Calibrating individual tree biomass models for contrasting tropical species at an uneven-aged site in the native Atlantic Forest of Brazil: A direct comparison of alternative approaches, sample sizes, and sample selection methods

https://doi.org/10.1016/j.foreco.2020.118306Get rights and content

Highlights

  • Calibration of existing species-specific models are viable for abundant tropical species.

  • Inclusion of tree height enhanced calibration performance of species-specific models.

  • Use of woody specific gravity improved prediction accuracy across species and sites.

  • One to three randomly selected trees were sufficient for effective model calibration.

Abstract

Tree biomass equations are important yet difficult, time-intensive, and expensive to develop. However, the calibration of previously developed, species-specific models could be a viable alternative, particularly for highly diverse and protected forests like the Atlantic Forest of Brazil. Consequently, the primary research goal of this study was to conduct a comprehensive evaluation of the potential to calibrate an existing individual tree aboveground biomass model for a new species and/or site by using linear mixed-effects. Specific research objectives were to determine the optimal approach for effective calibration by allowing sample selection method, sample size, and range of tree sizes sampled to vary. In particular, a certain set of species was used as a primary dataset to fit both generalized and species-specific biomass models, that were then calibrated for a secondary dataset at a different site and location. Both similar and divergent species at the secondary site were used to calibrate and evaluate the previous models. Our results suggested that species-level calibration was efficient for the majority of the species or individuals examined that can greatly improve the performance at much lower sample sizes required to develop a new equation, especially for the larger trees in the stand. In general, one to three randomly selected trees were sufficient to effectively calibrate a biomass model for a new species. We expect the combination of model calibration for abundant species associated with the use of the previous developed generalized model for less abundant species can drastically reduce the need for destructive sampling and improve predictions, which is important for highly threatened forests like the Atlantic Forest in Brazil. Overall, the results highlight the potential of model calibration to significantly improve both biomass and carbon estimates in species-rich forests like those in the tropics.

Introduction

Tropical forests are important for the global carbon cycle as many studies have quantified the carbon stocked in their aboveground components at varying scales including locally (Vieira et al., 2008, Vincent et al., 2015), regional (Nogueira et al., 2008a, Nogueira et al., 2008b, Scolforo et al., 2016, Scolforo et al., 2015, continental (Lewis et al., 2009), or global scales (Pan et al., 2011, Saatchi et al., 2011). Methods used for biomass estimation have varied according to levels of specificity as regional biomass conversion factors (Guangyi et al., 2017) as well as stand- and tree-level biomass equations have been used (Colmanetti et al., 2018, Valbuena et al., 2016, Van Breugel et al., 2011). However, only the latter method focuses on the basic unit in traditional forest inventories and consequently, it demands more detailed input data (Temesgen et al., 2015). Therefore, the tree-level approach is expected to provide improvements to other methods and may provide increased accuracy of biomass estimates, particularly in species-rich areas like tropical forests (Burt et al., 2020).

Some studies have suggested a better performance of species-specific models for individual tree biomass prediction (Nelson et al., 1999, Van Breugel et al., 2011), while mixed-effect models with species as a random effect can improve estimates in certain situations (Colmanetti et al., 2018, Sotomayor, 2013, Vismara, 2013). In addition to tree biomass, diameter increment (Kuehne et al., 2020), height increment (Russell et al., 2014), height-diameter (Crecente-Campo et al., 2014, Lam et al., 2017) and stem taper have also been improved by using species as random effect (MacFarlane and Weiskittel, 2016, Scolforo et al., 2018), highlighting the potential importance of this approach for multiple reasons. First, the entire dataset can be used, which can improve model extrapolation abilities and/or predictions for rarer species (Kuehne et al., 2020). Second, the method can allow additional hierarchies to be easily incorporated and properly accounted for such as species within genus, which can further improve predictions and/or allow predictions when more detailed species-level information is unavailable as common in tropical forests (Lam et al., 2017). Finally, the method offers local calibration potential, which is further described below. However, the approach might cause illogical behavior in certain species and needs to be used cautiously (Kuehne et al., 2020).

Mixed-effect models can often lead to higher accuracy and precision, but are generally restricted to the same species and/or individuals used during model fitting. This issue can be rather challenging for areas with high species diversity like tropical forests. Generally, the large abundance of a few hyper dominant species in these forests concentrates the majority of the biomass and carbon stocks (Fauset et al., 2015) so sampling often focuses solely on those species. This strategy is a feasible approach, but requires the need for species-specific models (Nelson et al., 1999, Scolforo et al., 2017, Van Breugel et al., 2011) and there is less clarity on how to address biomass and carbon quantification for the least abundant species, which can still have relatively high biomass and carbon within a given stand.

Although abundant species play an important role on biomass quantification at large spatial scales, significant variation in the most abundant species are often observed in tropical forests (Fauset et al., 2015). This variation can be seen across contrasting forest types (Eisenlohr and de Oliveira-Filho, 2014), regions (Réjou-Méchain et al., 2008, Slik et al., 2003), or even locally (Webb and Peart, 2000). Given this variation, species-specific models may not be an effective approach, particularly if being applied across broad spatial scales that include contrasting forest types or conditions. For example, Vismara (2013) highlighted this potential issue and proposed a calibration of the mixed-effects model for each new species sampled in an inventory. In addition, using the plot level information can also potentially improve the quality of the adjustment by incorporating in the model the variability of the biomass ratio and the parameters associated with the adjustment.

Calibrating single or multi-level mixed-effects models have been rather commonly used for single species stands (Arias-Rodil et al., 2015, Lappi, 1991, Vismara et al., 2015, de-Miguel et al., 2014). This approach is based on prediction of random effects using the best linear unbiased predictor (BLUP), where the variance–covariance matrix is altered by new observations using a single (Temesgen et al., 2008, Vismara et al., 2015, de-Miguel et al., 2014) or multiple levels (Arias-Rodil et al., 2015, Crecente-Campo et al., 2014) with one (Temesgen et al., 2008, Vismara et al., 2015) or more random effects on the parameters (Arias-Rodil et al., 2015, Crecente-Campo et al., 2014, Temesgen et al., 2008). Calibration using crossed random effects has also been used (Vismara et al., 2015). When compared to more traditional calibration methods, the use of mixed-effects approaches for calibration have been commonly shown to be superior, but the gains depend on a variety of factors like sample size and model covariates (Arias-Rodil et al., 2015, Crecente-Campo et al., 2014, Temesgen et al., 2008).

The calibration of mixed-effect models can be additionally improved by increasing the number of sample trees (Temesgen et al., 2008, Vismara et al., 2015, de-Miguel et al., 2014), widening the diameter at breast height (dbh) range (Temesgen et al., 2008), increasing the maximum dbh size (Crecente-Campo et al., 2014) or using stratified sampling methods (de-Miguel et al., 2014, Temesgen et al., 2008). Furthermore, mixed-effects model calibration has also been found to perform better than new species-specific models fitted by ordinary least squares (de-Miguel et al., 2014). Although calibration methods have been used for single species stands, these procedures have rarely been used for natural tropical forest where predictive gains could be rather high given the number of species present and great variability of biomass for a given dbh.

The Atlantic Forest is one of the most threatened ecosystems in the world (Myers et al., 2000), and a reduced number of existent datasets are available for the whole forest (Burger and Delitti, 2008, Colmanetti et al., 2018, Uller et al., 2019, Sotomayor, 2013, Tiepolo et al., 2002, Vismara, 2013), in the 16 million hectares remaining (Ribeiro et al., 2009). Consequently, this study aimed to calibrate species-specific models that could be potentially used for common species between different sites within the same forest type. We focused on the abundant species which concentrate the highest proportion of biomass in the stands. It was speculated that this calibration technique is more feasible than simply fitting species-specific equations across the sites, since it normally requires fewer number of sample trees, reducing the effort and cost in the inventories. We further expected the approach proposed in this study will support the integration of the information from the tropical tree species in an integrated database leading to drastically reducing in the need for destructive sampling and improvement of biomass estimation on a highly diverse and critical threatened tropical forests like Atlantic Forest in Brazil.

To evaluate the use of mixed-effect model calibration in tropical forests, we first fitted various generalized and species-specific models using a set of species at one site in the Atlantic Forest. At an independent yet similar secondary site in the Atlantic Forest, the performance and robustness of those generalized models were evaluated and new species-specific coefficients were obtained by calibrating the species-specific model. The performance of both generalized and locally calibrated species-specific models were evaluated using the independent dataset of the secondary site. Specific research objectives were: (i) calibrate linear mixed-effect (LME) biomass model using BLUP to estimate the random effect for a new species; (ii) assess the influence of varying sample sizes, selection of sample tree methods, and dbh range on calibration performance; and (iii) compare the calibration and alternative sample tree selection approaches to more generalized models. Additionally, we compared the previously species-specific model performance for common species in the two sites. Based on the prior literature on the topic, it was expected that LME calibration would outperform more generalized methods, while requiring fewer sample trees than developing a new equation would.

Section snippets

Study sites

The first site (referred here as São Paulo site) was a secondary Atlantic Forest located north of São Paulo City and southwest of Cantareira State Park (“Parque Estadual da Cantareira”, in Portuguese) at an altitude of approximately 840 m, and located at 23°26'33“S and 46°42'00”W (Fig. 1). The area was covered by vegetation classified as a moist forest with some species of seasonal semi-deciduous forest. The climate at the region according to Köppen’s climate classification adapted to Brazil is

Summary of available data by site

The summary of the species in the two sites is provided in Table 1. The São Paulo site had a larger range of dbh, total height (ht), number of species, number of trees and aboveground biomass. The two most common species observed were C. sylvestris and P. glabrata.

In Angatuba site, the largest trees also had the largest wsg, indicating this is in late advanced successional stage (Fig. 2). In contrast, the São Paulo site, where species with higher dbh had a small wsg, for instance C. speciosa

Generalized, species-specific and calibrated models

The generalized models have been extensively used for tropical forests biomass estimation (Brown et al., 1989, Chambers et al., 2001, Chave et al., 2001, Nogueira et al., 2008a, Overman et al., 1994, Scatena et al., 1993). This approach is advantageous and practical in the field, where most commonly only dbh measurements are taken. However, biased estimates are obtained when models fitted for a specific site are used at other locations (e.g. Nogueira et al., 2008a, Nogueira et al., 2008b). This

Conclusions

The results obtained in this study warrant the future use of model calibration using LME to develop more refined species-specific aboveground biomass predictions for diverse areas like the Atlantic Forest in Brazil by allowing relatively small and focused data collection efforts. We recommend the following steps in order to do that most effectively:

  • Abundant species, and species with higher dbh are the most representative in terms of biomass, so the calibration is recommended for those species.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by CAPES (scholarship process number: 88881.133157/2016-01). We thank the DERSA for logistical support, all members from CERAD for technical support.

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