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.

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.

No abstract

We propose and test the Limiting-Stress-Elimination Hypothesis (LSEH), as a decision axiom to guide in determining the optimal intervention strategy towards yield allocation in a savanna legume. We considered osmotic stress and soil nitrogen (N) limitation, which both characterize Guinea savanna agro-ecozone. We hypothesized that biomass allocation will increase when the limiting stress is eliminated at least until the next limiting stress impacts yield. We assessed responses of Vigna unguiculata (L.) Walp (cowpea) to osmotic stress treatments (non-hormonal biostimulant and exogenous metabolite) and N input by leaf level physiology, N-fixing capacity and biomass. The relative increase in biomass (%), and pod yields reveal that osmotic stress (45%) more than nitrogen (13%) is limiting to cowpea growth under Guinea savanna conditions, although N fertilization increased nodulation and maximized PSII quantum yield. In the Sprengel-Liebig’s decrement from the maximum concept, the decrement from the maximum for each stressor must be minimized in order to produce the absolute maximum production. However, this may not be economically feasible in many situations. Conversely, LSEH demonstrates that significant productivity is attainable by eliminating a relatively more limiting stress, osmotic stress, regardless of the limitation and natural demand for the relatively less limiting N in leguminous cowpea in the savanna.

No abstract

An alternative decision axiom to guide in determining the optimal intervention strategy to maximize cowpea production is proposed. According to the decrement from the maximum concept of Mitscherlich, the decrement from the maximum for each stressor must be minimized to produce the absolute maximum production. In crop production, this means all deficient nutrients must be supplemented to ensure maximum yield and laid the foundation in fertilizer formulation. However, its implementation is not economically feasible in many situations, particularly where multiple environmental factors impact crop productivity as in the case of low resource conditions. We propose and test the hypothesis that yield allocation will increase when the most limiting stressor among prevailing stressors is eliminated at least until the next limiting stressor impacts productivity. We selected drought limiting savanna conditions and cowpea (Vigna unguiculata), adapted to nitrogen dependence. To determine the limiting condition, we measured the response of cowpea to D-sorbitol, nitrogen, and non-hormonal biostimulant (nhB) treatments. The nhB treatment increased total biomass by 45% compared to nitrogen, 13%, and D-sorbitol, 17%, suggesting osmotic stress is more limiting in the observed savanna conditions. The effect of the biostimulant is due to antioxidants and key amino acids that stimulate metabolism and stress resistance. Where nitrogen becomes the next constraining factor, biostimulants can contribute organic nitrogen. The study supports the use of biostimulants as candidate intervention under conditions where crop productivity is limited by multiple or alternating constraints during crop growth.

No abstract