Does the Slope of the Self-thinning Line Remain a Constant Value across Different Site Qualities?—An Implication for Plantation Density Management

Ge, Fangxing; Zeng, Weisheng; Wörns, MA; Meng, Jinghui

doi:10.3390/f8100355

Cited by 14 publications

(12 citation statements)

References 77 publications

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“…Live tree density is expected to decline as trees grow in size, owing to increased individual demand for resources and growing space (i.e., competition) 16 , 23 . The expected magnitude of change in tree density, given some change in average tree size, varies considerably across forest communities 63 , site conditions 64 , and stand age classes 23 . Thus, we posit it is useful to contextualize observed changes in live tree density relative to those expected given shifts in average tree size within a stand.…”

Section: Methodsmentioning

confidence: 99%

Over half of western United States' most abundant tree species in decline

et al. 2021

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Changing forest disturbance regimes and climate are driving accelerated tree mortality across temperate forests. However, it remains unknown if elevated mortality has induced decline of tree populations and the ecological, economic, and social benefits they provide. Here, we develop a standardized forest demographic index and use it to quantify trends in tree population dynamics over the last two decades in the western United States. The rate and pattern of change we observe across species and tree size-distributions is alarming and often undesirable. We observe significant population decline in a majority of species examined, show decline was particularly severe, albeit size-dependent, among subalpine tree species, and provide evidence of widespread shifts in the size-structure of montane forests. Our findings offer a stark warning of changing forest composition and structure across the western US, and suggest that sustained anthropogenic and natural stress will likely result in broad-scale transformation of temperate forests globally.

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Section: Methodsmentioning

confidence: 99%

Over half of western United States' most abundant tree species in decline

et al. 2021

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“…This rule was supported by Yoda et al (1963) but researchers in Europe have often questioned it (Pretzsch and Biber 2005;Vacchiano 2005;Castagneri et al 2008). Recent studies demonstrated the need to evaluate the slope of plotted curves according to site quality (Ge et al 2017), and biases could result from the log-transformation of the data (Smith 1993), and questions have been raised on its biological validity (Packard 2014). Despite this, the use of logtransformed data versus nonlinear regression for analysing biological power laws remains a common approach.…”

Section: Introductionmentioning

confidence: 91%

“…?, respectively. The use of PWL is generally dropped in favour of logarithmic transformation of the data fitted using an ordinary least squares (OLS) function (Reineke 1933;Pretzsch and Biber 2005;Shaw 2006;Ge et al 2017). In this case, Eq.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear versus linearised model on stand density model fitting and stand density index calculation: analysis of coefficients estimation via simulation

Marchi

2019

J. For. Res.

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The stand density index, one of the most important metrics for managing site occupancy, is generally calculated from empirical data by means of a coefficient derived from the ''self-thinning rule'' or stand density model. I undertook an exploratory analysis of model fitting based on simulated data. I discuss the use of the logarithmic transformation (i.e., linearisation) of the relationship between the total number of trees per hectare (N) and the quadratic mean diameter of the stand (QMD). I compare the classic method used by Reineke (J Agric Res 46:627-638, 1933), i.e., linear OLS model fitting after logarithmic transformation of data, with the ''pure'' powerlaw model, which represents the native mathematical structure of this relationship. I evaluated the results according to the correlation between N and QMD. Linear OLS and nonlinear fitting agreed in the estimation of coefficients only for highly correlated (between -1 and -0.85) or poorly correlated ([ -0.39) datasets. At average correlation values (i.e., between -0.75 and -0.4), it is probable that for practical applications, the differences were relevant, especially concerning the key coefficient for Reineke's stand density index calculation. This introduced a non-negligible bias in SDI calculation. The linearised log-log model always estimated a lower slope term than did the exponent of the nonlinear function except at the extremes of the correlation range. While the logarithmic transformation is mathematically correct and always equivalent to a nonlinear model in case of prediction of the dependent variable, the difference detected in my studies between the two methods (i.e., coefficient estimation) was directly related to the correlation between N and QMD in each simulated/disturbed dataset. In general, given the power law as the ''natural'' structure of the N versus QMD relationship, the nonlinear model is preferred, with a logarithmic transformation used only in the case of violation of parametric assumptions (e.g. data distributed non-normally).

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“…Self-thinning is presumed to be a process intrinsic to many managed and unmanaged terrestrial plant communities, whose composition and structure are influenced by competition for resources available proportionally to space-whether aboveground (e.g., photosynthetically active radiation) or belowground (e.g., water and nutrients) (Zhang et al, 2011;Hecht et al, 2016). Therefore, w-p temporal trajectories of self-thinning have considerable implications for forest management practices (Ge et al, 2017;Zhang et al, 2019). It is to be noted, however, that p(t) reductions due to ice storms, hurricanes, fires, diseases, or other disturbances are not considered in the w − p relations described by self-thinning.…”

Section: The Self-thinning Rulementioning

confidence: 99%

Recovering the Metabolic, Self-Thinning, and Constant Final Yield Rules in Mono-Specific Stands

Mrad

Manzoni

Oren

et al. 2020

Front. For. Glob. Change

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Competition among plants of the same species often results in power-law relations between measures of crowding, such as plant density, and average size, such as individual biomass. Yoda's self-thinning rule, the constant final yield rule, and metabolic scaling, all link individual plant biomass to plant density and are widely applied in crop, forest, and ecosystem management. These dictate how plant biomass increases with decreasing plant density following a given power-law exponent and a constant of proportionality. While the exponent has been proposed to be universal and thus independent of species, age, environmental, and edaphic conditions, different theoretical mechanisms yield absolute values ranging from less than 1 to nearly 2. Here, eight hypothetical mechanisms linking the exponent to constraints imposed on plant competition are featured and contrasted. Using dimensional considerations applied to plants growing isometrically, the predicted exponent is −3/2 (Yoda's rule). Other theories based on metabolic arguments and network transport predict an exponent of −4/3. These rules, which describe stand dynamics over time, differ from the "rule of constant final yield" that predicts an exponent of −1 between the initial planting density and the final yield attained across stands. The latter can be recovered from statistical arguments applied at the time scale in which the site carrying capacity is approached. Numerical models of plant competition produce plant biomass-density scaling relations with an exponent between −0.9 and −1.8 depending on the mechanism and strength of plant-plant interaction. These different mechanisms are framed here as a generic dynamical system describing the scaled-up carbon economy of all plants in an ecosystem subject to differing constraints. The implications of these mechanisms for forest management under a changing climate are discussed and recent research on the effects of changing aridity and site "quality" on self-thinning are highlighted.

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Does the Slope of the Self-thinning Line Remain a Constant Value across Different Site Qualities?—An Implication for Plantation Density Management

Cited by 14 publications

References 77 publications

Over half of western United States' most abundant tree species in decline

Over half of western United States' most abundant tree species in decline

Nonlinear versus linearised model on stand density model fitting and stand density index calculation: analysis of coefficients estimation via simulation

Recovering the Metabolic, Self-Thinning, and Constant Final Yield Rules in Mono-Specific Stands

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