The use of trait-based approaches to understand ecological communities has increased in the past two decades because of their promise to preserve more information about community structure than taxonomic methods and their potential to connect community responses to subsequent effects of ecosystem functioning. Though trait-based approaches are a powerful tool for describing ecological communities, many important properties of commonly-used trait metrics remain unexamined. Previous work with simulated communities and trait distributions shows sensitivity of functional diversity measures to the number and correlation of traits used to calculate them, but these relationships have yet to be studied in actual plant communities with a realistic distribution of trait values, ecologically meaningful covariation of traits, and a realistic number of traits available for analysis. To address this gap, we used data from six grassland plant communities in Minnesota and New Mexico, USA to test how the number of traits and the correlation between traits used in the calculation of eight functional diversity indices impact the magnitude of functional diversity metrics in real plant communities. We found that most metrics were sensitive to the number of traits used to calculate them, but functional dispersion (FDis), kernel density estimation dispersion (KDE dispersion), and Raos quadratic entropy (Raos Q) maintained consistent rankings of communities across the range of trait numbers. Despite sensitivity of metrics to trait correlation, there was no consistent pattern between communities as to how metrics were affected by the correlation of traits used to calculate them. We recommend that future use of evenness metrics include sensitivity analyses to ensure results are robust to the number of traits used to calculate them. In addition, we recommend use of FDis, KDE dispersion, and Raos Q when ecologically applicable due to their ability to produce consistent rankings among communities across a range of the numbers of traits used to calculate them.

The use of trait-based approaches to understand ecological communities has increased in the past two decades because of their promise to preserve more information about community structure than taxonomic methods and their potential to connect community responses to subsequent effects of ecosystem functioning. Though trait-based approaches are a powerful tool for describing ecological communities, many important properties of commonly-used trait metrics remain unexamined. Previous work in studies that simulate communities and trait distributions show consistent sensitivity of functional richness and evenness measures to the number of traits used to calculate them, but these relationships have yet to be studied in actual plant communities with a realistic distribution of trait values, ecologically meaningful covariation of traits, and a realistic number of traits available for analysis. Therefore, we propose to test how the number of traits used and the correlation between traits used in the calculation of functional diversity indices impacts the magnitude of eight functional diversity metrics in real plant communities. We will use trait data from three grassland plant communities in the US to assess the generality of our findings across ecosystems and experiments. We will determine how eight functional diversity metrics (functional richness, functional evenness, functional divergence, functional dispersion, kernel density estimation (KDE) richness, KDE evenness, KDE dispersion, Rao's Q) differ based on the number of traits used in the metric calculation and on the correlation of traits when holding the number of traits constant. Without a firm understanding of how a scientist's choices impact these metric, it will be difficult to compare results among studies with different metric parametrization and thus, limit robust conclusions about functional composition of communities across systems.

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.