Are Botanical Trees Graph-Theoretic Trees? The Ups and Downs of the Network Approach to Plant Growth

Because of their vascular nature, showing differentiated and spatially distributed organs, it may at first seem obvious to use an algebraic topology approach, in particular graph theory, to mathematically model higher plants such as trees. In this paper I will show that a network approach to modelling plants is, not surprisingly, an old one. However, by taking a historical and epistemological look at more recent work, I will show that such an approach – while seductive with each new generation of researchers – has regularly encountered multiple obstacles, especially in the modelling of individual plants. To explain the recurring nature of this renewed but often disappointing fascination with networks, I would like to suggest that in the case of plants, perhaps earlier than in many other living systems, it is necessary to refuse to separate the topology – be it algebraic and graphical in the sense of graph theory – from the dynamics of the emergence of this topology in concrete and anisotropic geometric space, nor from the functional mechanisms at work in this space. This is where the network approach may still reach its limits. To illustrate this, I will finally and briefly evoke recent integrative functional-structural models of plant growth that have abandoned the network approach in favour of a mixed algebraic-stochastic-geometric approach.