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Small Sample Sizes Yield Biased Allometric Equations in Temperate Forests.

ABSTRACT: Accurate quantification of forest carbon stocks is required for constraining the global carbon cycle and its impacts on climate. The accuracies of forest biomass maps are inherently dependent on the accuracy of the field biomass estimates used to calibrate models, which are generated with allometric equations. Here, we provide a quantitative assessment of the sensitivity of allometric parameters to sample size in temperate forests, focusing on the allometric relationship between tree height and crown radius. We use LiDAR remote sensing to isolate between 10,000 to more than 1,000,000 tree height and crown radius measurements per site in six U.S. forests. We find that fitted allometric parameters are highly sensitive to sample size, producing systematic overestimates of height. We extend our analysis to biomass through the application of empirical relationships from the literature, and show that given the small sample sizes used in common allometric equations for biomass, the average site-level biomass bias is ~+70% with a standard deviation of 71%, ranging from -4% to +193%. These findings underscore the importance of increasing the sample sizes used for allometric equation generation.

SUBMITTER: Duncanson L

PROVIDER: S-EPMC4657147 | biostudies-literature | 2015 Nov

REPOSITORIES: biostudies-literature

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Small Sample Sizes Yield Biased Allometric Equations in Temperate Forests.

Duncanson L L Rourke O O Dubayah R R

Scientific reports 20151124

Accurate quantification of forest carbon stocks is required for constraining the global carbon cycle and its impacts on climate. The accuracies of forest biomass maps are inherently dependent on the accuracy of the field biomass estimates used to calibrate models, which are generated with allometric equations. Here, we provide a quantitative assessment of the sensitivity of allometric parameters to sample size in temperate forests, focusing on the allometric relationship between tree height and ...[more]

PMID: 26598233

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Project description:Limited sample sizes can lead to spurious modeling findings in biomedical research. The objective of this work is to present a new method to generate synthetic populations (SPs) from limited samples using matched case-control data (n = 180 pairs), considered as two separate limited samples. SPs were generated with multivariate kernel density estimations (KDEs) with unconstrained bandwidth matrices. We included four continuous variables and one categorical variable for each individual. Bandwidth matrices were determined with Differential Evolution (DE) optimization by covariance comparisons. Four synthetic samples (n = 180) were derived from their respective SPs. Similarity between observed samples with synthetic samples was compared assuming their empirical probability density functions (EPDFs) were similar. EPDFs were compared with the maximum mean discrepancy (MMD) test statistic based on the Kernel Two-Sample Test. To evaluate similarity within a modeling context, EPDFs derived from the Principal Component Analysis (PCA) scores and residuals were summarized with the distance to the model in X-space (DModX) as additional comparisons. Four SPs were generated from each sample. The probability of selecting a replicate when randomly constructing synthetic samples (n = 180) was infinitesimally small. MMD tests indicated that the observed sample EPDFs were similar to the respective synthetic EPDFs. For the samples, PCA scores and residuals did not deviate significantly when compared with their respective synthetic samples. The feasibility of this approach was demonstrated by producing synthetic data at the individual level, statistically similar to the observed samples. The methodology coupled KDE with DE optimization and deployed novel similarity metrics derived from PCA. This approach could be used to generate larger-sized synthetic samples. To develop this approach into a research tool for data exploration purposes, additional evaluation with increased dimensionality is required. Moreover, given a fully specified population, the degree to which individuals can be discarded while synthesizing the respective population accurately will be investigated. When these objectives are addressed, comparisons with other techniques such as bootstrapping will be required for a complete evaluation.

Project description:BACKGROUND:Application of allometric equations for quantifying forests aboveground biomass is a crucial step related to efforts of climate change mitigation. Generalized allometric equations have been applied for estimating biomass and carbon storage of forests. However, adopting a generalized allometric equation to estimate the biomass of different forests generates uncertainty due to environmental variation. Therefore, formulating species-specific allometric equations is important to accurately quantify the biomass. Montane moist forest ecosystem comprises high forest type which is mainly found in the southwestern part of Ethiopia. Yayu Coffee Forest Biosphere Reserve is categorized into Afromontane Rainforest vegetation types in this ecosystem. This study was aimed to formulate species-specific allometric equations for Albizia grandibracteata Tuab. and Trichilia dregeana Sond. using the semi-destructive method. RESULTS:Allometric equations in form of power models were developed for each tree species by evaluating the statistical relationships of total aboveground biomass (TAGB) and dendrometric variables. TAGB was regressed against diameter at breast height (D), total height (H), and wood density (?) individually and in a combination. The allometric equations were selected based on model performance statistics. Equations with the higher coefficient of determination (adj.R2), lower residual standard error (RSE), and low Akaike information criterion (AIC) values were found best fitted. Relationships between TAGB and predictive variables were found statistically significant (p???0.001) for all selected equations. Higher bias was reported related to the application of pan-tropical or generalized allometric equations. CONCLUSIONS:Formulating species-specific allometric equations is found important for accurate tree biomass estimation and quantifying the carbon stock. The developed biomass regression models can be applied as a species-specific equation to the montane moist forest ecosystem of southwestern Ethiopia.

Project description:BackgroundMediation analysis can be used to evaluate the effect of an exposure on an outcome acting through an intermediate variable or mediator. For studies with small sample sizes, permutation testing may be useful in evaluating the indirect effect (i.e., the effect of exposure on the outcome through the mediator) while maintaining the appropriate type I error rate. For mediation analysis in studies with small sample sizes, existing permutation testing methods permute the residuals under the full or alternative model, but have not been evaluated under situations where covariates are included. In this article, we consider and evaluate two additional permutation approaches for testing the indirect effect in mediation analysis based on permutating the residuals under the reduced or null model which allows for the inclusion of covariates.MethodsSimulation studies were used to empirically evaluate the behavior of these two additional approaches: (1) the permutation test of the Indirect Effect under Reduced Models (IERM) and (2) the Permutation Supremum test under Reduced Models (PSRM). The performance of these methods was compared to the standard permutation approach for mediation analysis, the permutation test of the Indirect Effect under Full Models (IEFM). We evaluated the type 1 error rates and power of these methods in the presence of covariates since mediation analysis assumes no unmeasured confounders of the exposure-mediator-outcome relationships.ResultsThe proposed PSRM approach maintained type I error rates below nominal levels under all conditions, while the proposed IERM approach exhibited grossly inflated type I rates in many conditions and the standard IEFM exhibited inflated type I error rates under a small number of conditions. Power did not differ substantially between the proposed PSRM approach and the standard IEFM approach.ConclusionsThe proposed PSRM approach is recommended over the existing IEFM approach for mediation analysis in studies with small sample sizes.

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Small Sample Sizes Yield Biased Allometric Equations in Temperate Forests.

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Small Sample Sizes Yield Biased Allometric Equations in Temperate Forests.

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