Tree size distribution as the stationary limit of an evolutionary master equation

Kelemen, Szabolcs and Józsa, Máté and Hartel, Tibor and Csóka, György and Néda, Zoltán (2024) Tree size distribution as the stationary limit of an evolutionary master equation. SCIENTIFIC REPORTS, 14 (1). ISSN 2045-2322

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The diameter distribution of a given species of deciduous trees is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data in mature semi-natural forest and ancient, traditionally managed wood-pasture from Central Europe. These distribution functions collapse on a universal shape if the tree sizes are normalized to the mean value in the considered sample. A new evolutionary master equation is used to model the observed distribution. The model incorporates four ecological processes: tree growth, mortality, recruitment, and diversification. Utilizing simple and realistic kernel functions describing the first three, along with an assumed multiplicative dilution due to diversification, the stationary solution of the master equation yields the experimentally observed Gamma distribution. The model as it is formulated allows an analytically compact solution and has only two fitting parameters whose values are consistent with the experimental data related to these processes. We found that the equilibrium size distribution of tree species with different ecology, originating from two contrastingly different semi-natural ecosystem types can be accurately described by a single dynamical mean-field model.

Tudományterület / tudományág

agricultural sciences > forestry and wildlife management


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Soproni Egyetem

Item Type: Article
SWORD Depositor: Teszt Sword
Depositing User: Csaba Horváth
Identification Number: MTMT:34521450
Date Deposited: 22 Jan 2024 09:50
Last Modified: 22 Jan 2024 09:50

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