Liocourt’s law for tree diameter distribution in forest stands

Liocourt’s legacy for the law on steady-state uneven-aged forests has been questioned. We propose a new interpretation of his results published in 1898 and refer to a manuscript dated 1900 to clarify that he established this law.

Abstract

Liocourt’s law states that in steady-state uneven-aged forests, the number of trees in successive diameter classes of equal width form a decreasing geometric series. When referring to this law, most authors cite a paper by Liocourt published in 1898. The 1898 paper does not contain any explicit mathematical expression, but its results can be interpreted as supporting a geometric series with ratio 2. We reviewed Liocourt’s paper of 1898 to provide a new mathematical interpretation of his results, and reviewed other texts by Liocourt to identify the origin of his law. The paper of 1898 supports a polynomial expression of degree 4 rather than a geometric series. The geometric series was explicitly introduced by Liocourt in a handwritten text dated 1900 that remains little-known. The 1898 text by Liocourt was a preliminary work on his law that was expressed in its current form in the manuscript dated 1900.