Despite the variability among plants in the properties of their water-conducting elements, all xylem types are formed by dead cells connected by specialized pit membranes in a network, whose behaviour may be affected by the topology of the conducting elements, the degree of connectivity of the network and the dynamics of the network. We previously applied graph theory to develop a model of xylem water transport accounting for connectivity among conduit elements (Loepfe et al 2007) and showed that maximum hydraulic conductivity and vulnerability to embolism can increase with xylem connectivity. Here, we use databases of xylem anatomical images to determine the average degree of connectivity of xylem elements for various xylem types and test the behaviour of the model.

Xylem anatomical images of trees were obtained from the Wood Anatomy Data Base. Radial sections were available for about 130 species. For each slide, we measured number and size of the conduits, number of contacts between conduits and statistics of their distribution based on Ripley's K function. The K function is a statistic for point pattern analysis, allowing comparing observed spatial distributions against expected Poisson distribution. Results were summarised by wood type (tracheid-based, diffuse porous, semi-ring porous and ring porous) and the values used to parameterise our model.
Results/Conclusions

Tracheid-based wood of gymnosperms showed uniquely a uniform distribution, whereas angiosperm wood varied in its spatial distribution along the gradient diffuse porous, semi-ring porous and ring porous, with a higher proportion of random and aggregate distributions in the latter two types. Using the measured values of vessel size, density and spatial aggregation, we then parameterised a version of the Loepfe model. Additional model constraints were derived from published allometric relationships between vessel diameter and length and area of pit membranes and length.

The model confirmed that significant differences exist across species in the degree of xylem connectivity, with ring porous species significantly more sensitive to the degree of connectivity and tracheid-based gymnosperms essentially insensitive. The observed spatial topologies (and associated conduit size and densities) suggest that important gradients exist across species in the degree by which system-level properties such as xylem connectivity can effectively limit both water transport under favourable conditions and the spread of embolisms during drought.

References.

Loepfe L., J. Martinez-Vilalta, Pinol J., M. Mencuccini, 2007. The relevance of xylem network structure for plant hydraulic efficiency and safety. J. Theor. Biol., 247:788-803.