Aboveground biomass (W) allometric models (AM) selection

From the eight AM used in the first empirical study, five models were selected by species and three by genus (see Table III.1). However, an AGB model for Abies duranguensis (Rojas-García et al., 2015a) has not been reported in Mexico, and due to the similarity in morphological characteristics an Abies religiosa model was used (Avendaño Hernandez et al., 2009). The impact of this bias is considered negligible because there was only one tree out of 4262 in the dataset.

For the third empirical study, Table VIII-1 (Appendix I) shows the list of 36 AMs used to estimate the AGB of the 346 species identified in the MNFI for the two periods studied. Five important features in the selection of AMs are discussed below:

i. 19 AMs estimated the AGB grouped by genus. The models used for Quercus spp and Pinus spp stand out, with 77 and 37 species.

ii. Desert communities and tropical dry forest were AM that estimated AGB for 73 genera (20 and 53 genera, respectively). Although these AMs were applied to genera of the same vegetation type, 60% and 30% of the trees using these models belong to genera that were not included in the studies where these models were fitted.

iii. 18 AMs used in this thesis were not fitted in Durango or the surrounding states, and six models were not fitted in Mexico.

iv. Only 16 AM were reported together with the MSE of the fitted model but did not include the information used to fit the model.

v. 15 of the AMs used were fitted with information from less than 30 sampled trees.

The first three features are related to the AMs developed in the state of Durango. Pinus spp and Quercus spp trees make up 88% of MNFI trees, and the commercial importance of these genera account for 89.5 and 6.9% of timber production in Durango (INEGI, 2016). The compilation of 346 models made by Rojas-García et al. (2015a), has 43 models developed in Durango, 33 of these models were made in Pinus spp (11 species) and seven in Quercus spp (three species). For this reason, tropical and desert species have more interest in neighboring states such as Sinaloa for tropical vegetation (Návar, 2009, 2010) and Sonora for desert vegetation (Búrquez et al., 2010). In our thesis work, the need for allometric models involving information from Pinus cembroides, Quercus eduardii, Q. magnoliifolia, Q. laeta and Q. grisea has been detected. Therefore, a clear adherence to procedures indicating the precision to obtain allometric models is suggested (Picard et al., 2012). These species are 18.6% of the trees in our study area and have not been reported models in Durango or neighboring states. Some of these species have also been detected as an area of opportunity in AM research, in studies such as that conducted by Rojas-García et al. (2015b), listing 40 priority species for the development of AM in Mexico.

The fourth feature is that AMs have been reported mostly with the determination coefficient (R²) only and not with the goodness-of-fit. Rojas-García et al. (2015a) reported that out of 346 AMs compiled from studies conducted in Mexico, only 39 models reported the MSE of the fitted model.

The models used in our thesis did not include the original data in their publications, with which the error of prediction of the mean and the error of prediction of the individual are estimated (Draper &

Smith, 1998). Since the original data were not available, the MSE was used as the uncertainty parameter due to AM, which corresponds to an overestimation of the prediction of the mean or SE (Yanai et al., 2010).

The fifth feature is associated with the information that was used to produce the AMs, i.e. the number of trees used to estimate the AM. Using less than 30 trees, according to Picard et al. (2012), assumes homogeneity of the species in a 10 ha sampling stand. In addition, Chave et al. (2004) found that increasing the sample size decreases the coefficient of variation in the estimated AM.

This implies that models with smaller sample sizes (less than 20 trees) may have greater uncertainty in the estimation of the AGB (Roxburgh et al., 2015). However, AMs that used less than 20 trees for their fitting, were still used in our thesis, when no other publications were found for that genus or species (Rojas-García et al., 2015a). It should be noted that this decision is considered to have a negligent impact on our AGB estimate because the AMs fitted in Durango State had sample sizes from 30 to 423 trees and were applied in 96% of the dataset.

On the variables used in the AMs, 23 of the selected models were fit with DBH data and 13 models added TH in the model fitting. Vargas-Larreta et al. (2017) found that for AMs of pines and oaks, TH was a significant predictor variable, improving the prediction of adjusted AMs in 12 of the 17

and eucalyptus (Bartelink, 1996; Reed & Tomé, 1998). In a sweet chestnut forest, Menéndez-Miguélez et al. (2013) found an increase in the accuracy in AGB estimation including TH. The 13 models including TH as a predictor variable in our study were used in AGB's estimate of 96.8% of the MNFI dataset.

An important consideration in the AMs selection is the correct identification of the sampled trees in the field. Although our thesis did not include an experiment that quantified the success in the identification of trees, it is explained below how this topic was approached. In the first empirical study, the identification of the trees is considered correct, because the members of the field crew were selected for their experience in the study area as suggest the NFI reviewed by (Tomppo et al., 2010). For the second empirical study, conifer and broad-leaved AMs were assigned, which are distinct vegetation groups. In the third empirical study, the trees in the MNFI database are assumed to be correctly identified according to the field manual (CONAFOR, 2009b). However, a

CONAFOR study, which aimed to verify the identification of MNFI species from 2013-2015, obtained results that contrast with the assumption of correct identification (Ricker et al., 2015). This study had 14035 samples, out of which 69.2% were identified in terms of species (9711 samples) and 30.8% (4324 samples) were identified in terms of the genus, family or unknown. A group of 47 biologists determined that 39.3% of the 9711 records were correctly identified, 28.1% were correct at the genus level, and 32.6% were misidentified. From 4324 collections, 1856 were not identified with traditional methods and required the use of molecular methods. Therefore, based on this study, 60.6% of the collections were correctly identified at the genus level, while only 27.2% were correct at the species level. In personal communication with Dr. Martin Ricker, the researcher responsible for the project, 89.9% of the collections coincided at the genus level in the state of Durango. From this information, it was decided to use the AMs at the genus level for the estimation of the AGB in the MNFI.

V.2.2 AGB estimation

In the Durango state, two empirical studies from this thesis estimated AGB. In the first study, the AGB in pine forest was 176.07 Mg ha^-1 and ranged from 86.61 to 228.41 Mg ha^-1. This estimate contrasts with the national estimate in Mexico of 63.43 Mg ha^-1 for this forest type (CONAFOR, 2017a). The major difference was found in tree density and tree height. While in the first study the average values were 1137 trees ha^-1 and 13.3 m of TH, at the national level, 455 trees ha^-1 and a 6.7 m of TH (CONAFOR, 2014a). On the other hand, the estimate of AGB was consistent with the study conducted by Vargas-Larreta et al. (2017), where they estimated 129.84 Mg ha^-1 in a range of 11.06 to 469.42 Mg ha^-1 for pine and mixed forests in Durango.

In the third empirical study, AGB in the temperate forest of Durango was estimated for two periods of the MNFI data. The mean AGB was 64.31 Mg ha^-1 for the period 2004-2009 and 64.77 Mg ha^-1 for 2009-2014. This AGB value lies intermediate to the estimates made in Durango ranging between 48.86 and 130 Mg ha^-1 from 2008 to 2012. However, those estimates were the result of different sampling designs and approaches, such as circular plots (Návar, 2009), permanent plots of 50 per 50 m (Martínez Barrón et al., 2016; Vargas-Larreta et al., 2017), or technical studies that calculate AGB from volume estimates (Profloresta, 2008). The National Forestry Commission of Mexico has not reported AGB in the last report of the state (CONAFOR, 2014a), and with MNFI data, the AGB reported to FAO was 54.08 and 54.11 Mg ha^-1 in 2007 and 2011 for temperate forest

(FAO, 2015). In our study, using MNFI data, the temperate forest registered larger AGB estimates in Durango State than at the National level in Mexico.

Inside the Durango temperate forest in the period 2004-2009, the mean estimate of AGB was 48.31 Mg ha^-1 in the conifer forest, 77.48 Mg ha^-1 in the mixed forest, and 35.52 Mgha^-1 in the oak forest.

In the second period (2009-2014), the mean values of AGB were 51.82, 73.12, and 36.84 Mg ha^-1, in the same order. These estimates could only be compared with the MNFI 2009-2014 report because it was the first report including the AGB estimate. In this report, the AGB was 63.43 Mg ha^-1 in the conifer forest, 53.66 Mg ha^-1 in the mixed forest and 34.25 Mg ha^-1 in the oak forest.

AGB in the oak forest was similar to that reported at the national level of Mexico. Conversely, our study estimated lower AGB in the conifer forest, but higher AGB in the mixed forest. This opposite behavior was caused since the mixed forest in Durango had more trees than the conifer forest (487>409), and higher mean DBH (16.94>16.75 cm).

In the second empirical study, conducted in Göttingen, the average AGB was 257.6 Mg ha^-1 in the beech forest. High accumulation of AGB is common in this area and has previously been registered by Brumme & Khanna (2009) with estimates of 431 Mg ha^-1 in a range of 128 to 660 Mg ha^-1 from a study conducted in the “Göttinger Wald”.

In all three empirical studies, the categories of DBH greater than the category of the mean DBH had a greater contribution to AGB. In first and third studies in Durango, trees with more than 20 cm (26 and 32% of the dataset, respectively) contributed to more than 58% of the AGB. In Göttingen, trees greater than 40 cm in DBH (22% of the dataset) contributed to 65% of the AGB. The categories greater than or equal to the category of the average DBH had fewer trees but a greater contribution to the AGB.