Pitfalls and Remedies for Cross Validation with Multi-trait Genomic Prediction Methods.

Incorporating measurements on correlated traits into genomic prediction models can increase prediction accuracy and selection gain. However, multi-trait genomic prediction models are complex and prone to overfitting which may result in a loss of prediction accuracy relative to single-trait genomic prediction. Cross-validation is considered the gold standard method for selecting and tuning models for genomic prediction in both plant and animal breeding. When used appropriately, cross-validation gives an accurate estimate of the prediction accuracy of a genomic prediction model, and can effectively choose among disparate models based on their expected performance in real data. However, we show that a naive cross-validation strategy applied to the multi-trait prediction problem can be severely biased and lead to sub-optimal choices between single and multi-trait models when secondary traits are used to aid in the prediction of focal traits and these secondary traits are measured on the individuals to be tested. We use simulations to demonstrate the extent of the problem and propose three partial solutions: 1) a parametric solution from selection index theory, 2) a semi-parametric method for correcting the cross-validation estimates of prediction accuracy, and 3) a fully non-parametric method which we call CV2*: validating model predictions against focal trait measurements from genetically related individuals. The current excitement over high-throughput phenotyping suggests that more comprehensive phenotype measurements will be useful for accelerating breeding programs. Using an appropriate cross-validation strategy should more reliably determine if and when combining information across multiple traits is useful

Bayesian Sparse Factor Analysis of Genetic Covariance Matrices

Quantitative genetic studies that model complex, multivariate phenotypes are important for both evolutionary prediction and artificial selection. For example, changes in gene expression can provide insight into developmental and physiological mechanisms that link genotype and phenotype. However, classical analytical techniques are poorly suited to quantitative genetic studies of gene expression where the number of traits assayed per individual can reach many thousand. Here, we derive a Bayesian genetic sparse factor model for estimating the genetic covariance matrix (G-matrix) of high-dimensional traits, such as gene expression, in a mixed effects model. The key idea of our model is that we need only consider G-matrices that are biologically plausible. An organism's entire phenotype is the result of processes that are modular and have limited complexity. This implies that the G-matrix will be highly structured. In particular, we assume that a limited number of intermediate traits (or factors, e.g., variations in development or physiology) control the variation in the high-dimensional phenotype, and that each of these intermediate traits is sparse -- affecting only a few observed traits. The advantages of this approach are two-fold. First, sparse factors are interpretable and provide biological insight into mechanisms underlying the genetic architecture. Second, enforcing sparsity helps prevent sampling errors from swamping out the true signal in high-dimensional data. We demonstrate the advantages of our model on simulated data and in an analysis of a published Drosophila melanogaster gene expression data set.Comment: 35 pages, 7 figure

Dissecting high-dimensional phenotypes with bayesian sparse factor analysis of genetic covariance matrices.

Quantitative genetic studies that model complex, multivariate phenotypes are important for both evolutionary prediction and artificial selection. For example, changes in gene expression can provide insight into developmental and physiological mechanisms that link genotype and phenotype. However, classical analytical techniques are poorly suited to quantitative genetic studies of gene expression where the number of traits assayed per individual can reach many thousand. Here, we derive a Bayesian genetic sparse factor model for estimating the genetic covariance matrix (G-matrix) of high-dimensional traits, such as gene expression, in a mixed-effects model. The key idea of our model is that we need consider only G-matrices that are biologically plausible. An organism's entire phenotype is the result of processes that are modular and have limited complexity. This implies that the G-matrix will be highly structured. In particular, we assume that a limited number of intermediate traits (or factors, e.g., variations in development or physiology) control the variation in the high-dimensional phenotype, and that each of these intermediate traits is sparse - affecting only a few observed traits. The advantages of this approach are twofold. First, sparse factors are interpretable and provide biological insight into mechanisms underlying the genetic architecture. Second, enforcing sparsity helps prevent sampling errors from swamping out the true signal in high-dimensional data. We demonstrate the advantages of our model on simulated data and in an analysis of a published Drosophila melanogaster gene expression data set

Master\u27s Project: Guiding Recreation at Travertine Hot Springs: An Environmental Assessment and Photo Monitoring Protocol

In a remote corner of eastern California, natural hot springs deposit tawny ribbons of travertine limestone within a mosaic of sagebrush steppe, pinyon-juniper woodland, and alkali meadows. Known as Travertine Hot Springs Area of Critical Environmental Concern, these 160 acres host tens of thousands of visitors each year. Trampled vegetation, illegal campfire rings, and two and a half miles of meandering informal paths attest to the heavy use the area sustains. In partnership with the Bureau of Land Management and the Bridgeport Indian Colony, I designed a trail system, a blueprint for interpretive signage, and a suite of infrastructural enhancements to guide visitors more gently through this landscape. Yet these management strategies are only the first step toward successful rehabilitation. Equally important is evaluating the effectiveness of the chosen approach. To that end, I developed a photo monitoring protocol that allows managers to assess erosion and vegetation recovery at key locations, and adapt their plans accordingly. By galvanizing citizen scientists and local stakeholders, this protocol will produce abundant monitoring data and may help to inspire a new ethic of stewardship at the site. While we cannot foresee all possible future recreation patterns and problems at Travertine Hot Springs, a robust photographic record will ensure that we are not blind to change

The Gender Wage Gap in Sports: Explaining the Pay Gap in Sports

Senior Project submitted to The Division of Social Studies of Bard College

Corruption in Nigeria: an Appraisal

Corruption pervades every continent of the world however it is endemic in Nigeria. It is said to be the root cause of every ill bedevilling the nation, the primary cause of stagnancy, gross underdevelopment, high rate of criminality and terrorism. This paper intends to examine corruption in Nigeria, causes and effects with a view to suggesting methods for effective amelioration

The Brandt Report—a Christian Reaction

Summary Christians have an obligation to support the cause of the underprivileged and this means working for economic reform. Whether we like it or not we are obliged to think in international terms and resolve some of our problems on the international stage—the Brandt Report provides a frame of reference for this endeavour. Resume Le rapport Brandt—une réaction d'un Chrétien Les Chrétiens doivent soutenir la cause des déshérités et s'attacher à promouvoir une réforme économique. Que cela nous plaise ou non, nous devons penser en termes internationaux et résoudre certains de nos problèmes au niveau international. Le rapport Brandt fournit des directives utiles à cet égard. ResumeN El Informe Brandt: una reacción cristiana Los cristianos tienen la obligación de apoyar la causa de los desprivilegiados y esto significa esforzarse por la reforma económica. Tanto si nos gusta como si no, estamos obligados a pensar en términos internacionales y resolver algunos de nuestros problemas en la escena internacional: el Informe Brandt proporciona un ámbito de referencia para este esfuerzo