Size-density trajectories for even-aged sessile oak (Quercus petraea (Matt.) Liebl.) and common beech (Fagus sylvatica L.) stands revealing similarities and differences in the mortality process

We studied the size-density trajectories of pure even-aged unthinned experimental sessile oak ( Quercus petraea (Matt.) Liebl.) stands in the ranges of 994–135,555 trees per hectare initial densities, observed from the ages of 5 to 38. We compared them to unthinned beech (Fagus sylvatica L.) stands from the same experimental area. An original piecewise polynomial function was fitted to the trajectories, giving way to various applications. For each species, the initial number of trees per hectare (N 0) and the mean girth at breast height at the onset of mortality (Cg 0) were parameters of the trajectory model, in addition to the parameters of the maximum size-density lines. The two former parameters (Cg 0, N 0) were tied by a linear relationship, which allowed the prediction of trajectories for initial densities not included in the study data. For oak and beech, mortality onset occurred at a constant relative density (RDI), for all initial stand densities, respectively, 0.35 and 0.29. The comparison of the size-density trajectories of oak and beech allowed to establish that oak needs more space than beech for comparable mean girth, and then is less efficient than beech in its space requirements.

Context This paper models the size-density trajectories of pure even-aged sessile oak stands, including the early development stage. It compares the oak results with those on common beech on the same site from a previous study.
Aims A novel approach to size-density trajectories, with an original polynomial piecewise function previously used for beech stands on the same site, was satisfactorily used again as a mortality model to provide references to managers of oak forests.
Material and methods A 38-year-old oak spacing trial, re-measured from year 5 to year 38, provided the opportunity to study the size-density trajectories of unthinned stands of this species.
Results The fit of the piecewise polynomial function allowed us to estimate the parameters of the size-density trajectories of all stands, which were the initial number of trees per hectare (N0) and the mean girth at breast height at the onset of mortality (Cg0), in addition to the intercept (a) and slope (b) of the maximum size-density line. A linear relationship between Ln(N0) and Ln(Cg0) (where Ln is the Neperian logarithm) allowed us to reduce the number of parameters needed to fit the trajectories and made it possible to predict a size-density trajectory from any initial density not observed in the experimental stands. Moreover, this later line appeared to be parallel to the maximum size-density line, and new data allowed to establish that this was also the case for the beech stands on the same site. This parallelism feature translates to the onset of mortality occurring at the same relative density for stands of every initial density that is 0.35 for oak and 0.29 for beech.
Conclusion Given the parameters of the maximum size-density line, a single-parameter function family could be used to predict the size-density trajectories of oak stands. The predicted trajectories have various applications in oak silviculture and growth simulators. The oak data and new data for beech stands on the same site allowed to compare the two species and draw conclusions on similitudes and differences concerning mortality and space requirements of both species.

Mortality, Intra-specific competition, Relative density, Size-density curve modeling, Piecewise function, Stand management

Ningre, F., Ottorini, JM. & Le Goff, N. Annals of Forest Science (2019) 76: 73.

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Data availability
The datasets generated and/or analyzed during the current study are available in the Portail Data Inra repository (Ningre 2019) at

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