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Revista mexicana de ciencias forestales

Print version ISSN 2007-1132

Rev. mex. de cienc. forestales vol.13 n.73 México Sep./Oct. 2022  Epub Oct 10, 2022

https://doi.org/10.29298/rmcf.v13i73.1252 

Scientific article

Structure and floristic composition of a Pinus-Quercus forest in El Porvenir, Chiapas State

Romeo de Jesús Barrios-Calderón1 

Javier Ernesto Pérez Pérez2 

Jony Ramiro Torres Velázquez3  * 

Juan Francisco Aguirre-Cadena1 

1Grupo Colegiado de Investigación en Sistemas Agrícolas y Forestal, Facultad de Ciencias Agrícolas. Universidad Autónoma de Chiapas, México.

2Universidad de Ciencias y Artes de Chiapas, Facultad de Ingeniería, subsede Motozintla. México.

3Tecnológico Nacional de México, Instituto Tecnológico del Valle del Yaqui. México.


Abstract

Pinus-Quercus forests are ecosystems of great ecological importance. Structure and composition are indicators of biodiversity in these forest associations, being two key elements for their stability and conservation. The objective of this study was to characterize a Pinus-Quercus forest based con the structural parameters and species composition present in the arboreal stratum in the municipality of El Porvenir, Chiapas. Six 400 m2 circular sites were established to evaluate the adult trees and their dasometric variables (total height, normal diameter and cover). The structural parameters of the forest (density, dominance, basal area and cover) were used to calculate the indexes of Importance Value, forest value, Holdrige complexity index and similarity index. The results showed the presence of six species; Pinus maximinoi exhibited a mean height of 18.88±6.72 m (p<0.0001, F= 5.46), which is greater than that of other species. In addition, it has the highest normal diameter (30.58±13.64 cm, p<0.0002, F=5.18), Importance Value (161.07 %) and forest value (108.08 %). The Holdrige complexity index of the forest is 45.22 %. The results obtained made it possible to identify the dimensions, structural parameters, and dominance of the species, with Pinus maximinoi being the most valuable.

Key words Forest arrangement; pine-oak forest; Sørensen's index; Holdrige complexity index; tree density; forest value index

Resumen

Los bosques de Pinus-Quercus constituyen ecosistemas de gran importancia ecológica. La estructura y composición son indicadores de la biodiversidad en estas asociaciones forestales, en las cuales esos dos elementos son clave para su estabilidad y conservación. El objetivo del presente estudio fue caracterizar un bosque de Pinus-Quercus a través de los parámetros estructurales y de la composición de especies presentes en el estrato arbóreo en el municipio El Porvenir, Chiapas. Se establecieron seis sitios circulares de muestreo, con una superficie de 400 m2 para evaluar el arbolado adulto y sus variables dasométricas (altura total, diámetro normal y cobertura). Los parámetros estructurales del bosque (densidad, dominancia, área basal y cobertura) se emplearon para calcular los índices de Valor de Importancia, valor forestal, complejidad de Holdrige y los índices de similitud. Los resultados mostraron la presencia de seis especies; Pinus maximinoi registró una altura media de 18.88±6.72 m (p<0.0001, F=5.46) superior a los otros taxones. Además, le correspondió el mayor diámetro normal (30.58±13.64 cm, p<0.0002, F=5.18), Valor de Importancia (161.07 %) y valor forestal (108.08 %). El índice de complejidad de Holdrige del bosque fue de 45.22 %. Los resultados obtenidos permitieron identificar las dimensiones, parámetros estructurales y dominancia de las especies; de ellas, Pinus maximinoi fue la de mayor valor.

Palabras clave Arreglo forestal; bosque de pino-encino; coeficiente de Sørensen; complejidad de Holdrige; densidad de arbolado; valor forestal

Introduction

Globally, forests are one of the largest reservoirs of biological diversity, covering 31 % of the earth's land surface, a percentage equivalent to approximately 39 million km2 (FAO, 2015). Resources obtained from forests such as timber, firewood, charcoal, construction material, non-timber products (i.e. medicinal plants) and certain environmental services: soil retention, water catchment, biomass, carbon sequestration, habitat and biodiversity conservation (Calderón et al., 2012; Saavedra and Perevochtchikova, 2017), are very important for the rural and urban population. Forests represent a source of monetary income for local people (Cortina-Villar et al., 2012), however, the availability of resources is determined by the composition and structure of their vegetation.

Mexico has 138 million hectares of forest area (70 % of the national territory), and temperate forests cover approximately 24 % of this area (Conafor, 2012). However, between 2005 and 2010, they were gradually reduced at a rate of 155 000 ha per year (INEGI, 2014). These alterations, which occur in ecosystems due to anthropogenic causes, can last for specific times and be irreversible (Thom and Seidl, 2016); therefore, it is essential to have a broad knowledge of the structure and distribution of forest species present in the forests (Méndez-Toribio et al., 2014).

The structure and diversity indices contribute to decision-making regarding forest management, as well as to the detection of natural succession processes and anthropogenic effects (López-Hernández et al., 2017), which in turn facilitates the establishment of type stands to implement management strategies (Wehenkel et al., 2014) that consider: i) spatial position or distribution, (ii) species diversity and mixture, and (iii) arrangement of vertical and horizontal differentiation (Castellanos-Bolaños et al., 2008).

Structural parameters are a key indicator of biodiversity, ecological stability and future stand development (Franklin et al., 2002; López-Hernández et al., 2017). When the forest has a very simplified composition, some ecosystem functions tend to decrease; on the contrary, a high complexity increases its productivity, diversity and persistence (Castellanos-Bolaños et al., 2008). The objective of this study was to characterize a Pinus-Quercus forest in order to obtain information regarding the structural parameters and the association of species present in the tree layer in a property in El Porvenir municipality, state of Chiapas.

The hypotheses that guided the present research were: i) There are no significant differences in the mean value of height and normal diameter of trees between the evaluated sites and species, ii) At least one dominant species of the Pinus genus is present with an Importance value index ≥200; and iii) The percentage affinity of tree species in the evaluated sites is ≥50 %, indicating that the species present have a medium-high similarity type.

Materials and Methods

Study area

El Porvenir municipality is 82.52 km² (5.72 % of the surface of the Sierra Mariscal region and 0.1 % of the surface of the state of Chiapas, Mexico), it is located between 1 200 and 3 100 masl (Mejía and Kauffer, 2007). Its climate is Am(w) ―i.e., humid temperate with abundant rainfall in summer―, its temperature is 12 to 24 °C, and rainfall fluctuates between 1 200 and 4 000 mm per year (INEGI, 2014).

The study was carried out in a 4 ha Pinus-Quercus forest plot called "parcela escolar Canadá" in the Malé ejido, El Porvenir, Chiapas, located between 1708786.84 and 1708554.43 N, and 582378.81 and 582695.54 E, at an average altitude of 2 840 m (Figure 1).

Figure 1 Location of the study area and distribution of sampling sites. 

Sampling design

Six randomly distributed circular sites with an area of 400 m2 (0.04 ha) were established for the tree inventory (Figure 1). This is equivalent to an inventoried area of 0.24 ha. The number of sites is sufficient to reach an admissible error of 10 %, which is within the interval established for circular sites (Aguirre et al., 1997) with a confidence level of 95 %:

E %=t (s %÷n) (1)

n=t5 s %t5 s %E %22 (2)

Where:

n = Number of sampling units (sample size)

t = Confidence level value

s % = Estimation of the coefficient of variation of the population

E % = Permissible error

According to Aguirre et al. (1997), the size of the sampling site is considered to be sufficient because it is a homogeneous forest with low variance, which allows obtaining significant results. At each site, a tree was considered as the center, from which four chords with a radius of 11.29 m were established in order to estimate the surface area of 400 m2.

Structure and composition of adult trees

A forest inventory was carried out in the Pinus-Quercus forest following the procedures of Villavicencio-Enríquez and Valdez-Hernández (2003). Woody vegetation with a crown differentiated from the stem was included; the normal diameter (ND) was conventionally established, being measured at a height of 1.3 m from the ground. The vertical structure (total tree height) was estimated using a Vertex III Haglöf ® hypsometer. Seven height classes were defined, the amplitude of each one corresponding to 5 m. The lower class limit (minimum tree height) was 2 m and the upper limit (maximum height) was >32 m.

The horizontal structure was represented mainly by tree density (D), normal diameter (ND) and basimetric area (BA). The density of standing adult trees and stumps with a ND≥2.5 cm was evaluated (Villavicencio-Enríquez and Valdez-Hernández, 2003; Zarco-Espinoza et al., 2010). ND was measured using a modelo 349-5-A Richter® 5 m diameter tape. Twelve diameter classes were defined with a 5 cm amplitude between each class. The maximum class was >58.5 cm ND. In order to determine the canopy cover, the crown diameter was measured using the formula for an ellipse: The crown diameter =π (axis a×axis b); two measurements were obtained (axis a: north-south and axis b: east-west) with the model Vertex III® Haglöf hypsometer. The average of both measurements was then calculated. The formulas applied by Zarco-Espinosa et al. (2010) were utilized: the basal area (BA) was estimated with the formula:

BA=π 4(ND) 2

Where:

π = 3.1416

The relative cover (RC) was obtained by applying the formula:

RC=Crown diameter of all speciesSampled area × 100

Where:

RC = Relative cover

Indexes calculation

In order to dimension the structural composition of the Pinus-Quercus forest, two indexes used by Zarco-Espinoza et al. (2010) were applied to denote the vertical and horizontal stratification of the species present in the forest: 1) Importance Value Index (IVI), and 2) Forest Value Index (FVI). Other indices were also determined to delimit the level of complexity and similarity of the species present at each study site: 3) Holdrige Complexity Index (Holdrige et al., 1971), and 4) Sørensen’s Affinity Index (Sørensen, 1948).

Statistical analyses

Statistical analyses were performed with the JMP Pro 14 software (Statistical Analysis System, 2019). The results were analyzed by analysis of variance (ANOVA) and comparison of means by Tukey (p<0.05) between the variables evaluated in the study sites. In order to contrast the Sørensen’s Affinity Index and corroborate the level of equality between sites with respect to the identified species, the Bray-Curtis (1957) similarity and Jaccard affinity analyses were applied with the Past software, version 3.2 (Hammer et al., 2009).

Results and Discussion

Floristic composition and structure

The Pinus-Quercus forest consists of six tree species. Pinus maximinoi H. E. Moore (with an average height [h] of 13.29 m and ND of 7.57 cm) and Pinus ayacahuite Ehrenb. ex Schltdl. (h of 11.01 m and ND of 22.51 cm). The Quercus genus was represented by two taxa: Quercus cortesii Liebm. (with average h of 8.67 m and DN 15.9 cm) and Quercus corrugata Hook (h of 11.1 m and DN of 21.5). Other associated species were Cupressus lindleyi Klotzsch ex Endl. (with an average h of 9.42 m and 26.28 cm of DN) and Prunus serotina Ehrh ssp. capuli (Cav.) Mc Vaugh (with h of 9.75 m and a ND of 13.5 cm).

Vertical structure

Tree height (h) registered a higher percentage for the 7.01 to 12 m height class (41.83 %), similar to that reported in other studies (Castellanos-Bolaños et al., 2010; García et al., 2019) that focus on this dominant class of the vertical stratum. The lowest percentage belonged to the >32 m class. Classes 2 to 7 m, 12.01 to 17 m and 17.01 to 22 m had similar percentages (16.73 %, 14.74 % and 15.14 %) (Figure 2).

Figure 2 Tree height classes of the Pinus-Quercus forest at El Porvenir, Chiapas. 

The percentage corresponding to the height classes for each of the analyzed species indicated that the highest value (42.86 %) corresponded to Cupressus lindleyi in the 2-to-7 m class and the lowest proportion (7.14 %), to the 17.01-to-22 m class. Although C. lindleyi can reach heights between 10 and 30 m and even of up to 40 m (Raddi et al., 2014), no trees were observed with heights greater than 22 m. P. ayacahuite had the highest percentage of individuals for the 7.01-to-12 m height class (33.33 %) and the lowest percentage was registered in the 22.01-to-27 m height class (9.8 %); thus, no trees taller than 27.01 m were found (Figure 3). This differs from the result cited by Ramírez-Martínez et al. (2018), who registered a mean height of 27.25 m in a Pinus ayacahuite forest in the state of Oaxaca, Mexico, where they note the presence of trees over 30 m tall. Pinus maximinoi had the highest proportion of individuals in the 17.01 to 22 m height class (46.48 %), the >32 m class had the lowest percentage (2.82 %) and the 22.01 to 27 m and 27.01 to 32 m classes had very similar percentages.

Figure 3 Height classes of the Pinus-Quercus forest species. 

The results presented here are similar to those documented for P. maximinoi in the study by Méndez et al. (2018), whose dominant strata are concentrated in the 15 to 22 m and 23 to 28 m height classes. The National Institute of Forest Science (Instituto Nacional del Bosques, INAB) (Cano, 2017) cites in Guatemala an average height of 17 to 19 m, similar to that recorded for P. maximinoi in El Porvenir where it reaches up to 35 m. Quercus corrugata and Q. cortesii recorded the highest percentage of individuals (60.87 %) for the 7.01 to 12 m height class (Figure 3). Although these species can reach 50 m in height, the suppression exerted by the Pinus genus on Quercus limits their optimal growth (Hélardot, 2015).

The results of the analysis of variance (ANOVA) indicated significant differences in the average height of the taxa, with a higher value for P. maximinoi (18.88±6.72 m) with respect to Prunus serotina (5.25±2.06 m), Cupressus lindleyi (9.12±1.77 m) and Q. corrugata (8.1±3.55 m), which presented the lowest heights (Figure 4).

Figure 4 Average height ± standard deviation of the analyzed tree species. 

Horizontal structure

Diameter class II had the highest number of trees (171 ind. ha-1) and class XI (8 ind. ha-1) had the lowest number of trees (Table 1A). The percentage of individuals in all diameter classes was higher for P. maximinoi, except in classes I and XII (Table 1B). The basimetric area of all species represented a total of 65.01 m2 ha-1, with class XII making the greatest contribution (Table 1C).

Table 1 Tree diameter classes, number (A), percentages (B), and basal area (C) characteristic of each species in the Pinus-Quercus forest. 

Species Class (cm) Total
I
2.5-
7.5
II
7.6-
12.6
III
12.7-
17.7
IV
17.8-
22.8
V
22.9-
27.9
VI
28-
33
VII
33.1-
38.1
VIII
38.2-
43.2
IX
43.3-
48.3
X
48.4-
53.4
XI
53.5-
58.5
XII
>58.5
A) Number of individuals/diameter class
Cupressus lindleyi Klotzsch ex Endl. 1 7 5 0 0 0 0 0 0 0 0 0 13
Pinus ayacahuite Ehrenb. ex Schltdl. 17 9 6 3 4 1 2 0 3 1 1 4 51
Pinus maximinoi H. E. Moore 6 22 17 16 19 7 6 8 3 4 1 19 128
Quercus corrugata Hook 6 2 6 2 1 1 1 1 0 0 0 0 20
Quercus cortesii Liebm. 0 1 0 0 0 1 0 0 0 0 0 1 3
Prunus serotina Ehrh ssp. capuli (Cav.) Mc Vaugh 4 0 0 0 0 0 0 0 0 0 0 0 4
Total (0.24 ha) 34 41 34 21 24 10 9 9 6 5 2 24 219
Total (1 ha) 142 171 142 88 100 42 38 38 25 21 8 100 913
B) Percentage of individuals/diameter class
Cupressus lindleyi Klotzsch ex Endl. 3 17 15 0 0 0 0 0 0 0 0 0
Pinus ayacahuite Ehrenb. ex Schltdl. 50 22 18 14 17 10 22 0 0 20 50 0
Pinus maximinoi H. E. Moore 18 54 50 76 79 70 67 89 0 80 50 17
Quercus corrugata Hook 18 5 18 10 4 10 11 11 0 0 0 79
Quercus cortesii Liebm. 0 2 0 0 0 10 0 0 0 0 0 0
Prunus serotina Ehrh ssp. capuli (Cav.) Mc Vaugh 12 0 0 0 0 0 0 0 0 0 0 4
Total 100 100 100 100 100 100 100 100 0 100 100 100
C) Total individuals/percentage/basal area for each diametric class
All the species 142 171 142 88 100 42 38 38 25 21 8 100 913
% All the species 16 19 16 10 11 5 4 4 3 2 1 11 100
Basal area (m2 ha-1) 0.07 0.83 1.69 1.98 2.24 2.69 4.86 5.11 9.67 10.04 8.05 20.11 65.01

The average ND of the sites evaluated showed significant differences with a higher value at site 3 (66.26±6.76 cm). At the species level, the ND showed significant differences, whose maximum value corresponded to Pinus maximinoi with a ND of 30.58±13.64 cm (Table 2), which is located within the average intervals of eight Pinus species evaluated by Corral-Rivas et al. (2019). The tree taxon with the lowest ND was Prunus serotina (3.79±1.08), while the ND´s of P. ayacahuite, Q. corrugata and Q. cortesii were very similar to that of P. maximinoi (Table 2).

Table 2 Normal diameter (ND) in sites and species ± standard deviation (S.D.), ANOVA, and Tukey's comparison of measures (p<0.05). 

Site ND (cm)+S.D. Statistics
P F5/214
1 26.27±20.73b <0.0001 9.03
2 24.21±18.22b
3 66.26±6.76a
4 31.43±4.43b
5 18.51±2.84b
6 22.91±2.78b
Species ND (cm) ± S.D. Statistics
P F5/214
Cupressus lindleyi Klotzsch ex Endl. 11.40±2.8b <0.0002 5.18
Pinus ayacahuite Ehrenb. ex Schltdl. 20.4±9.84ab
Pinus maximinoi H. E. Moore 30.58±13.64a
Quercus corrugata Hook 28.19±22.88ab
Prunus serotina Ehrh ssp. capuli (Cav.) Mc Vaugh 3.79±1.08c
Quercus cortesii Liebm. 15.67±9.75b

Structural parameters and indexes

Pinus maximinoi registered the highest density (533 ind. ha-1), basal area (50.34 m2 ha-1), frequency and dominance, which was reflected in its Importance Value Index (IVI=161.07) (Table 3). This index is high compared to that presented by P. maximinoi in other Pinus-Quercus forests, such as the one reported by Méndez et al. (2018). Table 3 shows the values corresponding to the parameters.

Table 3 Structural parameters in the Pinus-Quercus forest. 

Species AD
(Ind. ha-1)
BA
(m2 ha-1)
AF RD RDo RF IVI
Pinus maximinoi H. E. Moore 533 50.34 100 58.64 77.43 25 161.07
Pinus ayacahuite Ehrenb. ex Schltdl. 213 10.72 100 23.18 16.48 25 64.67
Quercus corrugata Hook 83 1.76 66.67 9.09 2.71 16.67 28.46
Prunus serotina Ehrh ssp. capuli (Cav.) Mc Vaugh 17 0.02 66.67 1.82 0.02 16.67 18.51
Cupressus lindleyi Klotzsch ex Endl. 54 0.47 33.33 5.91 0.72 8.33 14.96
Quercus cortesii Liebm. 13 1.71 33.33 1.36 2.63 8.33 12.33
Total 913 65.01 100 100 100 300

AD = Absolute density; BA = Basal area; AF = Absolute frequency; RD = Relative density; RDo = Relative dominance; RF = Relative frequency; IVI = Importance Value Index.

In relation to tree density (913 ind. ha-1) and the low level of fragmentation, the Pinus-Quercus forest evaluated is of a closed type, with a mean density higher than that cited by Santiago et al. (2012) in a closed Pinus-Quercus forest in the state of Jalisco (650 ind. ha-1), and Méndez et al. (2018) who counted 254 ind. ha-1 in another Pinus-Quercus forest located in the state of Guerrero, Mexico. Alanís et al. (2011) obtained 2 876 ind. ha-1 in a Pinus-Quercus forest, a figure three times higher than that obtained in El Porvenir. The basimetric area documented here (65.01 m2 ha-1) is much lower than that cited (242 m2 ha-1) by Santiago et al. (2012), however, in this research the trees exhibited larger diametric dimensions.

The highest Forest Value Index (FVI) corresponded to P. maximinoi (108.08 %). The second species with the highest FVI was P. ayacahuite (58.65 %), however, this value is higher than the value reported by Graciano-Ávila et al. (2017) on a property in the state of Durango, Mexico. The Holdrige Complexity Index (HCI) of the Pinus-Quercus forest corresponded to 45.22 % (Table 4), which is a normal value for temperate forests due to its characteristic homogeneity and low variability in the type of species. Table 4 shows the FVI, HCI and the values of ND, height and cover for all species.

Table 4 Forest Value Index (FVI) and Holdrige Complexity Index (HCI) of the species found in the study area. 

Specie ND
(cm)
H
(m)
Co
(m2)
AbND RND AbH RH AbCo RCo FVI HCI
Pinus maximinoi H. E. Moore 27.57 13.29 1 564.50 0.0028 21.64 0.0013 21.01 0.16 65.42 108.08 45.22
Pinus ayacahuite Ehrenb. ex Schltdl. 22.51 11.01 563.55 0.0023 17.68 0.0011 17.41 0.06 23.57 58.65
Quercus corrugata Hook 26.28 9.42 140.28 0.0026 20.64 0.0009 14.90 0.01 5.87 41.40
Prunus serotina Ehrh ssp. capuli (Cav.) Mc Vaugh 21.50 11.10 113.20 0.0022 16.88 0.0011 17.55 0.01 4.73 39.17
Cupressus lindleyi Klotzsch ex Endl. 13.60 9.75 5.11 0.0014 10.68 0.0010 15.42 0.00 0.21 26.31
Quercus cortesii Liebm. 15.90 8.67 4.71 0.0016 12.49 0.0009 13.71 0.00 0.20 26.39
Total 21.23 10.54 2 391.34 0.0127 100 0.0063 100 0.2391 100 300

ND = Normal diameter; H = Tree height; Co = Canopy cover; AbND = Absolute normal diameter; RDN = Relative normal diameter; AbH = Absolute height; RH = Relative height; AbCo = Absolute cover; RCo = Relative cover.

Complexity and similarity indexes

Sørensen and Bray-Curtis Indexes

The Sørensen Affinity Index (K) defined sites very similar to each other, with an average affinity of 74 % (greater than 50 %). Other studies with K<50 % show low species similarity (Santana et al., 2014), which is equivalent to more heterogeneous forests. The sites with 100 % affinity were site 1 with respect to site 4 and site 2 with respect to site 3 because they have the same dominant taxa. However, when contrasted with the Bray-Curtis Similarity Index, sites 2 and 3 were the only ones that maintained this percentage. This is expressed graphically in the cluster analysis, in which no distance was shown between sites 2 and 3 (Figure 5).

Figure 5 Sørensen index (K), Bray-Curtis Similarity Index and Jaccard cluster analysis for the six sites in the Pinus-Quercus forest. 

This analysis clearly showed the definition of two groups: the first at a distance of 28 % (sites 1, 2, 3 and 4), and the second, at a distance of 38% (sites 5 and 6).

Conclusions

Based upon the averages of total height (vertical structure) and ND (horizontal structure), the hypothesis (i) which establishes the non-significance between the mean values of the compared sites and species is rejected. Regarding the Importance Value of the dominant species of the genus Pinus, none of them exhibits an IVI≥200, thus the second hypothesis is rejected. Finally, the average percentage of affinity between tree species in the six sites is ≥50 %, therefore hypothesis (iii), which indicates that the species present have medium to high affinity, is accepted.

The results allow to identify the configuration of the structural parameters and dominance of the associated species of the Pinus-Quercus forests in the Sierra Mariscal region of the state of Chiapas, Mexico. Pinus maximinoi is the most important species in the evaluated sites. The two species of the Quercus genus show a high level of suppression compared to those of the Pinus genus. The understanding of the real dynamics of the Pinus-Quercus forest in the study area gives rise to some questions regarding the integrated management and conservation of the resource required to improve the goods and services provided by the ecosystem under study.

Acknowledgements

The authors thank the Graduate School of Agricultural Sciences of the Universidad Autónoma de Chiapas for the logistical support and transportation to the study sites, in addition to the facilities for the use of the Forest Laboratory. Likewise, to the Tecnológico Nacional de México (TecNM) (National Technological Institute of Mexico) for the financing under the project k3w1n7 (7703) approved for Scientific Research 2020 program, and the services of the Coastal Zone Ecology Laboratory (LEZCO).

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Received: February 13, 2022; Accepted: August 05, 2022

Conflicts of interest

The authors declare that no conflicts of interest.

Contribution by author

Romeo de Jesús Barrios-Calderón, Javier Ernesto Pérez Pérez and Jony Ramiro Torres Velázquez: conceptualization and organization of the research, field work, database integration and writing of the manuscript; Juan Francisco Aguirre-Cadena: writing of the manuscript, database integration and statistical analysis. Pablo Marroquín Morales: elaboration of graphs, map and documentary references; Alfredo Isaac Brindis-Santos and Humberto Osorio Espinoza: adjustments in the discussion of results, critical review of the document, contribution of comments and bibliographic review. All authors participated in the general revision and final corrections of the manuscript.

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