Maximum-likelihood estimation of xylem vessel length distributions

Our analysis demonstrates that most published methods estimate the conditional length distribution of vessels that cross an injection point, which is a size-biased version of the overall length distribution in the stem. We show the mathematical relationship between these distributions and provide methods to estimate either of them. According to our simulation experiments, vessel length distribution was best described by the more flexible models, especially the Weibull distribution. In simulations, the estimators were able to recover the parameters of the vessel length distribution if its functional form was known, achieving an overlap of 90% or more between the true and predicted length distribution when counting no more than 500 injected vessels in 10 cross-sections. This sample size nowadays can easily be reached with the help of automated image analysis.