Tree crowns grow into self-similar shapes controlled by gravity and light sensing

TL;DR

This paper introduces a length-free propagating front model to study how gravity and light sensing tropisms influence the self-similar shapes of tree crowns, revealing that shape diversity depends on the balance of these tropisms.

Contribution

The study develops a novel length-free growth model demonstrating how tropism balances determine tree crown shapes, explaining observed shape diversity.

Findings

Different tropism intensities produce various self-similar crown shapes.

Some emergent shapes resemble real tree species.

Shape singularities can occur depending on tropism balance.

Abstract

Plants have developed different tropisms: in particular, they re-orient the growth of their branches towards light (phototropism) or upwards (gravitropism). How these tropisms affect the shape of a tree crown remains unanswered. We address this question by developing a propagating front model of tree growth. This model being length-free, it leads to self-similar solutions, independent of the initial conditions, at long time. Varying the intensities of each tropism, different self-similar shapes emerge, including singular ones. Interestingly, these shapes bear similarities with existing tree species. It is concluded that the core of specific crown shapes in trees relies on the balance between tropisms.