TOPOLOGICAL METHODS FOR THE QUANTIFICATION AND ANALYSIS OF COMPLEX PHENOTYPES

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 morphology. This simplification may lose important information about the phenotype. Rather than reducing the structural information, we introduce a novel method, the Persistence Intensity Array, for studying complex traits using tools from the emergent field of Topological Data Analysis. This approach uses the complete geometry of the phenotype and represents it as a simpler summary of the key topological shape features contained in the data. We demonstrate this method's efficacy by through a simulated QTL analysis.