement. Although breeding has achieved spectacular progress in grain yield per area through improved tolerance to stresses, including intense crowding, yields at low plant population densities remain almost unchanged. Stagnated plant yield potential renders hybrids unable to take advantage of resource abundance at lower populations, designating them population dependent. Consequently, the optimum population varies greatly across environments. Generally, the due population increases as the environmental yield potential gets higher. As a remedy, relatively low populations are recommended for low-input conditions leading to inappropriate population in occasional adequacy of resources and considerable yield loss. For example, for a rain-fed hybrid tested at one location across 11 seasons, crop yield potential and optimum population on the basis of the quadratic yield-plateau model varied from 1,890 to 8,980 kg/ha and 4.56 to 10.2 plants/m 2 , respectively, while 100 % yield loss is computed in the driest season if the optimum population for the most favorable season is used. The article reviews the consequences in terms of crop sustainability under widely diverse environments imposed by climatic changes and proposes crop management strategies to address the situation. The major points are: (1) variableyielding environments require variable optimum populations, (2) population dependence is an insurmountable barrier in making a decision on plant population, (3) farmers suffer from considerable yield and income loss, (4) estimating the less population-dependent hybrids among the currently cultivated ones is a major challenge for agronomists, and (5) the development of population-neutral hybrids is a fundamental challenge for maize breeding. Honeycomb breeding is a valuable tool to pursue this goal since it places particular emphasis on the so-far stagnated plant yield potential that is essential for population-neutral hybrid development.

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Reproductive Allometry in Soybean, Maize and Sunflower

Cited by 139 publications

References 37 publications

Nonlinear Regression Models and Applications in Agricultural Research

Nonlinear Regression Models and Applications in Agricultural Research

Growth and Yield of Hybrid Maize (<i>Zea mays</i> L.) in Relation to Planting Density and Nitrogen Levels during Winter Season in Nepal

Adapting maize crop to climate change

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