# Fitting rectangles under vulnerability curves: optimal water flow through plants

## TL;DR

This paper models steady state water transport in plants, optimizing flow while considering hydraulic vulnerabilities, revealing bottleneck effects and supporting the leaf safety buffer hypothesis with experimental validation.

## Contribution

It introduces a geometric optimization model for plant water flow that accounts for embolism constraints, highlighting bottleneck phenomena and aligning with experimental data.

## Key findings

- Optimal water flow is limited by bottleneck segments.
- Leaves act as safety buffers against embolism.
- Model predictions agree with experimental measurements.

## Abstract

We study an optimization problem for a model of steady state water transport through plants that maximizes water flow subject to the constraints on hydraulic conductance due to vulnerability to embolism (air blockage of conduits). The model has an elementary geometric interpretation, and exhibits bottleneck behavior where one of the plant segments limits the overall optimal flow, sometimes in a counterintuitive way. The results show good agreement with experimental measurements and provide support for the hypothesis that leaves serve as a safety buffer protecting stems against excessive embolism.