Vessel redundancy: Modeling safety in numbers

We examined the concept that high vessel number provides xylem safety and also show that under certain circumstances high vessel number may increase rather than decrease the probability of mortality. The independent variable was the number of vessels per organ (redundancy). The dependent variable was the probability of organ death for which we set three thresholds for catastrophic runaway embolism (50, 75 and 90 % embolism). Results were calculated based upon the probability that any particular vessel would become embolized (p). When the modeled p was below the runaway embolism threshold, the safety benefits (decreased probability of organ death) increased dramatically in going from one to ten vessels and approached maximum levels of safety in organs with 100 or more vessels. Vessel redundancy conferred the greatest advantage when p approached, but was less than, the runaway embolism threshold of the organ. However, when p exceeded the runaway embolism threshold the redundancy relationship was reversed and safety was greatest in organs with lower vessel numbers. Having greater vessel redundancy increased the likelihood of an average result, i.e., mortality if p is above the threshold, and survival when p is below the threshold. Model predictions are discussed in terms of redundancy segmentation, stem splitting and various other ecological and evolutionary conditions.