# A spatio-temporal model of embolism propagation in leaf vein networks

## TL;DR

The paper introduces a new model to study how embolisms spread in leaf veins, showing that vein structure and thickness influence embolism patterns during drought or freeze events.

## Contribution

A novel spatio-temporal model is developed to quantify embolism propagation in leaf veins, incorporating spatial dependency and vein thickness.

## Key findings

- Embolism likelihood increases when adjacent veins are affected, showing spatial dependency.
- Incorporating vein thickness improves predictions of future embolism events.
- Leaves with more connected vein networks show stronger embolism progression from thicker to thinner veins.

## Abstract

Leaf veins hydrate and sustain leaf tissue for photosynthesis. During drought and freeze events, embolisms can form in xylem conduits, ceasing the transport of water. Understanding the formation and propagation of embolisms is crucial to predicting species’ responses to a changing climate. We develop a novel spatio-temporal model for embolism propagation, explore the dynamics of xylem cavitation through spatial survival analysis modelling, and quantitatively examine the relationship between leaf venation features and embolism propagation. Our work models embolism propagation through spatial survival modelling, allowing us to compare the importance of different factors (vein thickness and spatial dependency) in embolism formation and predict future embolism occurrences. The model is fitted to published spatio-temporal embolism data for leaves of eight evergreen tropical tree species collected using the optical vulnerability technique. Results derived from our analyses shed light on the role of venation patterns on embolism formation. We found that incorporating spatial dependency reduces uncertainty in estimating vulnerability curves and posterior predictive error, thus supporting the notion that embolism formation exhibits spatial dependence. Specifically, the likelihood of embolism in a vein segment increases when adjacent veins are affected. Furthermore, including vein thickness information improves the prediction of future embolism events. Additionally, our model revealed that leaves with more connected vein networks (i.e. the degree of connectivity) exhibit a more pronounced pattern of embolizing from thicker to thinner veins. Understanding the formation and propagation of embolisms is crucial to understanding species’ responses to a changing climate. The proposed model provides a statistical tool to extract quantifiable insights on embolism propagation and how it is associated with observable leaf features, such as network connectivity. This approach allows for a systematic assessment of species’ responses to a drying climate.

Our paper explores the complex spatio-temporal dynamics of embolism formation in leaf vein networks and its relationship to leaf venation features. Applying a novel spatial survival model to data from evergreen trees, we show that embolism formation is spatially dependent, with embolisms more likely in adjacent veins. Incorporating vein thickness improves predictions, revealing that thicker veins embolize first. Notably, leaves with more connected vein networks exhibit a stronger pattern of embolizing from thicker to thinner veins. These findings highlight the role of venation structure in embolism progression and provide a powerful tool for assessing species' resilience to drought and freeze events.