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Full-Text Articles in Life Sciences

Topological Methods For The Quantification And Analysis Of Complex Phenotypes, Patrick S. Medina, Rebecca W. Doerge May 2016

Topological Methods For The Quantification And Analysis Of Complex Phenotypes, Patrick S. Medina, Rebecca W. Doerge

Conference on Applied Statistics in Agriculture

Quantitative Trait Locus (QTL) mapping of complex traits, such as leaf venation or root structures, require the phenotyping and genotyping of large populations. Sufficient genotyping is accomplished with cost effective high-throughput assays, however labor costs often makes sufficient phenotyping prohibitively limited. In order to develop efficient high-throughput phenotyping platforms for complex traits algorithms and methods for quantifying these traits are needed. It is often desirable to study the spatial organization of these phenotypes from the images generated by high-throughput platforms. With the goal of quantifying the traits, many approaches try to identify several core traits useful in describing the phenotypic …


Bayesian Estimation Of Stability Indices Of Sorghum Variety Trials, Siraj Osman Omer, Abdel Wahab Hassan Abdalla, Mohammed Hamza Mohammed, International Center For Agricultural Research In The Dry Areas (Icarda), Amman, Jordan May 2016

Bayesian Estimation Of Stability Indices Of Sorghum Variety Trials, Siraj Osman Omer, Abdel Wahab Hassan Abdalla, Mohammed Hamza Mohammed, International Center For Agricultural Research In The Dry Areas (Icarda), Amman, Jordan

Conference on Applied Statistics in Agriculture

Multiple–environmental trials are routinely conducted by crop improvement programs for developing desired genotypes. Over a long run, these programs gather information on genotypic performance and variability. Bayesian approach can be used to utilize prior information to identify genotypes for high and stable yield. A set of 18 sorghum genotypes were evaluated in randomized complete block designs (RCBD) with four replications during three seasons, 2009-2012 at diverse locations, North-Gedarif and South-Gedarif, in Sudan. Data on grain yield was analyzed. The aim of this paper was to estimate stability indices such as regression coefficient, coefficient of variation (CV %) and coefficient of …


Strategies For Reducing Control Group Size In Experiments Using Live Animals, Matthew Kramer, Enrique Font May 2016

Strategies For Reducing Control Group Size In Experiments Using Live Animals, Matthew Kramer, Enrique Font

Conference on Applied Statistics in Agriculture

Reducing the number of animal subjects used in biomedical experiments is desirable for both ethical and practical reasons. Previous suggestions for reducing sample sizes in these experiments have focused on improving experimental designs and methods of statistical analysis; reducing the number of controls (thus, the number of overall animals used) is rarely mentioned. We discuss how the number of current control animals can be reduced, without loss of statistical power, by incorporating information from historical controls, i.e. animals used as controls in similar previous experiments. Using example data from the literature, we describe how to incorporate information from historical controls …


Alternative Estimation Techniques For Correlated Discrete Data, William J. Price Ph.D., Bahman Shafii Ph.D. May 2016

Alternative Estimation Techniques For Correlated Discrete Data, William J. Price Ph.D., Bahman Shafii Ph.D.

Conference on Applied Statistics in Agriculture

Binary or multinomial data often occur in agricultural and biological research. Advancements in measurement and video technologies now allow such data to be sequentially recorded through time or space. These data sets, however, can exhibit a serial correlation structure, which in turn, can bias and influence point estimates as well as inferences made regarding the data. Statistical methods using generalized mixed models and probability distributions such as the beta-binomial and correlated binomial have been proposed as potential solutions for estimating the parameters of interest in these cases. In this paper, we will explore the properties of these techniques through simulation …


Developing Prediction Equations For Fat Free Lean In The Presence Of An Unknown Amount Of Proportional Measurement Error, Zachary J. Hass, Bruce A. Craig, Allan Schinckel May 2016

Developing Prediction Equations For Fat Free Lean In The Presence Of An Unknown Amount Of Proportional Measurement Error, Zachary J. Hass, Bruce A. Craig, Allan Schinckel

Conference on Applied Statistics in Agriculture

Published prediction equations for fat-free lean mass are widely used by producers for carcass evaluation. These regression equations are commonly derived under the assumption that the predictors are measured without error. In practice, however, it is known that some predictors, such as backfat and loin muscle depth, are measured imperfectly with variance that is proportional to the mean. Failure to account for these measurement errors will cause bias in the estimated equation. In this paper, we describe an empirical Bayes approach, using technical replicates, to accurately estimate the regression relationship in the presence of proportional measurement error. We demonstrate, via …


Paired Competition Analysis Using Mixed Models, Patrick Gallagher, Bruce A. Craig, Tim Luttermoser, Grzegorz Buczkowski May 2016

Paired Competition Analysis Using Mixed Models, Patrick Gallagher, Bruce A. Craig, Tim Luttermoser, Grzegorz Buczkowski

Conference on Applied Statistics in Agriculture

Urban and rural colonies of odorous house ants (Tapinoma sessile) have very different social structures. Urban colonies are very large with hundreds of cohabiting queens, while rural colonies are small with only one queen. To investigate whether worker ant aggressiveness varies across these two colony types, an experiment was performed using an aggression assay, in which 50 ants from each of two colonies were placed in a petri dish and allowed to fight. The response was the total number of dead ants within 24 hours. Because the ants were all the same species and not marked by colony, …


Irrigated And Rainfed Crops Zea Mays L. (Maize) And Glycine Max (Soybean) Acting As A Source Or Sink For Atmospheric Warming At Mead, Nebraska, Jane A. Okalebo Dr., Kenneth G. Hubbard, Andy Suyker May 2016

Irrigated And Rainfed Crops Zea Mays L. (Maize) And Glycine Max (Soybean) Acting As A Source Or Sink For Atmospheric Warming At Mead, Nebraska, Jane A. Okalebo Dr., Kenneth G. Hubbard, Andy Suyker

Conference on Applied Statistics in Agriculture

Land Use and Land Cover Change (LULCC) influence the climate at a global and local scale. Using long term microclimate data (2002-2009, 2011-2012) from the Carbon Sequestration Project (CSP), Mead, NE, this study examines how crop selection and water management can mitigate heat in the atmosphere. Mitigation of global warming is dependent on the management of crop lands, and the amount and timing of rainfall during the growing season. Rainfed crops were found to heat the passing air. The irrigated maize crop was able to mitigate 20 to 62% of the sensible heat (H) compared to the rainfed maize counterpart, …


Should Blocks Be Fixed Or Random?, Philip Dixon May 2016

Should Blocks Be Fixed Or Random?, Philip Dixon

Conference on Applied Statistics in Agriculture

Many studies include some form of blocking in the study design. Block effects are rarely of intrinsic interest; instead they are included in a model so that that model reflects the study design. I consider the question of how these block effects should be modeled: as fixed effects or as random effects. I discuss the consequences of the choice, including the recovery of inter-block information when available, give a simple example to illustrate the connection between recovery of inter-block information and pooling two estimators of a treatment effect, and give an example where fitting a model with random block effects …


Comparing Linear Mixed Models For Preliminary Yield Trials That Follow Augmented Experimental Designs, Sudha Neupane Adhikari, Jixiang Wu, Melanie Caffe May 2016

Comparing Linear Mixed Models For Preliminary Yield Trials That Follow Augmented Experimental Designs, Sudha Neupane Adhikari, Jixiang Wu, Melanie Caffe

Conference on Applied Statistics in Agriculture

COMPARING LINEAR MIXED MODELS FOR PRELIMINARY YIELD TRIALS THAT FOLLOW AUGMENTED EXPERIMENTAL DESIGNS

Sudha Neupane Adhikari, Jixiang Wu, and Melanie Caffe-Treml

Agronomy, Horticulture, and Plant Science Department,

South Dakota State University, Brookings, SD 57007

Abstract

Ineffective control of spatial variation when analyzing field trials data may lead to biased conclusions, which in turn could impact selection efficiency in plant breeding programs. In this study, a group of 78 oats breeding lines were evaluated in preliminary yield trials at four locations in South Dakota in 2015. Four linear mixed models (with and without row and column effects) were compared regarding reduction …


A Bayesian Gwas Method Utilizing Haplotype Clusters For A Composite Breed Population, Danielle F. Wilson-Wells, Stephen D. Kachman May 2016

A Bayesian Gwas Method Utilizing Haplotype Clusters For A Composite Breed Population, Danielle F. Wilson-Wells, Stephen D. Kachman

Conference on Applied Statistics in Agriculture

Commercial beef cattle are often composites of multiple breeds. Current methods used to produce genomic predictors are based on the underlying assumption of animals being sampled from a homogeneous population. As a result, the predictors can perform poorly when used to predict the relative genetic merit of animals whose breed composition are different. In part, this is due to the changes in linkage disequilibrium between the markers and the quantitative trait loci as we move from one breed to the next. An alternative model based on breed specific haplotype clusters was developed to allow for differences in linkage disequilibrium across …


Editor's Preface And Table Of Contents, Perla Reyes May 2016

Editor's Preface And Table Of Contents, Perla Reyes

Conference on Applied Statistics in Agriculture

2016 Conference on Applied Statistics in Agriculture Proceedings


K-Mer Analysis On Developmental And Housekeeping Enhancer Peaks, Yunsi Yang, Anurag Sethi, Mark Gerstein Sep 2015

K-Mer Analysis On Developmental And Housekeeping Enhancer Peaks, Yunsi Yang, Anurag Sethi, Mark Gerstein

Yale Day of Data

The regulation of gene expression involves interaction between transcriptional enhancers and core promoters. However, the separation between developmental and housekeeping gene regulation remains unknown. Here, we present a method to detect if different core promoters exhibit specificity to certain enhancers within massively parallel assays for enhancer detection. We use k-mers of various length (3-8bp) as sequence features and compare k-mer frequencies between developmental and housekeeping enhancers. This method shows promoter specificity of enhancers in D. melanogaster.


Binocular 3d Motion Perception As Bayesian Inference, Martin Lages, Suzanne Heron May 2015

Binocular 3d Motion Perception As Bayesian Inference, Martin Lages, Suzanne Heron

MODVIS Workshop

The human visual system encodes monocular motion and binocular disparity input before it is integrated into a single 3D percept. Here we propose a geometric-statistical model of human 3D motion perception that solves the aperture problem in 3D by assuming that (i) velocity constraints arise from inverse projection of local 2D velocity constraints in a binocular viewing geometry, (ii) noise from monocular motion and binocular disparity processing is independent, and (iii) slower motions are more likely to occur than faster ones. In two experiments we found that instantiation of this Bayesian model can explain perceived 3D line motion direction under …


Using A Generalized Linear Mixed Model Framework To Account For Spatial Variability In A Comparison Of Orchard Sprayer Efficacy, William J. Price, Bahman Shafii, Don Morishita Apr 2015

Using A Generalized Linear Mixed Model Framework To Account For Spatial Variability In A Comparison Of Orchard Sprayer Efficacy, William J. Price, Bahman Shafii, Don Morishita

Conference on Applied Statistics in Agriculture

Uniform application of pesticides in vineyard and orchard systems can be difficult to achieve due to variability in the density and structure of the crop canopy. Depending on the equipment used and environmental conditions, applications can result in poor spray coverage, spray drift, and wasted spray which, in turn, are manifested as a combination of poor pesticide efficacy, economic losses and potential environmental problems for the grower. A study was therefore designed and carried out to test new sprayer equipment aimed at addressing these issues. Statistically, the study presented a unique replicated three dimensional spatial design which captured response variability …


Statistical Methods In Topological Data Analysis For Complex, High-Dimensional Data, Patrick S. Medina, R W. Doerge Jan 2015

Statistical Methods In Topological Data Analysis For Complex, High-Dimensional Data, Patrick S. Medina, R W. Doerge

Conference on Applied Statistics in Agriculture

The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data spaces. This paper provides an introductory overview of the mathematical underpinnings of Topological Data Analysis, the workflow to convert samples of data to topological summary statistics, and some of the statistical methods developed for performing inference on these topological summary statistics. The intention of this non-technical overview is to motivate statisticians who are interested in learning more about the subject.


Best Linear Unbiased Prediction: An Illustration Based On, But Not Limited To, Shelf Life Estimation, Maryna Ptukhina, Walter Stroup Jan 2015

Best Linear Unbiased Prediction: An Illustration Based On, But Not Limited To, Shelf Life Estimation, Maryna Ptukhina, Walter Stroup

Conference on Applied Statistics in Agriculture

Shelf life estimation procedures, following ICH guidelines, use multiple batch regression with fixed batch effects. This guidance specifically mandates estimates based on at least 3 batches. Technically, the fixed-batch model limits inference to the batches actually observed, whereas ICH requires resulting estimates to apply to all future batches stored under similar conditions. This creates a conflict between the model used and the inference space the model is intended to address. Quinlan, et al. (2013) and Schwenke (2010) studied the small sample behavior of this procedure. Both studies revealed large sampling variation associated with the ICH procedure, producing a substantial proportion …


Shiga Toxin-Producing Escherichia Coli In Meat: A Preliminary Simulation Study On Detection Capabilities For Three Sampling Methods, Julie Couton, David Marx, John Luchaansky, Randall Phebus, Anna Porto-Fett, Nicholas Sevart, Manpreet Singh, Harshavardhan Thippareddi Jan 2015

Shiga Toxin-Producing Escherichia Coli In Meat: A Preliminary Simulation Study On Detection Capabilities For Three Sampling Methods, Julie Couton, David Marx, John Luchaansky, Randall Phebus, Anna Porto-Fett, Nicholas Sevart, Manpreet Singh, Harshavardhan Thippareddi

Conference on Applied Statistics in Agriculture

Contamination by Shiga Toxin-producing Escherichia coli (STEC) is a continuing concern for meat production facility management throughout the United States. Several methods have been used to detect STEC during meat processing, however the excessive experimental cost of determining the optimal method is rarely feasible. The objective of this preliminary simulation study is to determine which sampling method (Cozzini core sampler, core drill shaving, and N-60 surface excision) will better detect STEC at varying levels of contamination present in the meat. 1000 simulated experiments were studied using a binary model for rare occurrences to find the optimal method. We found that …


Differential Methylation Methods In Multi-Context Organisms, Douglas Baumann, Yuqing Su, Iranga Mendis, Gayla R. Olbricht Jan 2015

Differential Methylation Methods In Multi-Context Organisms, Douglas Baumann, Yuqing Su, Iranga Mendis, Gayla R. Olbricht

Conference on Applied Statistics in Agriculture

DNA methylation is an epigenetic modification that has the ability to alter gene expression without any change in the DNA sequence. DNA methylation occurs when a methyl chemical group attaches to cytosine bases on the DNA sequence. In mammals, DNA methylation primarily occurs at CG sites, when a cytosine is followed by a guanine in the DNA sequence. In plants, DNA methylation can also occur in other cytosine sequences, such as when a cytosine is not followed directly by a guanine. Many of the statistical methods that have been developed to estimate methylation levels and test differential methylation in whole-genome …


On Fixed Effects Estimation In Spline-Based Semiparametric Regression For Spatial Data, Guilherme Ludwig, Jun Zhu, Chun-Shu Chen Jan 2015

On Fixed Effects Estimation In Spline-Based Semiparametric Regression For Spatial Data, Guilherme Ludwig, Jun Zhu, Chun-Shu Chen

Conference on Applied Statistics in Agriculture

Spline surfaces are often used to capture spatial variability sources in linear mixed-effects models, without imposing a parametric covariance structure on the random effects. However, including a spline component in a semiparametric model may change the estimated regression coefficients, a problem analogous to spatial confounding in spatially correlated random effects. Our research aims to investigate such effects in spline-based semiparametric regression for spatial data. We discuss estimators' behavior under the traditional spatial linear regression, how the estimates change in spatial confounding-like situations, and how selecting a proper tuning parameter for the spline can help reduce bias.


Small Sample Properties Of The Two Independent Sample Test For Means From Beta Distributions, Edward E. Gbur, Kevin Thompson Jan 2015

Small Sample Properties Of The Two Independent Sample Test For Means From Beta Distributions, Edward E. Gbur, Kevin Thompson

Conference on Applied Statistics in Agriculture

Researchers often collect proportion data that cannot be interpreted as arising from a set of Bernoulli trials. Analyses based on the beta distribution may be appropriate for such data. The SAS® GLIMMIX procedure provides a tool for these analyses using a likelihood based approach within the larger context of generalized linear mixed models (GLMM). The small sample behavior of likelihood based tests to compare the means from two independently sampled beta distributions were studied via simulation when the null hypothesis of equal means holds. Two simulation scenarios were defined by equal and unequal sample sizes and equal scale parameters. A …


Modeling The Occurrence Of Four Cereal Crop Aphid Species In Idaho, John W. Merickel, Bahman Shafii, Sanford D. Eigenbrode, Christopher J. Williams, William J. Price Jan 2015

Modeling The Occurrence Of Four Cereal Crop Aphid Species In Idaho, John W. Merickel, Bahman Shafii, Sanford D. Eigenbrode, Christopher J. Williams, William J. Price

Conference on Applied Statistics in Agriculture

Idaho is ranked 5th in the United States in overall wheat production and makes over $500 million in profit annually from wheat. Many pests have detrimental effects on wheat; some of the most predominant ones are aphids. Four species of aphids having economic effects on wheat crops in Idaho are: Diuraphis noxia, Metopolophium dirhodum, Rhopalosiphum padi, Sitobion avenae. Predictive regression models could be useful for better understanding of the occurrence of these aphid species. Count data for the four species were collected over 17 years via suction traps at 12 locations in wheat fields throughout …


Editor's Preface And Table Of Contents, Perla E. Reyes Jan 2015

Editor's Preface And Table Of Contents, Perla E. Reyes

Conference on Applied Statistics in Agriculture

These proceedings contain papers presented at the twenty-seventh annual Kansas State University Conference on Applied Statistics in Agriculture, held in Manhattan, Kansas, April 26 - April 28, 2015


Modeling Ratios With Potential Zero-Inflation To Assess Soil Nematode Community Structure, Joanna Zbylut, Leigh Murray, S. H. Thomas, J. Beacham, J. Schroeder, C. Fiore Apr 2014

Modeling Ratios With Potential Zero-Inflation To Assess Soil Nematode Community Structure, Joanna Zbylut, Leigh Murray, S. H. Thomas, J. Beacham, J. Schroeder, C. Fiore

Conference on Applied Statistics in Agriculture

The southern root-knot nematode (SRKN) and the weedy perennials, yellow nutsedge (YNS) and purple nutsedge (PNS) are simultaneously-occurring pests in the irrigated agricultural soils of southern New Mexico. Previous research has characterized SRKN, YNS and PNS as a mutually beneficial pest complex and has shown their enhanced population growth and survival when they occur together. In addition, it was shown that the density of nutsedge in a field could be used as a predictor of SRKN juveniles in the soil. In addition to SRKN, which is the most harmful of the plant parasitic nematodes, in southern New Mexico other species …


Developing Prediction Equations For Carcass Lean Mass In The Prescence Of Proportional Measurement Error, Zachary J. Hass, Ziqi Zhou, Bruce A. Craig Apr 2014

Developing Prediction Equations For Carcass Lean Mass In The Prescence Of Proportional Measurement Error, Zachary J. Hass, Ziqi Zhou, Bruce A. Craig

Conference on Applied Statistics in Agriculture

Published prediction equations for carcass lean mass are widely used by commercial pork producers for carcass valuation. These regression equations have been derived under the assumption that the predictors, such as back fat depth, are measured without error. In practice, however, it is known that these measurements are imperfect, with a variance that is proportional to the mean. In this paper, we consider both a linear and quadratic true relationship and compare regression fits among two methods that account for this error versus simply ignoring the additional error. We show that biased estimates of the relationship result if measurement error …


Check Based Stability Analysis Method And Its Application To Winter Wheat Variety Trials, Jixiang Wu, Karl Glover, Nathan Mueller Apr 2014

Check Based Stability Analysis Method And Its Application To Winter Wheat Variety Trials, Jixiang Wu, Karl Glover, Nathan Mueller

Conference on Applied Statistics in Agriculture

Finley-Wilson (FW) regression based stability analysis is highly dependent on the testing varieties and environments being used. In this study, we proposed a check based regression method to determine yield stability. One advantage of this method is its capability to determine yield stability through widely acceptable varieties and thus to provide more meaningful information to evaluate the potential use of new varieties. In addition, with integration a resampling technique, bootstrapping method, yield stability can be compared among different varieties/genotypes from either the same or different testing environments. As a demonstration, we applied this method to analyze the 2009- 2011 winter …


Use Of The Posterior Predictive Distribution As A Diagnostic Tool For Mixed Models, Matthew Kramer Apr 2014

Use Of The Posterior Predictive Distribution As A Diagnostic Tool For Mixed Models, Matthew Kramer

Conference on Applied Statistics in Agriculture

The posterior predictive distribution (the distribution of data simulated from a model) has been used to flag model-data discrepancies in the Bayesian literature, and several approaches have been developed. The approach taken here differs from the others both conceptually and as realized. It works by comparing the "distance" between the data and model (as represented by pseudo-data simulated from a model) with "distance" within the model. The distance within the model is calculated by generating pseudo-data from it, using each set of these pseudo-data to reestimate the model, and then generating pseudo-data from them, matching the way the original data …


Bayesian Inference For A Covariance Matrix, Ignacio Alvarez, Jarad Niemi, Matt Simpson Apr 2014

Bayesian Inference For A Covariance Matrix, Ignacio Alvarez, Jarad Niemi, Matt Simpson

Conference on Applied Statistics in Agriculture

Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of these problems requires a prior on the covariance matrix. Here we compare an inverse Wishart, scaled inverse Wishart, hierarchical inverse Wishart, and a separation strategy as possible priors for the covariance matrix. We evaluate these priors through a simulation study and application to a real data set. Generally all priors work well with the exception of the inverse Wishart when the true variance is small relative to prior mean. In this …


Modeling Sleep And Wake Bouts In Drosophila Melanogaster, Gayla R. Olbricht, V. A. Samaranayake, Sahitya Injamuri, Luyang Wang, Courtney Fiebelman, Matthew S. Thimgan Apr 2014

Modeling Sleep And Wake Bouts In Drosophila Melanogaster, Gayla R. Olbricht, V. A. Samaranayake, Sahitya Injamuri, Luyang Wang, Courtney Fiebelman, Matthew S. Thimgan

Conference on Applied Statistics in Agriculture

Adequate sleep restores vital processes required for health and well-being; but the function and regulation of sleep is not well understood. Unfortunately, a definition of adequate sleep is unclear. On an hours-long timescale, consolidated and cycling sleep results in better health and performance outcomes. At shorter timescales, older studies report conflicting results regarding the relationship between sleep and wake bout durations. One approach to this problem has been to simply analyze the distribution of bout durations. While informative, this method eliminates the time relationship between bouts, which may be important. Here, we develop a model that describes the relationship between …


Multivariate Statistical Analysis Of Coleoptera Spectral Reflectance, Sarah E.M. Herberger, Bahaman Shafii, Stephen P. Cook, Christopher J. Williams, William J. Price Apr 2014

Multivariate Statistical Analysis Of Coleoptera Spectral Reflectance, Sarah E.M. Herberger, Bahaman Shafii, Stephen P. Cook, Christopher J. Williams, William J. Price

Conference on Applied Statistics in Agriculture

The insect order Coleoptera, commonly known as beetles, comprises 40% of all insects which in turn account for half of all identified animal species alive today. Coleopterans frequently have large elytra (the hardened front wings) that can have a wide range of colors. Spectral reflectance readings from these elytra may be used to uniquely identify coleopteran taxonomic groups. Multiple samples of eleven species of wood boring beetles were selected from the University of Idaho William Barr Entomology Museum. Spectrometer readings for each specimen were then fit to normal distribution mixture models to identify multiple peak reflectance wavelengths. Eighteen prominent peaks …


Response Of Soybean Yield And Yield Components To Phosphorus Fertilization In South Dakota, Adams Kusi Appiah, Rebecca Helget, Yi Xu, Jixiang Wu Apr 2014

Response Of Soybean Yield And Yield Components To Phosphorus Fertilization In South Dakota, Adams Kusi Appiah, Rebecca Helget, Yi Xu, Jixiang Wu

Conference on Applied Statistics in Agriculture

Increased demand for soybean [Glycine max (L.) Merrill] production for industrial, human, and animal consumption has provided many incentives for farmers and producers to increase their production. In many soils used for soybean production, phosphorus (P) becomes a major limiting factor to soybean growth and grain production. A field experiment was conducted in five locations across Eastern South Dakota in 2013 to study the response of soybean yield and yield components to phosphorus fertilizer applications. The experiment was laid out in a randomized complete block (RCB) design with four replications. The treatments consisted of five P levels 0, 20, 40, …