Introduction

Degradation is a problem that affects the soil in any of its four modalities: water erosion, wind erosion, chemical degradation and physical degradation. The soils in forest areas are not exempt from exhibiting some kind of degrading factor. A significant proportion of the Mexican territory has problems of land degradation; however, these can be mitigated through the management of those forest areas that promote the development of goods and services obtained from natural resources (^{Conafor, 2015}). Therefore, it is necessary to evaluate how this type of protective function shows in soil and water resources in forest areas.

Accordingly, there are several studies that seek to identify the factors that influence the erosion of the soil, and which have yielded a comprehensive list of important variables, including:

Relief. Characteristic on which the speed of the surface water runoff and other particularities are dependent (^{Figueroa et al., 1991}).

Type of parent material. Directly influences the characteristics of the soil and its formation rate, which must be in balance with the erosion rate to maintain its productive capacity (^{Loredo-Osti et al., 2007}).

Climate conditions. These act as driving forces of soil erosion, among which the main eroding agent is precipitation (^{Figueroa et al., 1991}).

Type of vegetation and its conditions. These have protective functions in forest management (^{Miura et al., 2015}).

Land use. Mismanagement is a factor that influences susceptibility to erosion (^{Muñoz and Ferreira, 2013}; Duran et al., 2014).

Physical and chemical properties of the soil. These characteristics determine the susceptibility to erosion (^{Cabria et al., 2002}).

At present, studies are still being conducted at the global level for the purpose of reaching a better understanding of this current phenomenon in a relevant way; therefore, work is being done to identify, establish and validate monitoring that will adapt to the different existing vegetation types in the world. In 2015, the Japanese Forestry Agency, in conjunction with the National Forestry Commission (Conafor) of Mexico, assessed four methods for monitoring the protective functions of the vegetation on the soil resource (^{Conafor, 2015}); this resulted in a proposal for a hybrid method described in the "Field guide for rapid assessment of forest protective function for soil and water” (^{FAO, 2015}), which was the basis for the present research; the incorporation of other variables is considered to be important in this type of monitoring. Therefore, the objectives were to determine what factors have an influence on the erosion of the soil in temperate forest of Zoquiapan, Mexico, and to identify those that correlate with water erosion in forest areas, so that they can be used in future monitoring, for their practicality and efficiency.

Materials and Methods

Selection of sampling points

There was a prior characterization of the sampling site according to the methodology proposed by ^{Gómez (2008)}. Maps were generated for physiography, climate, land use and vegetation, with the help of a Geographic Information System (ArcGis 10.1). The maps were overlapped to obtain landscape units with homogeneous characteristics (biophysical units) for the purpose of facilitating sampling (Figure 1). 18 biophysical units were generated; of these, three were selected for their ecological importance, on which the sampling points were established with three replications (Table 1).

Figure 1 Graphic representation of the biophysical units with homogeneous characteristics in Zoquiapan, Mexico. 

Table 1 Coordinates and identification key of the sampling points on the selected landscape units. 

Biophysics Unit	Identification Key	Replication	Coordinates (UTM)
Sacred fir forest with a Cc(W2)(w)ig climate on a sloping hillside	SFF_LI	1	534494-E, 2133356-N
		2	534675-E, 2132688-N
		3	534906-E, 2131999-N
Pine forest with Cc(W2)(w)ig climate in an almost flat intermountain valley	PF_VI	1	533898-E, 2133370-N
		2	534394-E, 2134038-N
		3	535210-E, 2134024-N
Pine-alder forest with a Cc(W2)(w)ig climate in a sloping hillside	PAlF_LI	1	534274-E, 2130682-N
		2	534557-E, 2130007-N
		3	534748-E, 2131102-N

Sampling plot

The sampling plot named: "Subsampling by transect and dotted line" was used as the basis (^{FAO, 2015}) and was adapted for the lifting of new variables (Figure 2).

I, II, III and IV are the quadrants, A, B, C, and D whose measurements are detailed in the description of the information collection process.

Figure 2 Sub-sampling by transect and dotted line.  

Results and Discussion

Table 2 shows the results for aerial biomass, basimetric area, leaf litter thickness and mulch. These elements of the soil are important for mitigating erosion (^{Durán et al., 2014}). Other cover data measured in the field were the percentage covered by forest canopy at each sampling point, and the forest floor cover that was subdivided into the percentages of vegetation, waste, bare soil and rock that included stones (Table 2). In general, based on the analysis of the data collected in the field, the cover percentage was determined to be greater than 90 %, corresponding to a high category according to the proposal by ^{Miura et al. (2015)}.

Edaphic variables are shown in Table 3. The infiltration measured in most of the points ranged from fast to very fast, according to the classification of ^{USDA (2000)}. The data of resistance to penetration measured in the first 7.62 cm in depth are classified as low to moderate (^{Schoeneberger et al., 2012}). The first layer of soil (7.62 cm) was considered for analysis because it intervenes directly with the impacts or the erosive force of water. The soils were characterized as deep to very deep (^{FAO, 2015}).

Other soil properties were: 1) pH which proved to be severely acid to very severely acid (^{Castellanos et al., 2000}), attributable to andic properties of the soils and to the contents of organic matter (^{Castellanos et al., 2000}); 2) the organic matter recorded very high values; 3) the aggregate stability indicated that the soil has a high percentage of stable aggregates, which suggests that they are soils with persistent particles in the face of destructive forces by anthropogenic, climate, or other actions (^{Florentino, 1998}), in addition to the stable ground, it is also attributed to the amount of organic matter; 4) bulk density (BD) was in a range of 0.59 - 0.72 g cm^-3, which is considered as low (^{Etchevers et al., 2005}); this validates the perception that they are well aerated and well drained porous soils; 5) the texture was classified as loamy-sandy, and rated as average and characteristic of forest soils.

As shown in Table 4, the signs of erosion by pedestals were the only ones present in the sampling points, there was only a piece of data for the variable channels and null data for the variable gullies, so that the erosion on the site was nil to light, according to the classification of ^{Figueroa et al. (1991)}; this is attributed to the physical and chemical properties of the soil which give stability to their aggregates, as indicated above.

The correlation between the variables measured and the soil erosion represented by pedestals are described below. A statistical analysis was performed discarding those data that were the same or very similar to each other. The 20 covariates were selected because they influence the response variable; they were analyzed using the correlation matrix (Figure 3).

Figure 3 Correlation matrix and utilized code 

Table 5 shows the covariates of higher correlation with erosion, based on Pearson's correlation coefficient.

In the exploratory analysis with Principal Component Analysis (PCA), which is displayed in Figure 4, the variables that were significant in explaining the presence of pedestals (framed in yellow) were: bare soil, soil compaction, slope, thickness of the mulch, rocks and APD, which had a positive correlation. The organic matter, infiltration and soil depth were negatively correlated (framed in green). In this case, the greater the magnitude of the variables, the lesser the soil erosion in the form of pedestals. These results are in line with what was expected, since the deep soils and their high content of organic matter enhance their infiltration capacity, and they are very stable soils, which reduces the risk of erosion.

Figure 4 Exploratory analysis by means of Principal Components for all the analyzed variables. 

From the exposed statistical analysis, it is inferred that the erosion by pedestals is correlated with:

1) Soil Slope Variable, among those of greatest importance in the Pearson correlation (r = 0.59) and in the PCA, the angle formed by the two lines is sharp, which indicates positive correlations and shows the importance of the slope in the soil erosion, a fact that is consistent with the data cited by ^{Figueroa et al. (1991)} and ^{Durán et al. (2014)}.

2) Thickness of the mulch. It was important for the PCA, as the angle between this and the erosion is acute; which means that, increasing the thickness of topsoil, erosion in formation of pedestals was greater. The above can be associated to the fact that the mulch was in a stage of mid-term decomposition, and at this phase, as indicated by ^{Miura et al. (2015)}, the mulch is made up of large particles of vegetable waste still without a stable structure; this represents an obstacle to runoff, and therefore the water cannot drain, so that when its volume increases, it drags the residues and the soil.

3) Presence of rocks on the surface. The Pearson correlation associated with the runoff around these obstacles was positive (r = 0.57), and a larger water volume concentrates in open areas. For this reason, there can be detachment and drag of fine soil particles, which causes the exposure of the rocky or stony materials as an indication of erosion (^{Durán et al., 2014}).

4) Percentage of bare soil. The positive correlation observed through the PCA is an expected result; since, in the absence of a cover that protects the soil, the problem of erosion becomes more intensely evident, as has been indicated by various authors (^{Muñoz and Ferreira, 2013}; ^{Durán et al., 2014}; ^{Miura et al., 2015}).

5) Soil compaction. Positively related to soil erosion in pedestals, which means that the greater the compaction of the soil, the higher the pedestals measured in the field. The above is attributable to the fact that, when there is compaction, water infiltration is reduced, surface runoff increases, and all this causes erosion (^{Spaeth et al., 1996}).

6) Soil bulk density. Soil bulk density exhibited a high positive correlation (r = 0.64), attributed to the fact that the soils exhibited very stable particles, medium-textured and BD values < 1. Soils with thick textures are related to a higher BD and are susceptible to be eroded (^{Muñoz and Ferreira, 2013}).

7) Organic matter. The Pearson correlation was negative (r = -0.45), as shown by the PCA, in which the angle between organic matter and soil erosion was observed to be close to 180° (Figure 4), which means that the greater the amount of organic matter in the soil, the higher the rate of infiltration, and, in deep soils, the lesser the erosion by pedestals. The answer is the expected one and is associated with the fact that the organic matter is essential for the aggregation and soil stability, making it more resistant to erosion, coinciding with what ^{Muñoz and Ferreira (2013)} validated.

8) Soil depth. The deeper soils have more infiltration capacity, store more water and decrease the volume of surface flow; as a result, the erosion diminishes, and therefore the Pearson correlation was negative (r = -0.48).

9) Infiltration. The result for the infiltration shows that the greater the infiltration, the lesser the erosion, as ^{Morgan et al. (1984)} point out, because a greater penetration of water into the soil reduces the surface runoff.

When individually analyzing the other measured variables -percentage of canopy cover, percentage of vegetation cover, and percentage of residues-, no significant correlation with soil erosion by pedestals was obtained for the sampled sites. This is not to say that they lack importance, as the bare soil that results from subtracting the surface covered by all materials explained to a large extent the problem of erosion.

Conclusions

The use of the methodology makes it possible to determine the factors that account for the erosion in the study area. The slope of the site, the thickness of the mulch, the percentage of rock present on the surface, the compaction, and the apparent density exhibit a positive correlation with the erosion expressed as pedestals; so that, as its magnitude grows, the risk of presence of pedestals increases. The organic matter in the soil, infiltration rate and soil depth recorded a negative correlation, so that their presence with high values reduces the risks of soil erosion, due to absence or reduced incidence of pedestals. It is desirable that these factors be considered, primarily in subsequent monitoring studies.