Introduction

The characterization of the habitat of forest species is important for understanding their geographical distribution, abundance or presence at a given location. This information is helpful for making appropriate decisions when implementing conservation, integral management or preventive actions to counteract the degradation of the habitat or the extinction of the plants (^{Anderson et al., 2003}). Some of the most widely used variables are climatic, physiographic and edaphological (^{Guisan and Zimmermann, 2000}; ^{Arundel, 2004}; ^{González-Espinosa et al., 2004}) primarily, temperature, precipitation, altitude, slope and geographical orientation (^{Pliscoff and Fuentes-Castillo, 2001}; ^{Antúnez et al., 2017b}). Different methods are used for studying the relationship between these factors and the distribution and abundance of plants, including the correlative mathematic tools. Examples of these are the correlation analyses (^{Bravo et al., 2008}; ^{Bravo-Iglesias, 2010}), utilized in the forest area for identifying relevant population parameters or environmental factors that are important for the distribution and abundance (^{Bravo-Iglesias, 2010}; ^{Martínez-Antúnez et al., 2013}).

Multivariate analyses, in their various modalities, often applied to reduce the number of variables (^{Buira, 2017}; ^{Guisan et al., 1999}); multiple regression analysis, used to detect the factors with greatest influence on the abundance of plants (^{Martínez-Antúnez et al., 2015}), and generalized linear models (^{Guisan et al., 1999}). These three methods have yielded satisfactory results in similar studies, by identifying, out of a set of variables, those that significantly affect a variable of interest (^{Arredondo-Figueroa et al., 1984}; ^{Guisan et al., 1999}); this, in turn, makes it possible to distinguish high-impact covariables that may condition those localities where the forest species of interest are distributed (^{Araújo and Guisan, 2006}; ^{Antúnez et al., 2017a}).

On the other hand, 95 % of all forestry activities are concentrated in temperate forests, primarily in pine, pine-oak or oak-pine forests (^{Masera et al., 1997}). In this regard, the Northern Sierra of Oaxaca is one of the regions of southeastern Mexico where forestry activity has increased in the last decades, in keeping with an equally growing regional market (^{Castellanos-Bolaños et al., 2008}). Pinus patula Schiede ex Schltdl. et Cham and Pinus pseudostrobus Lindl. (currently known as Pinus oaxacana Mirov. by forest managers) stand out for their commercial interest (^{Antúnez et al., 2017a}), despite the prevalence of broadleaf species, particularly of the genus Quercus, for which, nevertheless, there is no stable or safe market (^{Alfonso-Corrado et al., 2014}).

The objective of this study was to identify the environmental variables that significantly affect the density of the ten most prevalent native forest species in Santiago Comaltepec, a locality of the Northern Sierra of Oaxaca. Three analysis methods were used for this purpose: non-parametric correlation coefficient, principal component analysis and generalized linear models.

Materials and Methods

The research was carried out in the forests of Santiago Comaltepec, located in the Northern Sierra of Oaxaca, in southeastern Mexico, between the coordinates 17°34’32’’ N and 96°29’45” W, at an altitude of 1 924 to 3 000 masl, on a surface area of approximately 26.5 km² (Figure 1). The predominant types in the area are humid temperate, humid warm and humid semi-warm, with summer rains and a mean annual temperature of 9.5 °C and 16.2 °C. The most common types are: Acrisol, Luvisol and Cambisol (^{Conabio, 1999}; ^{Inegi, 2012}).

Figure 1 Location of the study area. 

The ten most abundant tree species that turned out to be the most representative of Santiago Comaltepec and adjoining localities (San Pedro Yólox, San Juan Bautista Valle Nacional, Ayotzintepec, Ixtlán de Juárez, San Pablo Macuiltianguis and San Juan Quiotepec) were: Alnus acuminata Kunth, Alnus firmifolia Fern, Pinus ayacahuite C. Ehrenb. ex Schltdl., Pinus hartwegii Lindl., Pinus teocote Schiede ex Schltdl. et Cham., Quercus crassifolia Bonpl., Quercus laurina Bonpl., Quercus rugosa Née, Arbutus xalapensis var. pubescens Benth. and Prunus serotina Ehrh. subsp. capuli (Cav. ex Spreng.) McVaugh.

The data were collected in 433 privately-owned 1 000 m² round plots, systematically distributed according to such conditions as vegetation type, relief and quality of the season. This study utilized the same sampling design as the owners and forest managers in order to quantify the volumetric stock of extractable lumber. The tree species occurring in each plot were identified; individuals with a diameter equal to or above 7.5 cm (at 1.3 m above the ground) were counted, as the diameter was considered to be an indicator of both survival and growth (^{Sáenz et al., 2010}).

The density (number of individuals per plot) was used as indicator of abundance (^{Martínez-Antúnez et al., 2013}; ^{Antúnez et al., 2017a}). A total of 23 environmental variables were included; their acronyms and descriptive statistics are shown in Table 1. The climate records were obtained using a modeler of the Forest Service, Department of Agriculture of the United States, which estimated accurate values for each sampling unit based on a climate record of little more than 6 000 weather stations in Mexico, the south of the United States, Guatemala, Belize and Cuba, from 1961 to 1990 (^{Crookston et al., 2008}; ^{Sáenz-Romero et al., 2010}). The slope and exposure were measured in field with a Sunto^TM clinometer, and the altitude was registered using a Garmin^TM Global Positioning System (GPS) receiver.

Results and Discussion

The principal component analysis revealed that the variables that account for the largest percentage of variability of the abundance of Alnus acuminata, A. firmifolia, Pinus ayacahuite, P.teocote, Quercus crassifolia, Q. rugosa and Arbutus xalapensis were the temperatures above 5 °C (GSDD5 and DD5), the mean annual precipitation (MAP), the height above the sea level (HASL) and the April-September precipitation, with 96.5 % variability. This precipitation period is important for the plants because it coincides with the increase in the vegetative activity (^{Sáenz-Romero et al., 2010}; ^{Martínez-Antúnez et al., 2013}; ^{Antúnez et al., 2017b}). The rest of the variables accounted only for 3.4 % of the variability of the data (Figures 2A and 2B). For the abundance of P. hartwegii, Q. laurina and Prunus serotina, the most relevant variables were GSDD5, MAP, DD5, GSP and HASL (97.73 %). The rest accounted only for 2.13 % of the variability (Figure 2C and 2D).

Contribución = Contribution; Conponente = Component

The seven most important variables for Pinus ayacahuite (B) and the seven most important for Pinus hartwegii, Pinus serotina and Quercus laurina (D). GSDD5 = Degree-days > 5 °C accumulating within the frost-free period; DD5 = Degree-days > 5 °C; PMA = Mean annual precipitation (mm) (MAP),GSP = April to September precipitation; HASL = Height above the sea level; SMRP = Summer precipitation; WINP = Winter precipitation.

Figure 2 Variables that most contributed to explain the variability of Pinus ayacahuite C. Ehrenb. ex Schltdl. (A) and of P. harwegii Lindl. (C), according to the principal component analyses.  

Each species is affected by different variables (tables 2 and 3); for example, the mean annual precipitation and the April-September precipitation exhibited high coefficients, with an abundance of Q. laurina (0.99-0.99), P. ayacahuite (0.85-0.86) and P. hartwegii (0.99-0.99), but not with A. acuminata or A. xalapensis, which had low or null correlations (0.09-0.10) (0.001) (Table 2). Likewise, the abundance of Q. laurina, P. ayacahuite and P. hartwegii were significantly correlated (0.85 to 0.99) with the precipitations during spring, summer and winter (SPRP, SMRP and WINP), in agreement with authors like ^{Jabro et al. (2010)}, ^{Wittmer et al. (2010)} and ^{Meng et al. (2011)}, who highlight the importance of the intensity and the magnitude of the rains, as well as of the precipitation period, on the distribution of the plants.

Furthermore, the slope and the exposure had high levels of association with certain species like Arbutus xalapensis (0.97), Alnus firmifolia (0.85-0.81), P. ayacahuite (0.96-0.99) and P. teocote (0.92); conversely, low values were observed with A. acuminata (0.12), P. serotina (0.18) and P. hartwegii (0.01-0.46). As for the variables that exhibited high, significant coefficients, several did not contribute significantly to the generalized models. This suggests a poor causal relationship (Table 3), given that the incidence of most of the variables may have an indirect impact, enhancing or inhibiting those variables that may have a direct effect (^{Antúnez et al., 2017b}). Variables with low associations indicate a limited linear relationship. For example, physiographic variables exhibited low, non-significant coefficients for most species, consistently with the findings of ^{Martínez-Antúnez et al. (2013)}, who cite very low association coefficients (<0.70) between the physiographic variables exposure and slope and the abundance of the species. In this study, only 35 out of 72 taxa exhibited significant coefficients (p<0.05). However, in other studies, physiographic variables like altitude or terrain slope play an important role in the distribution of pine and oak taxa, as in the case of Q. glaucescens Bonpl., Q. elliptica Née, Q. corrugata Hook., Q. ocoteifolia Liebm. and Q. macdougallii Martínez in Chinantla (^{Poulos and Camp, 2005}; ^{Meave et al., 2006}), or exposure, as in the case of Quercus potosina Trel. and Juniperus deppeana Steud. in Sierra Fría, Aguascalientes, where the northern exposure proved adequate for both species (^{Díaz et al., 2012}).

The generalized models indicated that at least one variable has a significant effect on the abundance of seven species (p<0.05), which implies a potential causal relationship between these variables and the abundance of the taxa (Table 3). Thus, the mean annual temperature, the mean annual precipitation and the terrain slope were the most important variables for Alnus acuminata (Table 3). Slope was the only variable with significant effects on the seven species (Table 3). There were few variables that had a limited linear relationship with the abundance of forest species in the study area; this was pointed out also by ^{Antúnez et al. (2017a)}, who ascribed this fact to the rough, uneven topography of the study area, resulting in different microclimates even within distances of 200 m (^{Antúnez et al., 2017a}).

The results of the principal components analysis showed that the most important variables for the abundance of most species is temperature above 5 °C; however, it is uncertain whether this relationship is causal or merely a correlation. Several results of this analysis agreed with those yielded by the correlation analysis, particularly in regard to temperature above five degrees, with significant coefficients for the abundance of A. xalapensis, A. acuminata and Q. rugosa, whose values ranged between 0.81 and 0.96 (Table 2).

The volume and intensity of the rainfall is one of the key factors in the distribution and abundance of forest vegetation; for example, according to ^{Álvarez-Moctezuma et al. (1999)}, the precipitation and altitude variables are the most important for the distribution of Quercus peduncularis Née, Q. polymorpha Schltdl. et Cham, Q. rugosa, Q. sebifera Trel. and Q. segoviensis Liebm. in the Central Plateau of Chiapas, Mexico. In the present study, the mean annual precipitation and the April-September precipitation accumulated mean were significantly correlated to P. ayacahuite (0.86-0.85), P. hartwegii (0.99-0.99) and Q. laurina (0.99-0.99) (Table 2), which suggests that these three would be the taxa most severely affected by a modification of the above variables (^{Sáenz-Romero et al., 2010};^{Antúnez et al., 2017a}).

As for precipitation, results suggest that the April-September precipitations have a stronger impact than the mean annual precipitation on the abundance of P. ayacahuite, P. hartwegii and Q. laurina, with coefficients above 0.85 (Table 1). The influence of precipitation in various seasons (spring, summer, winter or April-September) on the abundance of certain conifers has been observed to be even stronger than the annual mean or the temperature variables (^{Martínez-Antúnez et al., 2013}; ^{Antúnez et al., 2017a}). Conversely, the abundance of Abies durangensis Martínez, Quercus resinosa Liebm., Q. acutifolia Née, Q. urbanii Trel. and P. leiophylla Schiede ex Schltdl. et Cham is highly associated to the April-September precipitation, as well as to the mean annual precipitation (^{Martínez-Antúnez et al., 2013}). Other species like Quercus peduncularis, Q. polymorpha, Q. rugosa, Q. sebifera and Q. segoviensis appear to respond to the variations in precipitation, although modified by the altitude (^{Álvarez-Moctezuma et al., 1999}). As for frosts (SDAY, FDAY and FFP), high correlations were observed with the abundance of Q. laurina, P. ayacahuite and P. hartwegii, which exhibited correlation coefficients ranging from 0.85 to 0.99. In this sense, ^{Martínez-Antúnez et al. (2013)} document similar values with covariance coefficients above 0.90 for Pseudotsuga menziesii (Mirb.) Franco and Pinus arizonica Engelm. in northwestern Mexico.

In general, the results obtained using the three analysis methods are an important contribution to the characterization of the habitat of the most abundant species of the study area, since they indicate that the associated environmental variables appear to have no causal relationship with the abundance of each of the taxa under multicolinearity conditions. However, since the results of the three methods utilized did not agree in several cases, other analysis methods will be tested in the future in order to determine whether or not the same variables exhibit solid evidence of significant effects on the studied species, taking into account the multicolinearity or the spatial self-correlation (^{Antúnez et al., 2017a}), according to the results of the present study. The tools that may be tested in the future include the regression trees or additive models in their various modalities (^{Hastie and Tibshirani, 1986}; ^{Nelder and Wedderburn, 1972}; ^{Wood, 2006}), as well as mapping in order to more accurately identify those variables that have a major impact on the abundance of each of the studied taxa.

Conclusions

Results suggest that three groups of species are located in the study area. On one hand, three broadleaf species were identified as the most sensitive to temperature-related variables, particularly to the minimum temperature and temperatures above 5 °C, the number of frost-free days and the aridity index: Arbutus xalapensis, Alnus acuminata and Quercus rugosa. The second group consists of those species that appear to be highly sensitive to the amount of precipitation in the various seasons of the year, particularly the spring, summer and winter mean precipitations, the mean April-September precipitation and variables resulting from dividing some of these data between others; this group includes Pinus ayacahuite, Pinus hartwegii and Quercus laurina. The other taxa have weak evidences of any strong or significant impact, except for the predominant site slope, which has a strong effect on Pinus teocote and Alnus firmifolia. In general, the results are an initial step in the characterization of the bioclimatic niche of the most abundant tree species in the Northern Sierra of Oaxaca, Mexico.