Study area

The research was carried out in the Cerro Mohinora Natural Protected Area (NPA), located in Guadalupe y Calvo municipality, Chihuahua, northwestern Mexico (between 25°40'48'' and 26°13'12'' N and 106°31'48'' and 107°06'00'' W) (Figure 1). Average annual precipitation varies between 200 and 1 800 mm, with a monthly average of 0-40 mm in the driest month. The average annual temperature varies from 5 to 12 °C, with an average of -3 to 18 °C in the coldest month (^{Arriaga et al., 2000}).

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

Sampling design

A total of 37 circular sampling sites with a size of 1 000 m² each were established randomly and distributed in six north-facing stands, because in this exposure there are mostly populations of such genera as Pseudotsuga, Picea and Abies. These genera are of conservation interest due to their protected status (^{García-Arévalo, 2008}; ^{Semarnat, 2019}) at an altitude gradient ranging from 2 200 to 3 200 masl, where three altitude levels were defined to cover the maximum altitudinal range, and the different types of vegetation registered in the management program of the NPA (^{Conanp, 2017}): Level 1 (2 200-2 600 m), Level 2 (2 600-2 800 m), and Level 3 (2 800-3 200 m). Two stands were considered at each altitude level to include the different vegetation types present, and a sampling intensity of 2 % was applied.

In each of the 1 000 m² sites, mensuration information of the tree stratum was collected, focusing on individuals with a normal diameter (ND) ≥7.5 cm. The tree variables recorded included total height (h) and ND. The height was estimated using a Suunto^® Pm-5 clinometer, while the normal diameter was measured using a Haglöf^® Mantax Blue aluminum caliper. The distance from the trees to the center of the site was recorded with a 20 m Truper^® TP20ME tape measure. In addition, a Brunton GEO^® Pocket compass was used to obtain the azimuth. The correct nomenclature and identity of the species was verified using the Tropicos^® platform (^{Tropicos, 2022}).

Data analysis

The spatial distribution patterns were determined with structural parameters based on the relationships between a reference tree (i) and its four nearest neighbors, which appropriately expresses the spatial structural characteristics of the plant communities and allows the design of more appropriate management practices for the specific conditions of the forests (^{Hui and Gadow, 2002}; ^{Pastorella and Paletto, 2013}; ^{Rubio-Camacho et al., 2023}).

According to ^{Gadow et al. (1998)}, the angle uniformity index (W _i ) is based on the measurement of the angles between neighbors to a reference tree i and their comparison with a standard angle α, and acquires values from zero to one; a value close to zero reflects regularity; values close to 0.5 show a predisposition to randomness, and those close to one indicate clustering scenarios.

Where:

W _i = Index value for the reference tree j ^th

n = Number of neighboring trees considered

V _ij = Variable 1 when the j ^th angle α between two next neighboring trees is less than or equal to the standard angle α, otherwise, it takes a value of 0

The species mix was determined based on the species mix index (M _i ). ^{Füldner (1995)} defines it as the proportion of the nearest neighbors n that are not of the same species as the reference tree.

Where:

M _i = Index value for the reference tree j ^th

n = Number of neighboring trees considered

V _j = Equal to 0 when the tree j belongs to the same species as reference tree i, and equal to 1 otherwise (^{Gadow et al., 2007}).

The height dominance between genera was tested with the size dominance index (U _i ), which reflects the proportion of neighboring trees that are smaller than the reference tree i (^{Gadow et al., 1998}).

Where:

U _i = Index value for the reference tree j ^th

n = Number of neighboring trees considered

V _j = Equal to 1 if the tree j is smaller than the reference tree i, and 0 otherwise

With four neighboring trees, the (U _i ) dominance index takes five values and is useful for interpreting the relative dominance of a species or genus (^{Aguirre et al., 2003}; ^{Gadow et al., 2007}).

The indexes were analyzed using the R Studio software (Versión: 2023.09.1+494) (^{R Core Team, 2019}), within an observation window (W) (sampling sites) where the previously described formulas are run. In this observation window, the edge effect was considered. This effect plays an important role in the proper interpretation of the spatial structure, as within the sampling sites there are trees that are located close to the edge, while their nearest neighbors are regularly located outside the edge, which results in errors in the estimation of the neighborhood values of the trees that are inside the sampling sites (^{Pommerening and Stoyan, 2006}).

In order to prevent these errors, the nearest neighbor edge correction estimator (NN1: Nearest-neighbour edge-correction concepts) was applied, which consists of excluding as reference tree (i) those whose distance to their j ^th nearest neighbor is less than the distance between (i) and the edge of the sampling site (W). Also, those trees may be part of other close neighboring structural groups (^{Pommerening and Stoyan, 2006}).

Statistical analysis

All indexes, graphs and statistical analyses were performed with the R software (^{R Core Team, 2019}). The means and their 95 % confidence intervals (CI) were calculated by site and altitude level using BOOTSTRAP simulations (999). In addition, the statistical contrasts between treatments were determined with the percentile method of the BOOTSTRAP distribution for two independent samples, using the pb2gen function in R (^{Mair and Wilcox, 2020}).

Mensuration characteristics

Table 1 shows the means of the estimated mensuration variables for all the species recorded. Four Pinus species were present in Level 1. No individuals of the species Pinus engelmannii Carrière were observed in levels 2 and 3, because its distribution range varies from 1 600 to 2 600 m (^{Jiménez and Méndez, 2021}). The opposite was the case for the density of individuals of Pinus durangensis Martínez and P. strobiformis Engelm. in Level 2, where it is higher than in levels 1 and 3, as these pines develop optimally at altitudes equal to or above 2 400 masl (^{Pérez-Olvera and Dávalos-Sotelo, 2008}). In the case of Quercus, four species reached their highest density at Level 1 (2 200-2 600 m) and decreased in number or were absent at levels 2 and 3; this reduced occurrence at higher altitudes may be ascribed to the fact that usually, Quercus species are not abundantly distributed at altitudes around 2 800 and 3 000 masl (^{Martínez-Calderón et al., 2017}; ^{Uribe-Salas et al., 2019}).

It is important to note that the presence and patterns of vegetation along altitude gradients are generated by virtue of the complex interaction of various factors such as altitude, exposure to solar radiation, and the topographic position of plant populations, among other observable elements (^{Girardin et al., 2014}; ^{Jadán et al., 2017}; ^{Cabrera et al., 2019}).

In this sense, a significant dominance of Abies durangensis Martínez and Pseudotsuga menziesii (Mirb.) Franco is observed at Level 3, where environmental conditions are adverse for most Pinus and Quercus species, as altitude influences temperature and humidity both in the environment and in the soil. This can result in reduced growth of individuals, reduced regeneration survival, impact on seed viability, and deterioration of vegetation vitality (^{Champo-Jiménez et al., 2012}; ^{Gutiérrez and Trejo, 2014}; ^{Villanueva-Díaz et al., 2018}).

Spatial distribution of trees in the altitudinal gradient

Figure 2 illustrates the spatial distribution of trees in each of the Level 1 sites based on the NN1 estimator, which means that only those trees that could be considered as tree i of the structural group are represented. A total of 393 structural groups consisting of a reference tree and four neighboring trees were used in the analysis of the neighborhood indexes. Furthermore, the Quercus and Pinus genera were identified as having the highest number of structural groups, amounting to 192 and 141, respectively.

Figure 2 Spatial distribution of trees in each of the sites by genus at Level 1. 

On the other hand, Figure 3 shows the spatial distribution of trees in each of the Level 2 sites. 183 structural groups were included in this analysis. Sites 2, 8, and 1 had the highest number of clusters with 36, 28 and 27, respectively. In this case, Pinus was represented in terms of structural groups by 51, while Quercus was part of only one structural group.

Figure 3 Spatial distribution of trees in each of the sites by genus at Level 2. 

Finally, Figure 4 shows the spatial distribution of trees in each of the Level 3 sites, in which 403 structural groups were considered. As for Pinus species, 26 structural groups were registered for P. arizonica Engelm., 12 for P. strobiformis, and three for P. durangensis. No structural groups were obtained for Quercus sideroxyla Bonpl., the only oak species present at this altitude.

Figure 4 Spatial distribution of trees in each of the sites by genus at Level 3. 

It was observed that, the lower the tree density, the lesser the number of structural groups, as shown in Level 2, however, the distance between trees is also a determining factor. ^{García-García et al. (2021)} cited 203 groups for a density of 254 N ha^-1 in a Pseudotsuga menziesii forest with presence of Pinus and Quercus. ^{Rubio-Camacho et al. (2017)} carried out a genus analysis and identified a total of 213 Pinus and 193 Quercus clusters in one of the studied plots. In the second plot, 129 Pinus and 189 Quercus clusters were recorded. These results were associated with densities of 242 and 211 individuals per hectare, respectively. ^{Castellanos-Bolaños et al. (2010)} document between 123 and 365 groups for various Pinus-Quercus associations, with the exception of the association dominated by Pinus patula Schltdl. & Cham., for which they obtained 1 176 groups.

Angle uniformity index (W_i)

According to an overall analysis of W _i , the structural groups of the Pinus and Quercus genera exhibited contrasting results (Figure 5): on the one hand, Pinus structural groups occurred at all three altitudinal levels, while Quercus groups, only at levels 1 and 2. Quercus registered a mean value of 0.545, with a confidence interval (CI) of 0.498, 0.609; while Pinus obtained a W _i =0.527 [CI, 0.493, 0.57] at Level 1, although this difference was not statistically significant. At Level 2, Pinus (W _i =0.53 [CI, 0.469, 0.611]) did exhibit a significant difference (d=0.28 [CI, 0.22, 0.35], p<0.001], unlike the Quercus group (W _i =0.25 [CI, 0.25, 0.25]).

Figure 5 Angle uniformity index (W _i ) by genus and altitude level. 

The specific analysis showed that Pinus species maintain a mean of approximately 0.50, with the exception of P. strobiformis in Level 1, where it exhibited a mean of 0.66 [CI, 0.47-0.84]. It should be noted that P. engelmannii did not occur at sites 2 and 3.

The same trend was observed for the Quercus species, as all four species present had average uniformity values, although the average index for Q. sideroxyla decreased to 0.25 [CI, 0.25-0.25]. The mean uniformity in both genera indicates that two of the four neighboring trees have an angle of less than 90° with respect to the reference tree, resulting in a random distribution.

This index has been applied in forests under conservation near the study area, where both Quercus (=0.47 [CI, 0.39-0.53]), and Pinus (=0.49 [CI, 0.40-0.57]) have a random distribution (^{García-García et al., 2021}). Likewise, ^{Rubio-Camacho et al. (2017)} indicate that the average value for two evaluated plots in a pine-oak forest is 0.49. ^{Graciano-Ávila et al. (2020)} cite the same distribution in Pinus and Quercus dominated forests in Durango, Mexico.

Species mix index (M_i)

The spatial mix of species also shows contrasting results among the analyzed groups (Figure 6). In first place, Quercus registered a mean value of 0.559 [CI, 0.385, 0.724], while Pinus had a M _i =0.545 [CI, 0.432, 0.645] at Level 1, with no statistically significant difference. At Level 2, Pinus (M _i =0.673 [CI, 0.509, 0.844]) did exhibit a significant difference (d=0.321 [CI, 0.168, 0.493], p<0.001) in relation to the Quercus group with an M _i equal to 1. This indicates that Quercus is surrounded by trees of different genera.

Figure 6 Species mix index (M _i ) by genus and altitude level. 

Particularly, the Pinus species with the highest degree of mixing are Pinus strobiformis (P1 =0.87, P2 =0.66 y P3 =0.87) and P. durangensis (P1 =0.86, P2 =0.85 y P3 =1.00), these values indicate that most of the reference trees are surrounded by individuals of species other than the reference tree.

Conversely, P. arizonica (=0.45) and P. engelmannii (=0.36) showed less mixing in P1, while in levels 2 and 3 P. arizonica expanded its mix to =0.66 and =0.71, respectively. Quercus crassifolia Bonpl. (=0.59), Q. fulva Liebm. (=0.73), and Q. rugosa Née (=0.68) exhibited a medium-high degree of mixing in P1, where only Q. sideroxyla had a low degree of mixing (=0.28), that is, it corresponds to a species that is usually surrounded by individuals of the same species or with a tendency to group together.

The mixing index (M _i ) has been evaluated in several temperate forests of the country with predominance of Pinus and Quercus, in which lower mean values of mixing than those documented herein have been recorded. In comparison, the forest that is the object of the present study have an outstandingly high diversity and coexistence of species, except for P. arizonica and P. engelmannii in P1, which have a similar or lower value (^{Castellanos-Bolaños et al., 2010}; ^{Graciano-Ávila et al., 2020}; ^{Silva-González et al., 2022}).

Height dominance index (UHi)

The height dominance index showed that Pinus species tended to be medium to high; its highest average value of UH _i of 0.633 [CI, 0.556, 0.705] was recorded at Level 1, while Quercus had 0.396 [CI, 0.305, 0.503]. These differences were statistically significant (d=0.235 [CI, 0.108, 0.357], p<0.01) and were repeated at Level 2 (d=0.293 [CI, 0.204, 0.390], p<0.001) with Pinus as the dominant genus, having a UH _i =0.541 [CI, 0.452, 0.632], unlike Quercus, which exhibited a UH _i =0.25 [CI, 0.25, 0.25] (Figure 7).

Figure 7 Distribution of the height dominance index (UH _i ) of Quercus species by altitudinal level. 

The dominance of P. durangensis stands out, having obtained an average of =0.82, =0.52, and =0.75 for levels 1, 2, and 3, respectively; these values show that when this species is a reference tree, it tends to be taller than its closest neighbors. The rest of the taxa in the three levels had means of 0.41-0.63, with the exception of P. arizonica, whose mean value in P2 (0.34) was low. Quercus species maintained a downward trend, among them Q. sideroxyla obtained the highest mean (=0.42) in P1, which showed that this species regularly has a lower height than its neighbors.

The results obtained herein agree with those reported by other authors, who also evaluated temperate forests, and indicate that structural groups dominated by Pinus are dominant in height (^{García-García et al., 2021}); while Quercus tends to surround itself with much larger neighbors (^{Rubio-Camacho et al., 2017}). A decrease in the mean number of Pinus individuals was observed at levels 2 and 3, which may be due to the fact that at these levels the forest is dominated in density by other genera such as Pseudotsuga and Abies, which tend to be taller (Table 1).