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On the challenge of fitting tree size distributions in ecology.

Taubert F, Hartig F, Dobner HJ, Huth A - PLoS ONE (2013)

Bottom Line: We test whether three typical frequency distributions, namely the power-law, negative exponential and Weibull distribution can be precisely identified, and how parameter estimates are biased when observations are additionally either binned or contain measurement error.We show that uncorrected MLE already loses the ability to discern functional form and parameters at relatively small levels of uncertainties.We conclude that it is important to reduce binning of observations, if possible, and to quantify observation accuracy in empirical studies for fitting strongly skewed size distributions.

View Article: PubMed Central - PubMed

Affiliation: Department of Ecological Modelling, Helmholtz Centre for Environmental Research, Leipzig, Saxony, Germany. franziska.taubert@ufz.de

ABSTRACT
Patterns that resemble strongly skewed size distributions are frequently observed in ecology. A typical example represents tree size distributions of stem diameters. Empirical tests of ecological theories predicting their parameters have been conducted, but the results are difficult to interpret because the statistical methods that are applied to fit such decaying size distributions vary. In addition, binning of field data as well as measurement errors might potentially bias parameter estimates. Here, we compare three different methods for parameter estimation--the common maximum likelihood estimation (MLE) and two modified types of MLE correcting for binning of observations or random measurement errors. We test whether three typical frequency distributions, namely the power-law, negative exponential and Weibull distribution can be precisely identified, and how parameter estimates are biased when observations are additionally either binned or contain measurement error. We show that uncorrected MLE already loses the ability to discern functional form and parameters at relatively small levels of uncertainties. The modified MLE methods that consider such uncertainties (either binning or measurement error) are comparatively much more robust. We conclude that it is important to reduce binning of observations, if possible, and to quantify observation accuracy in empirical studies for fitting strongly skewed size distributions. In general, modified MLE methods that correct binning or measurement errors can be applied to ensure reliable results.

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Related in: MedlinePlus

Scheme of the evaluation procedure of virtual data sets.
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pone-0058036-g002: Scheme of the evaluation procedure of virtual data sets.

Mentions: The calculations result in parameter values for each distribution dependent on or. We fit the raw and modified virtual data sets by applying standard MLE as well as multinomial MLE or Gaussian MLE. This allows us to compare the estimation bias for each type of observation uncertainty and offers the opportunity to evaluate the capability of error correction (Fig. 2). For the binned virtual data we use the centre of the bins as data values when evaluated with the standard MLE.


On the challenge of fitting tree size distributions in ecology.

Taubert F, Hartig F, Dobner HJ, Huth A - PLoS ONE (2013)

Scheme of the evaluation procedure of virtual data sets.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3585190&req=5

pone-0058036-g002: Scheme of the evaluation procedure of virtual data sets.
Mentions: The calculations result in parameter values for each distribution dependent on or. We fit the raw and modified virtual data sets by applying standard MLE as well as multinomial MLE or Gaussian MLE. This allows us to compare the estimation bias for each type of observation uncertainty and offers the opportunity to evaluate the capability of error correction (Fig. 2). For the binned virtual data we use the centre of the bins as data values when evaluated with the standard MLE.

Bottom Line: We test whether three typical frequency distributions, namely the power-law, negative exponential and Weibull distribution can be precisely identified, and how parameter estimates are biased when observations are additionally either binned or contain measurement error.We show that uncorrected MLE already loses the ability to discern functional form and parameters at relatively small levels of uncertainties.We conclude that it is important to reduce binning of observations, if possible, and to quantify observation accuracy in empirical studies for fitting strongly skewed size distributions.

View Article: PubMed Central - PubMed

Affiliation: Department of Ecological Modelling, Helmholtz Centre for Environmental Research, Leipzig, Saxony, Germany. franziska.taubert@ufz.de

ABSTRACT
Patterns that resemble strongly skewed size distributions are frequently observed in ecology. A typical example represents tree size distributions of stem diameters. Empirical tests of ecological theories predicting their parameters have been conducted, but the results are difficult to interpret because the statistical methods that are applied to fit such decaying size distributions vary. In addition, binning of field data as well as measurement errors might potentially bias parameter estimates. Here, we compare three different methods for parameter estimation--the common maximum likelihood estimation (MLE) and two modified types of MLE correcting for binning of observations or random measurement errors. We test whether three typical frequency distributions, namely the power-law, negative exponential and Weibull distribution can be precisely identified, and how parameter estimates are biased when observations are additionally either binned or contain measurement error. We show that uncorrected MLE already loses the ability to discern functional form and parameters at relatively small levels of uncertainties. The modified MLE methods that consider such uncertainties (either binning or measurement error) are comparatively much more robust. We conclude that it is important to reduce binning of observations, if possible, and to quantify observation accuracy in empirical studies for fitting strongly skewed size distributions. In general, modified MLE methods that correct binning or measurement errors can be applied to ensure reliable results.

Show MeSH
Related in: MedlinePlus