Self-thinning tree mortality models that account for vertical stand structure, species mixing and climate

David I Forrester,Thomas G Baker,Stephen R Elms,Martina L Hobi,Shuai Ouyang,John C Wiedemann,Wenhua Xiang,Jürgen Zell,Minna Pulkkinen

doi:10.1016/j.foreco.2021.118936

Abstract

Self-thinning dynamics are often considered when managing stand density in forests and are used to constrain forest growth models. However, self-thinning relationships are often quantified using only data at a conceptualised self-thinning line, even though self-thinning can begin before the stand actually reaches a self-thinning line. Also, few self-thinning relationships account for the effects of species composition in mixed-species forests, and stand structure such as relative height of species (in mixtures), and/or size or age cohorts in uneven-aged forests. Such considerations may be important given the effects of global climate change and interest in mixed-species and uneven-aged forests.The objective of this study was to develop self-thinning relationships based on changes in the tree density relative to mean tree diameter, instead of focusing only on data for state variables (e.g. tree density) at the self-thinning line. This was done while also considering how the change in tree density is influenced by site quality and stand structure (species composition and relative height).The relationships were modelled using data from temperate Australian Eucalyptus plantations (436 plots), subtropical forests in China (88 plots), and temperate forests in Switzerland (1055 plots). Zero-inflated and hurdle generalized linear models with Poisson and negative binomial distributions were fit for several species, as well as for all-species equations.The intercepts and slopes of the self-thinning lines were higher than many published studies which may have resulted from both the less restrictive equation form and data selection. The rates of self-thinning often decreased as the proportion of the object species increased, as relative height increased (species or size cohort became more dominant), and as site (quality) index increased. The effects of aridity varied between species, with self-thinning increasing with aridity index for Abies alba, Pinus sylvestris, Quercus petraea and Quercus robur, but decreasing with aridity index for Eucalyptus nitens, Fagus sylvatica and Picea abies as sites became wetter and cooler. Self-thinning model parameters were not correlated with species traits, including specific leaf area, wood basic density or crown diameter – stem diameter allometry. All-species self-thinning relationships based on all data could be adjusted using a correction factor for rarer species where there were insufficient data to develop species-specific equations.The approach and equations developed could be used in forest growth models to calculate how the tree density declines as mean tree size increases, as height changes relative to other cohorts or species, as species proportions change, and as climatic and edaphic conditions change.

Highlights

Many decades after the development of indices of the effects of density on self-thinning and of maximum size – density relationships in even-aged monospecific forests (Reineke, 1933; Yoda et al, 1963) there remains debate about data selection and statistical methods for fitting the relationship (Vanclay and Sands, 2009; Burkhart and Tome, 2012; Trouve et al, 2017)
Self-thinning trajectories were fit for species with at least 100 pairs of successive measurements (Table 2)
There is no reason that the equations in this study are less accurate than those from the literature because they were based on large data sets, including many plots that had never been thinned (e.g. E. globulus and E. nitens plots) or only lightly thinned, nor do the statistics suggest a low quality of fit

Summary

Introduction

Many decades after the development of indices of the effects of density on self-thinning and of maximum size – density relationships in even-aged monospecific forests (Reineke, 1933; Yoda et al, 1963) there remains debate about data selection and statistical methods for fitting the relationship (Vanclay and Sands, 2009; Burkhart and Tome, 2012; Trouve et al, 2017). Self-thinning relationships for mixedspecies or uneven-aged forests have received much less attention than even-aged monocultures. Self-thinning relationships are often described as a straight-line relationship between logarithmically transformed tree density versus mean tree size: (). Ln(N) + 1.605ln dq = intercept (2) ln(N ) + 2 3 ln(v) = intercept (3)

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Conclusion