The -3/2 law applied to some gorse communities, with consideration of line fitting

Wilson, J. Bastow; Lee, W. G.

doi:10.1080/0028825x.1988.10410112

Cited by 6 publications

(3 citation statements)

References 10 publications

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“…Gorse is known to follow the − 3/2 law of self-thinning ( Wilson & Lee 1988). A study of stand structure in gorse thickets of different ages showed that stem density declined from 32 to 6 stems m -2 over 15 years, when the stand was considered to be mature (Lee, Allen & Johnson 1986).…”

Section:    mentioning

confidence: 99%

Large−scale disturbances, biological control and the dynamics of gorse populations

Rees

Hill

2001

Journal of Applied Ecology

326

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Summary 1.Simulation and analytical models were developed for gorse Ulex europaeus . The simulation model incorporated spatially local density-dependent competition, disturbance, asymmetric competition between seedlings and established plants, a seed bank, local seed dispersal, an age structured established plant population, and temporal variation in the probability of disturbance. The analytical models were simple approximations of the simulation. 2. The models extended our previously published model for Scotch broom Cytisus scoparius to include large-scale disturbances and possible management options, such as the use of fire, herbicides and oversowing with perennial grasses. Fire was assumed to influence established plant mortality, seed survival in the seed bank, and the probability of germination. 3. We reviewed published data on the demography of gorse in New Zealand, the current management techniques, and the ongoing biological control programme. 4. Over a wide range of biologically reasonable parameter values, the analytical models accurately predicted the outcome of the simulations. The analytical models worked well, providing gorse occupied a high proportion of the available sites and large-scale disturbances did not occur too frequently. 5. The potential impact of seed-feeding biological control agents on gorse abundance was assessed, using the models, for several environmental and management scenarios. In particular, we explored how large-scale disturbance, such as fire and herbicide application, influences the outcome of biological control. 6. The success of a biological control programme was found to depend critically on the frequency and intensity of disturbance, whether disturbed sites became suitable for recruitment, and the effects of disturbance on germination and seed mortality. 7. The models highlight the need to manage recruitment opportunities carefully in order to maximize the effect of biological control agents. The models also indicate that details of plant population biology can have a profound effect on the success of any management strategy.

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Section:    mentioning

confidence: 99%

Large−scale disturbances, biological control and the dynamics of gorse populations

Rees

Hill

2001

Journal of Applied Ecology

326

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“…Historically, there are several regression methods used to estimate the two coefficients of the maximum size-density line, such as (1) arbitrarily hand fitting a line above an upper boundary of data points (Yoda et al 1963;Drew and Flewelling 1977), (2) fitting an ordinary least squares regression (OLS) or weighted least squares regression (WLS) through data points selected on a density-dependent mortality criterion (Ford 1975;Wilson and Lee 1988), and (3) estimating coefficients via major axis analysis or principal components analysis (PCA) based on chosen data (Mohler et al 1978;Hutchings and Budd 1981;Bi and Turvey 1997;Wilson et al 1999). The last two methods define an "average" maximum size-density line (Osawa and Sugita 1989) rather than a "biological" maximum size-density line (Smith and Woods 1997).…”

Section: Introductionmentioning

confidence: 99%

A comparison of alternative methods for estimating the self-thinning boundary line

Zhang¹,

Bi²,

Gove³

et al. 2005

Can. J. For. Res.

136

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The fundamental validity of the self-thinning "law" has been debated over the last three decades. A long-standing concern centers on how to objectively select data points for fitting the self-thinning line and the most appropriate regression method for estimating the two coefficients. Using data from an even-aged Pinus strobus L. stand as an example, we show that quantile regression (QR), deterministic frontier function (DFF), and stochastic frontier function (SFF) methods have the potential to produce an upper limiting boundary line above all plots for the maximum size-density relationship, without subjectively selecting a subset of data points based on predefined criteria. On the other hand, ordinary least squares (OLS), corrected ordinary least squares (COLS), and reduced major axis (RMA) methods are sensitive to the data selected for model fitting and may produce self-thinning lines with inappropriate slopes. However, statistical inference is very difficult with the DFF and QR methods. Although SFF produces a self-thinning line lower than the upper limiting boundary line because of the nature of the method, it can easily produce the statistics for inference on the model coefficients, given that there are no significant departures from underlying distributional assumptions.Résumé : La validité fondamentale de la « loi » d'autoéclaircie a été débattue au cours des trois dernières décennies. Une préoccupation de longue date porte sur la façon de sélectionner objectivement les données pour ajuster la droite d'autoéclaircie et sur la méthode de régression la plus appropriée pour estimer les deux coefficients. À l'aide de données provenant d'un peuplement équienne de Pinus strobus L. comme exemple, les auteurs montrent que les méthodes de régression quantile (RQ), de fonction déterministe frontière (FDF) et de fonction stochastique frontière (FSF) ont la capacité de produire une droite qui constitue la limite supérieure au-dessus de toutes les parcelles pour la relation maximale de la dimension en fonction de la densité sans sélectionner subjectivement un sous-ensemble de points basés sur des critères prédéfinis. D'un autre côté, la méthode ordinaire des moindres carrés, la méthode ordinaire corrigée des moindres carrés et la méthode des axes majeurs réduits sont sensibles aux données sélectionnées pour l'ajustement du modèle et peuvent produire des droites d'autoéclaircie avec des pentes inappropriées. Cependant, l'inférence statistique est très difficile avec les méthodes FDF et RQ. Même si la méthode FSF produit une droite d'autoéclaircie plus basse que la droite qui constitue la limite supérieure maximale, à cause de la nature de la méthode, elle peut facilement produire les statistiques pour déduire les coefficients du modèle, étant donné qu'il n'y a pas de démarcation significative des hypothèses sous-jacentes de distribution.[Traduit par la Rédaction] Zhang et al. 1514

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“…There are several statistical methods to estimate the two parameters of the self-thinning line, such as (1) placing a line by hand above an upper boundary of data points [ 3 , 7 ], (2) fitting least squares regressions[ 19 – 21 ], (3) estimating parameters through quantile regression [ 22 ], principal components analysis and reduced major axis regression (RMA) [ 23 , 24 ], and RMA method combined with jackknife estimation [ 25 ], (4) bisector regression approach [ 26 ], and (5) adopting stochastic frontier function to estimate the self-thinning line [ 27 , 28 ]. Zhang et al .…”

Section: Introductionmentioning

confidence: 99%

A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China

Zhang

Duan

2015

PLoS ONE

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Self-thinning is a dynamic equilibrium between forest growth and mortality at full site occupancy. Parameters of the self-thinning lines are often confounded by differences across various stand and site conditions. For overcoming the problem of hierarchical and repeated measures, we used hierarchical Bayesian method to estimate the self-thinning line. The results showed that the self-thinning line for Chinese fir (Cunninghamia lanceolata (Lamb.)Hook.) plantations was not sensitive to the initial planting density. The uncertainty of model predictions was mostly due to within-subject variability. The simulation precision of hierarchical Bayesian method was better than that of stochastic frontier function (SFF). Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables (site quality, soil type, aspect, etc.) on self-thinning line, which gave us the posterior distribution of parameters of self-thinning line. The research of self-thinning relationship could be benefit from the use of hierarchical Bayesian method.

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The -3/2 law applied to some gorse communities, with consideration of line fitting

Cited by 6 publications

References 10 publications

Large−scale disturbances, biological control and the dynamics of gorse populations

Large−scale disturbances, biological control and the dynamics of gorse populations

A comparison of alternative methods for estimating the self-thinning boundary line

A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China

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