Maximum-likelihood estimation of xylem vessel length distributions

Area of Science:

• Plant Biology
• Plant Physiology
• Xylem Anatomy

Background:

• Vessel length is a key functional trait in plant hydraulics, influencing xylem hydraulic efficiency.
• Current methods for estimating vessel length distribution rely on injecting substances into stem segments and analyzing infusion profiles.
• The statistical basis of existing algorithms for vessel length estimation has not been rigorously analyzed.

Purpose of the Study:

• To derive a general mathematical expression for infusion profiles based on vessel length distribution.
• To provide analytical solutions for common distributions and develop maximum likelihood estimators.
• To compare the performance of new estimators against existing methods using Monte Carlo simulations.

Main Methods:

• Derivation of a general mathematical expression for infusion profile shape.
• Analytical solutions for exponential, Erlang(2), gamma, Weibull, and log-normal distributions.
• Development of maximum likelihood estimators and R implementations for two sampling schemes.
• Monte Carlo experiments to evaluate estimator performance.

Main Results:

• Most existing methods estimate a size-biased conditional vessel length distribution, not the overall distribution.
• The study provides methods to estimate both conditional and overall vessel length distributions.
• The Weibull distribution, among flexible models, best described vessel length distribution in simulations.
• Accurate parameter recovery was achieved with sample sizes of 500 vessels across 10 cross-sections.

Conclusions:

• The developed statistical framework improves the accuracy of vessel length distribution estimation.
• Understanding vessel length distribution is critical for a comprehensive analysis of plant hydraulic efficiency.
• Automated image analysis facilitates the collection of sufficient data for robust estimation.