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Revista mexicana de ciencias forestales
Print version ISSN 2007-1132
Rev. mex. de cienc. forestales vol.12 n.67 México Sep./Oct. 2021 Epub Oct 25, 2021
https://doi.org/10.29298/rmcf.v12i67.997
Scientific article
Biomass and carbon growth and increases of Pinus teocote Schltdl. et Cham. and Pinus oocarpa Schiede., state of Guerrero, Mexico
1Universidad Autónoma de Nuevo León, Facultad de Ciencias Forestales. México.
2Colegio de Postgraduados, Campus Montecillos. México.
The modeling of growth in biomass can be one of the most important techniques for
determining the carbon stock in any interval of development in the plant,
allowing to make decisions about the management of the species for climate
change mitigation. The goal of this study was to adjust growth models to
quantify biomass increments (B) and estimate the carbon uptake
(C) in Pinus teocote and Pinus
oocarpa forests in the mountain region of the state of
Guerrero. Twenty-four trees per species were felled, tree
trunk analyses were performed, and five growth models were adjusted in order to
estimate the increments in biomass and the inflection points of the current
annual increase (CAI), mean annual increase (MAI), and the technical shift where
CAI and MAI intersect. Weibull’s model exhibited the best adjustments for
determining biomass growths; the equation for estimating biomass in P.
teocote was:
Keywords: Trunk analysis; growth rings; mature forest; modeling; Pinus oocarpa Schiede.; Pinus teocote Schltdl. et Cham
La modelización del crecimiento en biomasa es una de las técnicas más importantes
para conocer el stock de carbono en cualquier intervalo de
desarrollo en una planta, y permite tomar decisiones de manejo forestal para
fines de mitigación del cambio climático. El objetivo de este estudio fue
ajustar modelos de crecimiento para cuantificar incrementos en biomasa
(B) y captura de carbono (C) en bosques
maduros de Pinus teocote y Pinus oocarpa, en
la región de la montaña del estado de Guerrero. Se derribaron 24 árboles por
especie, y mediante la técnica de análisis troncales se ajustaron cinco modelos
de crecimiento, posteriormente se determinaron los puntos de inflexión del
incremento corriente anual (ICA), incremento medio anual (IMA) y el turno
técnico. El modelo de Weibull presentó los mejores ajustes para
determinar el crecimiento en biomasa aérea (B); la ecuación
resultante en P. teocote fue
Palabras clave: Análisis troncales; anillos de crecimiento; bosque maduro; modelización; Pinus oocarpa Schiede.; Pinus teocote Schltdl. et Cham
Introduction
Forests are important carbon sinks for the planet, helping to mitigate climate change caused mainly by high concentrations of carbon dioxide (CO2) in the atmosphere (Ordóñez et al., 2015; Palacios-Cruz et al., 2020).
Generally, forests that grow faster in juvenile stages and have net growth are able to capture more carbon dioxide (CO2) than they emit through respiration, until this process gradually stabilizes in mature stages (Orihuela-Belmonte et al., 2013; Casiano et al., 2018); these include fast-growing plantations (Téllez et al., 2019; Jiménez et al., 2020).
However, rapid plant growth in early stages may also be the result of the presence of anthropogenic factors such as forest fires or land use changes involving secondary successions in the ecosystem (Aryal et al., 2014). It has even been documented that forest management activities through silvicultural practices have a positive impact on carbon sequestration and storage, due to the type of forest and management conditions (Monárrez et al., 2018; Palacios-Cruz et al., 2020).
Growth modeling is the most powerful management tool for decision making, as it allows to determine the most appropriate strategies for the use and conservation of forest resources, both in the present and in the future (Salas et al., 2016; Santiago et al., 2020). It is also vital to know the productivity of ecosystems, determine growth and increment, and define forestry shifts and the use of a species according to the time and quality of the site (Aguirre, 2015).
Biomass modeling for carbon estimation, in particular, is a reliable tool for measuring the storage capacity of trees as a climate change mitigation strategy and is also an important aspect to consider in carbon inventory planning (Fonseca et al., 2021), contributing to the development of sustainable management practices and species conservation strategies, in which timber production is not the main function (Cuevas and Aquino, 2020).
In recent years, about 90 research papers related to carbon estimation from chronosequences have been cited (Casiano et al., 2018), of which 8 % are related to carbon sequestration through the analysis and modeling of growth rings (Reyes et al., 2020); most of these studies have focused on young forest plantations (Pompa and Sigala, 2017).
Therefore, in the present research the goodness of fit of five growth models to efficiently estimate biomass stock and carbon sequestration through growth rings for individual trees in mature Pinus teocote Schltdl. et Cham. and Pinus oocarpa Schiede. forests of the mountainous region of the state of Guerrero, Mexico was tested. The null hypothesis (H0) stated in this research is that there are no differences in carbon uptake between the two species studied.
Materials and Methods
Study area
The study area is located between 17°01'45" and 17°15'30" N, and 98°39'24" W (Figure 1), at an altitude of 1 800 to 2 100 m (Figure 2) (INEGI, 2014). It includes Iliatenco and Malinaltepec municipalities in the mountain region of the state of Guerrero, Mexico. The predominant vegetation is pine-oak forests, where P. teocote and P. oocarpa grow naturally in pure stands.
Figure 2 Distribution of residuals (kg) for biomass estimation (kg) in two pinaceae trees in Guerrero: a) Pinus teocote Schltdl. et Cham., b) Pinus oocarpa Schiede.
The zone has a A(c) w₂ (2) climate, which corresponds to semi-warm temperate, with intense rainfall in the months of July-August; the minimum and maximum temperatures vary from -3 to 26 °C, respectively. The soil type is mostly Regosol, with abundant organic matter (INEGI, 2008; INEGI, 2014).
Database
Twenty four dominant trees per species were felled from mature unispecific stands representing all diameter categories (5-60 cm) (Marroquín et al., 2018; Martínez et al., 2019), selected in 20 circular sites of 500 m2 and randomly distributed in each stand (Ancira-Sánchez and Treviño, 2015). The number of individuals per site was then obtained and extrapolated to individuals per hectare (ind ha-1): 210 ind ha-1 for P. teocote, and 190 ha-1 for P. oocarpa.
Forest profiles were constructed by measuring and analyzing different diameters and recording the respective ages of the slices according to the log analysis technique (Klepac, 1976); the slices were obtained from each tree at the heights of 0.30 m, 1.30 m, and subsequently every 2 m, until reaching the tip (Hernández et al., 2020). The slices were prepared with a DWE6411 DeWalt orbital sander and LT-0100 SAYER clear varnish for high gloss wood (Pineda et al., 2015) to facilitate direct reading of annual rings using the conventional method (González et al., 2016).
Variables analysis
Unbarked diameters were measured with a 50 cm Arly 3003 ruler on the 5 and 10 year rings of each slice along the entire length of the stem (Reyes et al., 2019); the basimetric area (G) in m2 was then determined; the volume (m3) per section i was estimated using the individual summation by dendrometric type (Uranga et al., 2015) ―stump, logs and tips―, based on the formula of the cylinder (1), Smalian (2), and cone (3), in order of mention:
Where:
StV = Stump volume
G = Basimetric area in m2 of the stump section
LV = Log volume (m3)
G 1 = Basimetric (m2) of the largest section of the log
G 2 = Basimetric (m2) of the smallest section of the log
G 3 = Basimetric (m2) of the tip section
L= Length of the section (m)
The biomass per section was determined with the indirect method (Brown et al., 1989; Chave et al., 2005; Fonseca, 2017), which uses the values of the forest volume per section and the average basic density (BD) according to the following Equation (4); the BD was 450 kg m-3 for P. teocote, and 500 kg m-3 for P. oocarpa (Ríos, 2021).
Where:
Sb = Stem biomass (kg) per age section i
BD = Basic density (kg m-3)
SV = Stem volume per age section i
The aboveground biomass (B) of each section of age i was obtained with the expression (5), which adds the average percentage (%) of leaf-branch biomass (Bhr) previously determined by Ríos (2021), of 24.6 % in P. oocarpa and 29.6 % in P. teocote.
Where:
B = Aboveground biomass (kg) per age section i
SB = Stem biomass (kg)
L-BB = Leaf-branch biomass (kg)
The Carbon (C) fixed in the B of each species at age i, was calculated as the product of B times the percentage of C quoted by Yerena et al. (2012) for P. teocote (47 %); the percentage used for P. oocarpa was 48 % ―a conservative figure compared to the one estimated by the IPCC (2006), which corresponds to 50 % of the tree biomass.
Analyzed growth models and increments
Five growth models were fitted: Schumacher, Gompertz, Chapman-Richards, Weibull and Logistic, all of which are widely used for their practicality and satisfactory fits in several forest growth studies (Kiviste et al., 2002), as depicted in Table 1. The current annual increase (CAI), was derived as follows, the mean annual increase (MAI), and the maximum value of CAI (max CAI) were calculated using the integral formula of the best adjusted growth model. Based on these values, the technical shift corresponding to the optimum point of maximum biomass growth rate characterized by the intersection of the CAI and MAI, was estimated.
Table 1 Growth and biomass increment equations used.
| Growth model | Integral form | Current annual increase (CAI) | Average annual increase(MAI) | I |
|---|---|---|---|---|
| Schumacher |
|
|
|
(6) |
| Gompertz |
|
|
|
(7) |
| Chapman-Richards |
|
|
|
(8) |
| Weibull |
|
|
|
(9) |
| Logistic |
|
|
|
(10) |
Y = Biomass increase (kg); X = Age in years; e = Natural exponential base; nl = Natural logarithm; a, b and c = Regression parameters; I = Identifier.
The growth in B and the accumulation of C in tons per unit of area (t ha-1) were estimated using Equations 11 and 12:
Where:
Y = Growth model chosen to estimate the B for each species transformed into tons (t ha-1)
N = Average number of trees ha-1 in the sampling sites
tC/t = Carbon conversion factor
Fitting method and model selection
The adjustment was performed with the full information maximum likelihood
method (FIML), using the MODEL procedure of the SAS
statistical software (SAS Institute,
2008). The best model was chosen based on the level of
significance of the parameters (p<0.05), the highest
adjusted coefficient of determination (adjR
2
) (13), the minimum root mean squared error (RMSE)
(14), and bias (
Where:
adj R 2 = Adjusted coefficient of determination
RMSE = Root mean square error
p = Number of parameters to be estimated
n = Number of observations
Y i = Observed values
A continuous time autoregressive model, CAR(X), was utilized to correct the autocorrelation problem, based on the proposal of Zimmerman and Núñez-Antón (2001):
Where:
P k = Autoregressive parameter of order k to be estimated
Since most growth models are heteroscedastic (Quiñonez-Barraza et al., 2018), this problem was corrected by employing a weighting function on the residuals using a variance power function based on the inverse of the independent variable (Hernández et al., 2017; Guzmán et al., 2020) and expressed as:
Where:
y’ = Residuals with corrected weights
y= Residual value of the growth equation
A = Age (years)
Results and Discussion
Sample characteristics
For P. teocote, a diameter range between 1 and 53 cm and a total height (TH) of 0.3 to 24.2 were estimated. For P. oocarpa, the ND ranged from 1.5 to 59.8 cm; however, the TH ranged from 1.2 to 29 m (1.2 to 29 m) (Table 2).
Table 2 Dasometric characteristics of Pinus teocote Schltdl. et Cham. and Pinus oocarpa Schiede, Guerrero, Mexico.
| Species | Variable |
|
|
|
|
|
|
|---|---|---|---|---|---|---|---|
| P. teocote | A | 35.6 | 22.9 | 64.3 | 2.39 | 8 | 92 |
| ND | 19.9 | 14.18 | 71.3 | 1.48 | 3.5 | 53 | |
| TH | 10.4 | 6.34 | 61.0 | 0.66 | 0.3 | 24.2 | |
| G | 0.044 | 0.052 | 118.2 | 0.01 | 0.0002 | 0.2124 | |
| V | 0.356 | 0.49 | 137.6 | 0.05 | 0.0027 | 2.128 | |
| B | 242.8 | 344.8 | 142.0 | 35.95 | 0.7 | 1547 | |
| P. oocarpa | A | 32.43 | 24.17 | 52.2 | 2.1 | 4 | 104 |
| ND | 22.9 | 15.9 | 69.5 | 3.2 | 2.5 | 59.8 | |
| TH | 14.4 | 8.3 | 42.3 | 1.5 | 1.2 | 29 | |
| G | 0.060 | 0.068 | 114.1 | 3.6 | 0.0002 | 0.2809 | |
| V | 0.639 | 0.8 | 103.4 | 0.1 | 0.0053 | 3.3589 | |
| B | 335.6 | 473.2 | 136.3 | 25.4 | 1.2 | 2359 |
A = Age (years); ND =
Normal diameter (cm); TH = Total height
(m); G = Basal area (m2);
V= Stem volume (m3);
B = Aboveground biomass (kg);
In regard to the biomass area (B), the minimum and maximum values obtained were 0.7 (ND=3.5 cm) and 1547 kg (ND=53 cm) in P. teocote. In P. oocarpa, the range was 5 to 2 359 kg of B (ND=4.6 and 59 cm, respectively).
Biomass growth function
All models of biomass growth in mature forests of the two
Pinus species evaluated presented problems of
heteroscedasticity (TW<0.05); after the residual
correction procedure, the logistic model in P. teocote
continued to present problems of heteroscedasticity.
(TW=0.016); Schumacher’s and Chapman-Richards’ models
exhibited the same problem in P. oocarpa
(TW<0.05); they were therefore discarded. With the
remaining models, we were able to minimize the heteroscedasticity and thus
obtained a better distribution of residuals (Guzmán et al., 2020). Of these growth models,
the Weibull model exhibited the highest values for
adj
R
2
=0.73 and 0.88, the lowest RMSE values (184.2 and 155.9), and an
average bias (
The estimated goodness-of-fit of the five growth models was higher in P. oocarpa (0.80<adjR 2 <0.88) than in P. teocote (0.65<R 2 adj<0.73), which could be due to the variation of biomass in each age category, although this variation was more noticeable in P. teocote. Montes de Oca et al. (2012) obtained similar values when determining carbon increments for a natural regeneration of Pinus durangensis Martínez, with an adjR 2 of 0.85 when using the exponential model; the same modeling adjustments occurred in the estimation of the growth in the B of a young (12 year-old) plantation of P. pseudostrobus Lindl., with values of adjR 2 = 0.95 (Méndez et al., 2011). Návar et al. (2003) reported an adjR 2 of 0.90 with the Clutter model for carbon sequestration in 6 and 20 year-old conifer plantations in Durango State, Mexico; these values may be directly attributed to the diameter and age range of trees in young forest plantations (López et al., 2016), with respect to mature forests (with a larger sample size and age group va/riation) (Aguilar et al., 2016; Murillo et al., 2017).
Table 3 Statistical indicators of growth models in the B of Pinus teocote Schltdl. et Cham. and Pinus oocarpa Schiede Guerrero.
| Ec | adjR 2 | RMSE |
|
DW | WT | Parameter | Estimator | SE | T Value | Pr>F |
|---|---|---|---|---|---|---|---|---|---|---|
| P. teocote | ||||||||||
| 6 | 0.65 | 203.8 | 148 | 2.09 | 0.0983 | a | 2 064.01 | 399.4 | 5.17 | <0.0001 |
| b | 90.02 | 5.669 | 15.88 | <0.0001 | ||||||
| 7 | 0.72 | 185.1 | 136 | 1.83 | 0.0078 | a | 1 445.54 | 405.2 | 3.57 | 0.0006 |
| b | 8.6199 | 1.067 | 8.08 | <0.0001 | ||||||
| c | 0.03639 | 0.006 | 5.64 | <0.0001 | ||||||
| 8 | 0.68 | 208.3 | 129 | 1.74 | 0.0630 | a | 1 207.94 | 543.6 | 2.22 | 0.0288 |
| b | 0.03252 | 0.008 | 3.72 | 0.0004 | ||||||
| c | 5.44790 | 0.827 | 6.59 | <0.0001 | ||||||
| 9 | 0.73 | 180 | 125 | 1.85 | 0.0720 | a | 1 722.1 | 997.4 | 3.73 | <0.0001 |
| b | 3.933E-6 | 5.6E-6 | 7.70 | <0.0001 | ||||||
| c | 2.79286 | 0.4871 | 5.75 | <0.0001 | ||||||
| 10 | 0.72 | 193.8 | 186 | 1.78 | 0.016 | a | 835.004 | 116.8 | 7.15 | <0.0001 |
| b | 5.854 | 0.402 | 14.54 | <0.0001 | ||||||
| c | 0.11195 | 0.0121 | 9.27 | <0.0001 | ||||||
| P. oocarpa | ||||||||||
| 6 | 0.80 | 211.7 | 137.4 | 1.94 | 0.0587 | a | 2 520.58 | 325.8 | 7.74 | <0.0001 |
| b | 72.348 | 4.87 | 14.85 | <0.0001 | ||||||
| 7 | 0.84 | 187.3 | 129.3 | 1.97 | 0.2306 | a | 1 619.03 | 268.1 | 6.04 | <0.0001 |
| b | 7.0362 | 0.363 | 19.35 | <0.0001 | ||||||
| c | 0.03909 | 0.0040 | 9.74 | <0.0001 | ||||||
| 8 | 0.88 | 158 | 117.1 | 1.87 | 0.0570 | a | 4 525.89 | 2 833.6 | 1.60 | 0.1132* |
| b | 0.01223 | 0.0055 | 2.20 | <0.0300 | ||||||
| c | 2.6788 | 0.3213 | 8.34 | <0.0001 | ||||||
| 9 | 0.88 | 155.5 | 108.2 | 1.83 | 0.1036 | a | 3 186.791 | 789.5 | 1.58 | 0.0300 |
| b | 0.000033 | 0.603 | -24.95 | 0.004 | ||||||
| c | 2.210347 | 2E-04 | 4.85 | 0.002 | ||||||
| 10 | 0.84 | 185.4 | 114.7 | 1.92 | 0.060 | a | 1 509.85 | 148.9 | 10.4 | <0.0001 |
| b | 4.9016 | 0.209 | 23.36 | <0.0001 | ||||||
| c | 0.0859 | 0.006 | 14.17 | <0.0001 | ||||||
adjR
2
= Adjusted coefficient of determination;
RMSE = Root mean square error (kg);
WT = White’s test; DW
= Durbin-Watson test; P>F = Significance
of the model; a, b, c = Estimated
parameters; SE = Standard error (kg);
Pr>T = Probability value of the
Student's t-distribution;
The equations for estimating biomass growth are expressed as follows: for P. teocote, the generated model was:
For P. oocarpa, the growth equation was:
Figure 3 shows the projected growth curves in the B (kg) with the selected model, as well as their equivalence in C. The accumulation of biomass and carbon over time was higher in Pinus oocarpa.
Estimation of annual increases
The analysis of the results indicates an annual increase of 13.3 kg tree-1 in the B of P. teocote until the technical shift (at 107 years of age); while, in P. oocarpa the maximum increments were reached at 126 years (19.7 kg of B). The above reflects an uptake of 1.5 times more B and C between the two species and represents a difference of ~6.4 kg (Figure 4a); the carbon uptake rate is similar to that indicated in 12-year old young forest plantations by Méndez et al. (2011), who determined that P. pseudostrobus captured on average 1.6 times more carbon than P. devoniana, up to the technical shift (12 years); however, the difference was 50.8 kg of B between both taxa.
MAI =Mean annual increase (MAI); CAI = Current annual increase.
Figure 4 Sequence of the annual increase in B in kg (a) and in t ha-1 yr-1 in Pinus teocote Schltdl. et Cham. and Pinus oocarpa Schiede in the mountains of Guerrero, Mexico.
Instant growth (max CAI) was 21.93 kg in P. teocote at 76 years of age, representing 4.6 t ha-1 yr-1 of B and 2.16 t ha-1 yr-1 of C; for P. oocarpa, the max CAI value was 27.4 kg at 84 years of age (Figure 4a), which projected to t ha-1 yr-1 was 5.21 (B) and 2.50 (C). This would result in increases up to the technical shift (CAI=MAI) of 2.81 and 1.32 t ha-1 yr-1 of B and C, respectively, in P. teocote; for P. oocarpa the increases would be of 3.64 (B) and 1.74 (C) t ha-1 yr-1 (Figure 4b).
Figure 5 shows the cumulative projection for B in t ha-1, which could extend outside the limits of biological growth according to the prediction of the selected growth model. Therefore, we should consider as a limit the inflection point when CAI = MAI (technical shift); in this sense, P. teocote would reach up to 303.6 t ha-1 of B, which represents 142.69 t ha-1 of C. In turn, in P. oocarpa the limit would be 463 t ha-1 of B (222 t ha-1 of C). The above would only be valid if all the trees present per hectare reach the technical turn together.
Figure 5 Projection of cumulative growth in t ha-1 of B and C up to the technical shift and base age (50 years) in Pinus teocote Schltdl. et Cham. y Pinus oocarpa Schiede, Mountains of Guerrero, Mexico.
When considering as a reference a base age of 50 years, which is commonly used for site index estimations in Pinus forests (Vargas et al., 2010; Pimienta-de la Torre et al., 2020), it was inferred that P. teocote would capture 71 t of B ha-1 (33 t of C ha-1), and P. oocarpa, on average, would accumulate 103 t of B ha-1, which represent 49 t of C ha-1. These results exceed those obtained by Alberto and Elvir (2008), who reported 39 t B ha-1 accumulated in highly competitive mature P. oocarpa forests in Honduras. However, Rodríguez-Larramendi et al. (2016) estimated 172 and 190 t of B ha-1 aged up to 120 years in Pinus patula Schltdl. et Cham. and Pinus maximinoi H. E. Moore forests; while Figueroa et al. (2010) registered 166 and 186 t ha-1 of B in 25-year old stands of P. patula under thinning; López et al. (2016) documented up to 128 t ha-1 of B in 51 year-old Hevea brasilensis (Willd. ex A.Juss.) Müell. Arg. forest plantations; this value is higher than those obtained in the present study. These differences may be attributed to the density (ind ha-1) reflected in competition (crown cover), anatomical conformation or basic wood density of the species (Valencia and Vargas, 2001).
When comparing the results with young forest plantations, Pacheco et al. (2007) indicated 37.5 t of B for P. greggi Engelmn.; Méndez et al. (2011) indicated 10.42 t of B ha-1 for 12 year-old plantations of P. devoniana Lindl. and Pinus pseudostrobus ―figures well below those estimated in this study and directly attributed to the age of the taxa.
According to Villar et al. (2004), the vegetation cover and net assimilation rate are the factors that most positively influence the biomass growth of a plant; that is, although two plant species grow under similar conditions, they differ markedly in their ability to grow due to the abundance of water, nutrients and, most importantly, the genetic component.
Conclusions
The trunk analysis technique in combination with basic wood density values allows estimating the growth in biomass area and carbon sequestration in mature stands of P. oocarpa and P. teocote, which will have an impact on improving forestry interventions adjusted to the forest planning objective, such as carbon inventories. The Weibull growth model presents the best statistics for estimating biomass growth and inferring carbon sequestration for the two species studied. In general, P. oocarpa accumulates 1.5 times more biomass and carbon over a longer time interval than P. teocote in mature forests in the mountainous region of the state of Guerrero.
Acknowledgments
The authors thank the Consejo Nacional de Ciencia y Tecnología, Conacyt (National Council for Science and Technology) for the grant that contributed to the financial support required by the research work, as well as the Intercultural University of the State of Guerrero (UIEG) for arranging permits for the study and for providing equipment for drying the samples in the laboratory.
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Received: December 04, 2020; Accepted: July 26, 2021
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