The Persistent Homology Mathematical Framework Provides Enhanced Genotype-to-Phenotype Associations for Plant Morphology.

Efforts to understand the genetic and environmental conditioning of plant morphology are hindered by the lack of flexible and effective tools for quantifying morphology. Here, we demonstrate that persistent-homology-based topological methods can improve measurement of variation in leaf shape, serrations, and root architecture. We apply these methods to 2D images of leaves and root systems in field-grown plants of a domesticated introgression line population of tomato (Solanum pennellii). We find that compared with some commonly used conventional traits, (1) persistent-homology-based methods can more comprehensively capture morphological variation; (2) these techniques discriminate between genotypes with a larger normalized effect size and detect a greater number of unique quantitative trait loci (QTLs); (3) multivariate traits, whether statistically derived from univariate or persistent-homology-based traits, improve our ability to understand the genetic basis of phenotype; and (4) persistent-homology-based techniques detect unique QTLs compared to conventional traits or their multivariate derivatives, indicating that previously unmeasured aspects of morphology are now detectable. The QTL results further imply that genetic contributions to morphology can affect both the shoot and root, revealing a pleiotropic basis to natural variation in tomato. Persistent homology is a versatile framework to quantify plant morphology and developmental processes that complements and extends existing methods.

Classification of grass pollen through the quantitative analysis of surface ornamentation and texture.

Taxonomic identification of pollen and spores uses inherently qualitative descriptions of morphology. Consequently, identifications are restricted to categories that can be reliably classified by multiple analysts, resulting in the coarse taxonomic resolution of the pollen and spore record. Grass pollen represents an archetypal example; it is not routinely identified below family level. To address this issue, we developed quantitative morphometric methods to characterize surface ornamentation and classify grass pollen grains. This produces a means of quantifying morphological features that are traditionally described qualitatively. We used scanning electron microscopy to image 240 specimens of pollen from 12 species within the grass family (Poaceae). We classified these species by developing algorithmic features that quantify the size and density of sculptural elements on the pollen surface, and measure the complexity of the ornamentation they form. These features yielded a classification accuracy of 77.5%. In comparison, a texture descriptor based on modelling the statistical distribution of brightness values in image patches yielded a classification accuracy of 85.8%, and seven human subjects achieved accuracies between 68.33 and 81.67%. The algorithmic features we developed directly relate to biologically meaningful features of grass pollen morphology, and could facilitate direct interpretation of unsupervised classification results from fossil material.