“Branch thinning and the large-scale, self-similar structure of trees”

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Lars Hellström, Linus Carlsson, Daniel Falster, Mark Westoby, and Åke Brännström (July 2018)

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Researchers present a model for wood-litter production that assumes a branch carrying capacity and allows analytical predictions

A new way to think about plant development: the large-scale branching structure of trees emerge as branches reach carrying capacity and discard subbranches

This tree, Angophora costata, exhibits an emergent, self-similar, branching structure that may have arisen as a result of carrying capacity constraints on the number of branch tips that can be maintained.
(Credit: Daniel Falster)

The intricate branching patterns of trees have fascinated humans throughout recorded history. In this international study, researchers from Sweden and Australia propose that these patterns can be understood as the result of independent branches growing and reaching a maximum carrying capacity, after which subbranches are discarded from the tree. This elementary principle is used to develop a simple, yet powerful, analytical theory of tree growth that is used to make predictions on branching structure and the rate and size-distribution of discarded branches. Offering support for their new perspective, the predictions of the analytical model are compared with empirical measurements from two different sources and found to be in agreement. By allowing explicit calculations on wood-litter production, these results potentially enable more explicit modelling of woody tissues in ecosystems worldwide, with implications for the build-up of flammable fuel, nutrient cycling, and understanding of plant growth.

The institutions participating in the study are Umeå University, Sweden, Mälardalen University, Sweden; the University of New South Wales, Australia; and Macquarie University, Australia. For further information about the study, please contact Åke Brännström (ake.brannstrom@umu.se, phone +46-72-5232554) or Daniel Falster (daniel.falster@unsw.edu.au, phone +61 2 9385 8431).


Abstract

Branch formation in trees has an inherent tendency towards exponential growth, but exponential growth in the number of branches cannot continue indefinitely. It has been suggested that trees balance this tendency towards expansion by also losing branches grown in previous growth cycles. Here, we present a model for branch formation and branch loss during ontogeny that builds on the phenomenological assumption of a branch carrying capacity. The model allows us to derive approximate analytical expressions for the number of tips on a branch, the distribution of growth modules within a branch, and the rate and size-distribution of tree wood-litter produced. Although limited availability of data makes empirical corroboration challenging, we show that our model can fit field observations of Red Maple, Acer rubrum, and note that the age distribution of discarded branches predicted by our model is qualitatively similar to an empirically observed distribution of dead and abscised branches of Balsam Poplar, Populus balsamifera. By showing how a simple phenomenological assumption—that the number of branches a tree can maintain is limited—leads directly to predictions on branching structure and the rate and size-distribution of branch loss, these results potentially enable more explicit modelling of woody tissues in ecosystems worldwide, with implications for the build-up of flammable fuel, nutrient cycling, and understanding of plant growth.