Study area and site locations

The study was carried out in the Pueblo Nuevo municipality, located in the El Salto region, which is part of the southwestern part of the state of Durango, Mexico, and within the Western Sierra Madre (Figure 1). Geographically, it is located between parallels 23°42'34.48" and 23°49'28.18" N, and meridians 105°30'11.83" and 105°40'6.56" W. It has an altitude of 2 500 to 2 900 masl. The soil types present are Lithosol, Cambisol, and Regosol with predominantly coarse to medium texture. The dominant rock type is acidic extrusive igneous (^{INEGI, 2015}). In this zone, climates of type (A)C(w₂), C(w₂), C(E)(M) and C(E)(w₂) prevail, with an average annual rainfall of 945.3 mm and an average temperature of 11.5 ºC (^{Inegi, 2017}).

Figure1. Location of the study area and location of the Permanent Forestry and Soil Research sites under the individual tree selection silvicultural treatment. 

The vegetation of the region is composed of mixed forests of Pinus, Quercus, Juniperus, Arbutus and Alnus species (^{Luján-Soto et al., 2015}; ^{Colín et al., 2018}).

Obtaining mensuration data

The data were obtained from 12 Permanent Forestry and Soil Research Sites (SPIFyS), which were established according to ^{Corral-Rivas et al. (2009} and ²⁰¹³⁾ ―three in 2007 and nine in 2008 (first inventory)― and were remeasured 10 years later (second inventory), in the years 2017 and 2018, respectively. The evaluated sites exhibit evidence of forest management by the selection method, whose silvicultural intervention was carried out in different annual periods: at four sites, the treatment was applied one year after establishment; at one site, at three years; at one site, at six years; at one site, at seven years, and at the remaining three sites, at five years after establishment.

For each site, the following dasometric information was recorded: number of trees, species, normal diameter (>7.5 cm) (model 122450 Ben Meadows^® diameter tape), total height (m) (model Pm5/360 Suunto^® altimeter), azimuth, and distance from each of the individuals to the center of the site, whose surface area was 50 x 50 m (2 500 m²).

Diversity

The Shannon-Wiener index (H') was used to estimate species diversity (^{Shannon, 1948)}:

Where:

pi = Proportion of individuals of the species i, is obtained by the (ni/N) ratio

ni = Number of individuals of species i

N = Total number of individuals

ln = Natural logarithm

In order to determine whether there were significant differences in species diversity between the evaluation periods (first and second inventory), a Student's t-test modified by Hutcheson (Hutcheson's t-test) was performed (^{Magurran, 1988}) according to Equation 2, and the degrees of freedom (df) were estimated using Equation 3 (^{Hutcheson, 1970}). Several authors utilize this test for comparisons between evaluation periods of temperate forests under management (^{Moreno, 2001}; ^{Solís-Moreno et al., 2006}; ^{Corral-Rivas et al., 2005}; ^{Alanís-Rodríguez et al., 2010}).

Where:

Hˊ ₁ = Shannon-Wiener index of the first inventory

Hˊ ₂ = Shannon-Wiener index of the second inventory

VarHˊ ₁ = Variance obtained in the first inventory

VarHˊ ₂ = Variance obtained in the second inventory

N ₁ = Total number of individuals in the first inventory

N ₂ = Total number of individuals in the second inventory

The estimation of the variances of the first and second inventories, respectively, was carried out with Equation 4.

Where:

pi = Proportion of individuals of the species i, is obtained by the (ni/N) ratio

ni = Number of individuals of species i

N = Total number of individuals

ln = Natural logarithm

S = Number of species

Ecological indicators

For each tree species, the relative abundance values (RA) were determined according to the number of trees; the relative dominance (RD), as a function of basal area; the relative frequency (RF), based on the presence of the species at the sites. The Importance Value Index (IVI) was also estimated, with the average of the previous ecological indicators in percentage values from 0 to 100 for each evaluation period (^{Magurran, 2004}; ^{Alanís-Rodríguez et al., 2020}).

The statistical analysis of the ecological indicators (abundance and dominance) was performed based on the normal distribution of density and basal area in each measurement period. The means were compared using Student's t-test for dependent samples, or alternatively, the nonparametric Wilcoxon Ranks test, which compares the mean rank of two related samples and determines whether there are differences between them (^{Quispe-Andía et al., 2019}).

Structure composition

Site structure was characterized using three methodologies: species mix, spatial distribution and size difference. These indices were calculated using the structural group as a sampling unit consisting of a set of five trees, of which one serves as a reference and includes the four closest neighboring trees with which it coexists (^{Pommerening, 2002}; ^{Kint et al., 2003}; ^{Castellanos-Bolaños et al., 2008} and ²⁰¹⁰).

The degree of mixing of tree species was described in terms of Gadow's Mixing Index (Mi) (Füldner, 1995) which evaluates the species diversity of the neighborhood of a reference tree i, being defined as the proportion of the n neighbors that do not belong to the same species. Its value ranges from 0 to 1; values close to zero indicate that the taxa analyzed tend to group together and that they do not mix with the rest; on the other hand, values close to one indicate a preference for mixing with one another.

In order to quantify the spatial distribution of trees, the Angle Uniformity Index (Wi) was used, which is based on the measurement of angles between two trees neighboring the reference tree i and their comparison with the standard angle α; so that if four neighbors to the reference tree are considered, the Wi can take values of 0 to 1, where a value close to zero represents conditions of regularity, values close to 0.5 imply a tendency to randomness, and values close to one signify clustering of species.

In the present study, a standard angle of 72º was used for the estimation of the Wi, because in the simulations of ^{Gadow and Hui (2002)} this value was defined as the optimal standard angle, with an average of the Wi = 0.5 for a random distribution.

The variation in tree size was quantified with the Dominance Index (Ui) (^{Aguirre-Calderón et al., 2003}), which is defined by the ratio of the four neighbors with different diameters to the reference tree. As with the other structure indices used, the values vary from 0 to 1: Ui = 0, if the four neighbors are larger than the reference tree i (deleted); Ui = 0.25, if three of the neighbors are larger than the reference tree i (intermediate); Ui = 0.50, if two of the neighbors are larger than the reference tree i (co-dominant); Ui = 0.75, if one of the neighbors is larger than the reference tree i (dominant), and Ui = 1, if none of the neighbors is larger than the reference tree i (very dominant). The five values of Ui correspond to the social classes developed by ^{Kraft (1884)}. Table 1 shows the formulas for the structure indexes used.

The statistical analysis of the structure indexes was performed by means of a Student's t-test with the mean of the values obtained in each evaluation period (first and second inventory) (^{Silva-González et al., 2021}). Once the normality of the data for each index was obtained, a comparison was used to determine whether there are significant differences between evaluation periods, with a confidence level of 95 %. Statistical procedures were performed with the IBM SPSS Statistics 25 statistical package (Statistical Package for the Social Sciences).

Elimination of the border effect

The structure indexes were estimated using the SAS statistical program (^{Statistical Analysis System Institute, 2009}). The calculation of the indexes analyzed in this work will always be biased to those trees that stand close to the edges of the sites, the reason being that these individuals are problematic because their potential neighbors may be located outside the area of interest. The nearest neighbor edge correction method proposed by ^{Pommerening and Stoyan (2006)} was implemented in order to eliminate the edge effect and obtain unbiased information of the structural variables. By reducing the number of reference trees and assessing whether all n nearest neighbors of tree i are located within the observation sites; individuals located very close to the edges of the research site were eliminated.

The four nearest neighbors to a reference tree were listed in ascending order according to their distance; thus, all reference trees whose mean distance to the fourth tree was greater than the distance to the nearest edge were ignored.

Diversity

According to the Shannon-Wiener Index in the first and second inventories (H'₁ = 1.86 and H'₂ = 1.94), there were no significant statistical differences when Hutcheson's t-test was applied, α = 5 % (t = 0.026).

Ecological indicators

The total density of individuals showed an increase of 9.67 trees ha^-1, but without significant differences (p = 0.268). The most abundant genus was Pinus, with 381.33 trees ha^-1, which represented 68.14 % of relative abundance (RA) in the first inventory; value that decreased for the second sampling to 355.33 trees ha^-1 and 62.41 % RA. Quercus spp. exhibited an increase of 20 trees ha^-1, which corresponded to 3.17 % of RA; Arbutus increased by 4.67 trees ha^-1 (0.75 % de AR); Juniperus and Alnus increased their density with 2.33 and 8 trees ha^-1, respectively, corresponding to 0.34 and 1.34 % of RA (Table 3).

The dominance represented by basal area (BA) showed an increase of 1.44 m² ha^-1, with no significant statistical differences (p = 0.73) between evaluation periods. At the genus level, Pinus presented the highest values of basal area, 18.41 m² ha^-1 in the first sampling and 18.34 m² ha^-1 in the second, with a decrease of 0.08 m² ha^-1 corresponding to -4.11 % of relative dominance (RD); Quercus increased by 1.02 m² ha^-1 (2.56 % de RD); Arbutus and Juniperus registered an increase of 0.17 m² ha^-1 and 0.14 m² ha^-1, with a RD of 0.48 % and 0.42 %, respectively.

Pinus durangensis Martínez and Quercus sideroxyla Bonpl. were present in all sites in both inventories, and their highest relative frequency (RF) corresponded to 13.48 % in the first inventory and 12.12 % in the second. Abies durangensis, Juniperus durangensis, and Pinus engelmannii were recorded in the first inventory, with 1.12 % RF for each, but were displaced in the next measurement; in contrast, for the second inventory, Pseudotsuga menziesii and Prunus serotina were incorporated, representing a RF of 1.01 %. In general, Pinus presented a decrease in relative frequency of 6.79 %, Quercus, of 0.02 %, and Juniperus, of 0.91 %; the genera Arbutus and Alnus increased their RF values by 4.47 % and 1.34 %, respectively. This behavior is due to the silvicultural treatment applied, which is specifically aimed at Pinus taxa.

The highest IVI in both measurements corresponded to P. durangensis, followed by Q. sideroxyla and P. cooperi C. E. Blanco. Pinus presented an IVI of 62.43 % in the first inventory, which was lower than the IVI of the second (56.89 %), with a decrease of 5.54 %; the IVI of the Juniperus genus decreased 0.5 %; while Quercus and Arbutus registered an increase of 1.6 %, and Alnus, an increase of 1.12 % (Table 3).

Structure composition

Table 4 summarizes the number of individuals registered in the two inventories per site, in addition to the values for each of the indices used (species mixture, angle uniformity and dominance) and the average for each of them. Site 6 exhibited the lowest values of species mixture in both samplings (Mi ₁ = 0.173, Mi ₂ = 0.311); in contrast, the highest values were registered at sites 4 and 11. The Student's t-test performed to compare the means between evaluation periods showed no significant differences, which indicated that the selection method applied at the sites did not modify the existing species mix (p = 0.081).

The spatial distribution analysis showed several changes between pairs of sites; however, there are no significant statistical differences (p = 0.971). The distribution of species was maintained. Most of the plots had a random distribution with a tendency to form clusters. ^{Gadow and Hui (2002)} values below 0.475 suggest a regular distribution, and those above 0.517 suggest a random distribution with a tendency to form clusters, which coincides with what was observed for most of the sites in this study, as well as for the average for each evaluation period (Wi = 0.531).

The dominance index did not reflect changes in tree diameter dimensions, according to p = 0.073, with no significant differences between evaluation periods; the averages obtained UI ₁ = 0.512 and UI ₂ = 0.521, for the first and second inventory, respectively, indicate that the sites have trees of different sizes, so that any selected tree can have two neighbors with a larger diameter and two with a smaller diameter, a characteristic of the irregular forests under management in the state of Durango (^{Soto-Cervantes et al., 2021}).

Diversity

The average values recorded according to the Shannon-Wiener index (H' ₁ = 1.86 and H' ₂ = 1.94) are higher than those cited by ^{Hernández-Salas et al. (2013)}, in a cool temperate forest with silvicultural practices using the selection method in the El Largo ejido y Anexos, in the Madera municipality of Chihuahua, Mexico, in three assessments, conducted in the years 1986 (H' ₁ = 0.400), 1996 (H' ₂ = 0.401) and 2006 (H' ₃ = 0.347), and that documented by ^{Solís-Moreno et al. (2006)} for a temperate forest in Tepehuanes, Durango, where a value of H' = 1.21 was reported. The same is true for other similar studies. Thus, ^{Ramírez-Santiago et al. (2019)} obtained a value of H' = 1.25, when the group selection method was applied in a temperate forest in the Sierra de Oaxaca; ^{Vásquez-Cortez et al. (2018)} registered an H' = 1.14 for an area intervened with a root killer in Ixtlán de Juárez, Oaxaca, and ^{Návar-Cháidez and González-Elizondo (2009)} cite a H' = 0.55 in an area with 100 % removal of the basal area, intervened 15 years before the tree assessment, in San Dimas municipality, Durango.

The difference in the Shannon-Wiener index values obtained in this study, with respect to the results of various authors, is due to a greater diversity of species recorded and to the proportions of each one of them.

Hutcheson's t-test revealed that there are statistically no significant changes in species diversity between evaluation periods, which indicates that despite the application of the selection method no major changes occur. This finding differs from those of the records of ^{Hernández-Salas et al. (2013)}, who point out that the tree diversity recorded in 2006 is different from that determined 10 and 20 years earlier, with greater diversity in 1986 and 1996. The above responds to the number of trees ha^-1 and the RA of each species in the evaluation periods; in the SPFyS evaluated in Durango, a difference of ten individuals was obtained in the ten-year period, while ^{Hernández-Salas et al. (2013)} registered higher values.

Ecological indicators

The total density of individuals did not show significant changes over the 10-year period, with an increase of 9 trees ha^-1; ^{Hernández-Salas et al. (2013)} cite a reduction of 179.35 trees ha^-1 from 1996 to 2006, and of 45 trees ha^-1 from 1986 to 1996, but without significant statistical difference (F = 2.865, gl = 2, P = 0.060).

The total basal area increased from 25.58 to 27.02 m² ha^-1; ^{Hernández-Salas et al. (2013)} document basal area increases of 4.12 m² ha^-1 from 1986 to 1996, and a decrease of 1.54 m² ha^-1 in the period from 1996 to 2006; in both studies, the genus Pinus presented the highest values of basal area (BA) and relative dominance (RD).

In the present investigation, P. durangensis had the highest values in DR: 51.18 % and 47.43 % for the first and second measurement, respectively; while ^{Hernández-Salas et al. (2013)} registered P. arizonica Engelm. with values of 67.02 %, 68.36 %, and 68.61 % RD in their three evaluations.

The Quercus genus increased its RD values from 22.52 % to 25.05 %; this is due to the fact that, in the selection treatment, Pinus individuals are mainly used because they are the most commercially valuable; ^{Hernández-Salas et al. (2013)} reported a reduction in RD in Quercus spp. from 15.1 % in 1986 to 5.4 % in 2006, due to the application of silvicultural interventions that favor the development of other genera, particularly Pinus, as it is the dominant genus in the region. ^{Ramírez-Santiago et al. (2019)} recorded an increase in BA of 5.95 m² ha^-1 for an area intervened by the group selection method during a 5-year evaluation period; in addition, a decrease of 4.43 m² ha^-1 in an area intervened by the parent tree method during the same period.

The most important ecological species was P. durangensis, with an IVI of 33.66 % after the silvicultural intervention; this species has been indicated as the one with the highest ecological value by ^{Hernández-Salas et al. (2013)} and ^{Graciano-Ávila et al. (2017)}. At the genus level, Pinus presented an IVI of 56.89 %, a lower value than those documented by ^{Alanís-Rodríguez et al. (2011)}, ^{Hernández-Salas et al. (2013)}, and ^{López-Hernández et al. (2017)}, who cite values higher than 80 % in forests of Nuevo León, Chihuahua and Puebla, respectively. ^{Rendón-Pérez et al. (2021)}, in an analysis of three tree associations dominated by Pinus montezumae Lamb., Pinus pseudostrobus Lindl. and Pinus patula Schiede ex Schltdl. & Cham., operated under the Silvicultural Development Method obtained the following IVI values: 67.5, 45.8, and 62.2 %, respectively.

Structure composition

The average value of the Mi after silvicultural intervention was 0.57, which indicates that, more often than not, out of every four neighbors to the reference tree, two are of the same species and two differ from each other. ^{Castellanos-Bolaños et al. (2008)} indicate a Mi = 0.69 for an old forest condition in Ixtlán de Juárez in Oaxaca; i.e., on average, of the four closest neighbors to the reference tree, three belong to different species; ^{Castellanos-Bolaños et al. (2010)} obtained an Mi = 0.346 for an average of five circular sites of 500 m², in a community of Pinus rudis Endl. The above indicates that most of the trees have one or two neighbors of different species. In the study documented here, site six presented a similar value (Mi = 0.311), and it is assumed that there is a clear dominance of P. durangensis.

^{Solís-Moreno et al. (2006)} recorded values of Mi = 0.30 and Mi = 0.44 for plots intervened by thinning and selective cutting, respectively; values lower than the average obtained in this study: Mi = 0.539 for the first inventory, and Mi = 0.57 for the second inventory. Species abundance is more heterogeneous in sites with thinning treatments, as these favor the growth of species of higher commercial value (^{Solís-Moreno et al., 2006}). ^{Silva-González et al. (2021)} cite average values of Mi = 0.51 for 10 sites evaluated over a 5-year period under thinning management in the Sierra de Durango.

According to the average values of Wi = 0.531 in both measurements, the spatial distribution in the SPFyS studied turned out to be random, but with a tendency to form clusters; ^{Solís-Moreno et al. (2006)} cite a spatial distribution in aggregates with values of Wi = 0.57; ^{Castellanos-Bolaños et al. (2008)} document a random distribution (Wi = 0.54) in a plot with medium forest condition. ^{Aguirre-Calderón et al. (2003)} register random distributions (Wi = 0.50, 0.52, and 0.5) on three plots excluded from forest management for coniferous forests in Durango; ^{Pommerening (2002)} reports a random distribution (Wi = 0.57) for adult plantations dominated by Quercus petraea (Matt.) Liebl. and Fagus sylvatica L., in the German federal state of Rhineland-Palatinate. Random distributions are more common in areas without intensive management (^{Aguirre-Calderón et al., 2003}; ^{Corral-Rivas et al., 2005}; ^{Solís-Moreno et al., 2006}); whereas, regular distributions are often the result of treatments such as thinning, since their objective is to eliminate competition and provide equal growing space for the remaining species. This did not occur in the present research, because individuals were removed, leaving space for the new growth, so that the spatial structure tends to be occupied by new individuals.

The dominance index exhibited average values close to 0.5, which indicates that the vegetation is heterogeneous, and two of the trees closest to the reference tree are larger and two are smaller; these values are characteristic of forests managed by selection methods, in which individuals of different diameter categories can be found. ^{Solís-Moreno et al. (2006)} registered values of UI = 0.44 in a plot treated by the selection method; ^{Castellanos-Bolaños et al. (2008)} indicate UI values of 0.52 for the pole stand; of 0.56 for young shafts; of 0.70 for the mid-range shafts, and of 0.83 for old forests. This is because, as the tree stand develops, so does the dominance of a certain species, until, in the old-growth condition, it becomes the dominant taxon, and three of its nearest neighbors are thinner than the reference tree.