Abstract
Relationships between tree size and growth are sometimes assumed to show increasing growth with increasing size only until intermediate sizes are reached, followed by a phase where growth rates decline with further increases in size. However, this “rise-and-fall” pattern has been challenged by studies suggesting continuously increasing growth with size. This study examined relationships between tree diameter and above-ground biomass (AGB) growth and how such relationships can differ depending on whether they represent an individual tree through time (longitudinal analyses) or whether the relationship was fit to many trees within a stand at a single point in time (cross-sectional analyses). Using 949 long-term plots in Switzerland (measured between 1888 and 2014) including several species, sites and management regimes, segmented regressions were used to describe the longitudinal and cross-sectional relationships between stem diameter and AGB growth. The slopes of the last segments of cross-sectional analyses indicated that AGB growth generally increased with tree diameter. However, last-segment slopes of longitudinal analyses showed that AGB growth of 12% of trees had actually declined for several decades. This number increased to 44%, when considering only the last growth periods for each tree, corresponding to about 16 years of growth. The contrast between cross-sectional and longitudinal patterns results because declines in tree growth occur at different times or sizes for different individuals (longitudinal analyses), but this is averaged out and rarely evident from cross-sectional analyses unless many individuals decline at similar times or sizes.The last-segment slopes of individual trees were positively correlated with the last-segment slopes of relationships between diameter and tree light absorption or light-use efficiency (AGB/light absorption). Interestingly, last-segment slopes were not correlated with light absorption, only the change in light absorption. This reiterates the potential of thinning to delay the onset of growth declines. When all data were combined (e.g. an aggregated longitudinal analysis), AGB growth was most strongly influenced by diameter, followed by relative height, neighbourhood basal area, climatic conditions, silviculture, and lastly, tree species diversity.Cross-sectional analyses often show AGB growth continuously increasing with diameter, because firstly, they represent patterns averaged across may trees within a stand and secondly, because they represent only one point in time. However, the AGB growth of individual trees doesn’t always continuously increase with tree diameter (longitudinal analyses). This highlights the importance of carefully considering which type of analysis (cross-sectional or longitudinal) is appropriate to the question being addressed.
Highlights
Whether or not the growth rates of large trees continue to increase as their size increases, or instead follow a unimodal “rise-and-fall” pattern, remains the subject of confusion (Stephenson et al, 2014; Sheil et al, 2017)
This study examined relationships between tree diameter and above-ground biomass (AGB) growth and how such relationships can differ depending on whether they represent an individual tree through time or whether the relationship was fit to many trees within a stand at a single point in time
Last-segment slopes of longitudinal analyses showed that AGB growth of 12% of trees had declined for several decades
Summary
Whether or not the growth rates of large trees continue to increase as their size increases, or instead follow a unimodal “rise-and-fall” pattern, remains the subject of confusion (Stephenson et al, 2014; Sheil et al, 2017). Several approaches are used to examine tree size-growth relation ships (Fig. 1). These can lead to different size-growth patterns (Sheil et al, 2017) and warrant clear definitions to avoid confusion. One important consideration is the type of analysis used in terms of whether the size-growth relationship is intrinsic, cross-sectional or longitudinal. An intrinsic relationship could refer to growth when there were few or no external factors reducing growth from its potential under ideal
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