The study area

As areas of study, the pine forest, the pine-oak forest and the oyamel forest (^{Inegi, 2013}) with a buffer of 1 km were selected, which are located mainly in the Sierra Madre Occidental and in the Sierra Madre Oriental, among other mountainous reliefs. In these types of vegetation, the climate is temperate subhumid with average temperatures of 10 to 22 °C; the precipitation varies from 600 to 1 000 mm per year (^{Conagua, 2012}). The altitudinal interval goes from 400 m to 4 000 m.

Forest pest records

The data on forest pests were provided by the National Forestry Commission (National Forestry and Soil Inventory 2009-2014, INFyS). To these data, a purification was applied to verify that they were located within the polygon of study area that corresponds to all the coniferous forests of the country; This was done through the QGIS program (^{QGIS, 2016}) and those that did not comply with this condition were eliminated. There were 4 004 unique records (geographical coordinates) of four types of pest: 316, 546, 1 527 and 1 615, for borers (B), defoliators (d), bark beetles (D) and mistletoe (M), respectively; INFYS information does not specify the pest species observed in the field, so it was decided to organize presence records in the four groups mentioned above. It is further assumed that the group of mistletoe refers to the dwarf mistletoe, since the reference information is reduced only to observations of these organisms.

Variables and distribution models

The bioclimatic variables proposed by ^{Hijmans et al. (2005)}, which are variants of precipitation and temperature and have an approximate resolution of 1 km² (http://www.worldclim.org). were used. Additionally, forest mensuration variables were generated (Aba: basimetric area ha^-1, Arb: number of trees ha^-1, Dnp: average normal diameter ha^-1, Nsp: number of species), with INFyS data, which were tabulated and were extrapolated to hectare for subsequent interpolation to the study area, using the Inverse Distance Interpolation (IDW) method, because it was better adjusted to the real data.

Of the bioclimatic and forest mensuration variables, those with a correlation greater than 0.6 were eliminated (^{Contreras et al., 2010}), for which the corselect function of the fuzzySim package (^{Barbosa, 2015}) of the R program (^{R Core Team, 2017}), in order to minimize collinearity in the resulting models (^{Contreras et al., 2010}). The bioclimatic variables selected for the modeling were: average annual temperature (°C), B01; isothermality of temperature, B03; seasonality of temperature, B04; average minimum temperature of the coldest period (°C), B06; average temperature of the wettest annual quarter (°C), B08; average temperature of the warmest annual quarter (°C), B10; annual precipitation (mm), B12; precipitation of the driest period (mm), B14; seasonality of precipitation (mm), B15; precipitation of the warmest annual quarter (mm), B18; precipitation of the coldest annual quarter (mm), B19.

The records and the variables selected for each type of pest were used to generate models of potential distribution in the R program (^{R Core Team, 2017}) with the help of MaxEnt version 3.4.1 (^{Phillips et al., 2006}) and the dismo package. (^{Hijmans et al., 2016}) by R (^{R Core Team, 2017}). To create the distribution models, the presence data of each type of pest was divided into five random groups (k-fold), with which the same number of iterations is made, in each of which a defined group is taken. for verification and the rest of them as model training; the process is repeated according to the number of k-folds (^{Hijmans et al., 2016}).

The AUC statistic (Area Under the Curve) was used to know the accuracy of the models (^{Elith, 2000}) in the prediction of the potential distribution of the types of pest treated in this work. The distribution models were projected into the geographical space and the probability of presence was defined above the minimum threshold of known presence suggested by ^{Pearson et al. (2007)}.

Bioclimatic profile of forest pests

With MaxEnt, a Jackknife test was carried out that helped identify the most important variables in the test of potential distribution models; of these variables the maximum and minimum values corresponding to the presence records were extracted to generate the bioclimatic profile of each type of pest.

Adjustment of potential distribution models

The models generated are considered adequate to predict the distribution of forest pests, by their values of AUC greater than 0.85, which according to ^{Elith (2000)}, when these are greater than 0.75 are useful for predicting the potential distribution. The highest AUC was for defoliators and the lowest for bark beetles, while the minimum known presence threshold (^{Pearson et al., 2007}) was 0.05 on average for the studied types of pest (Figure 1).

PO = Probability of occurrence; AUC = Area Under the Curve

A = Borers; B = Defoliators; C = Mistletoes; D = Decorticators

Figure 1 Potential distribution of pests that affect the coniferous forests of Mexico. 

As for the fit, the AUC value (0.97) calculated by ^{Mendoza et al. (2011)} in the distribution of Dendroctonus rhizophagus in the Sierra Madre Occidental is higher than that of this research (0.85), which is mainly due to the specificity of both studies; on this occasion, it has been worked on the genus, while other studies address the level of species, and in so far as it is more localized, the prediction of the models is better (^{Allouche et al., 2006}). Likewise, ^{Salinas et al. (2010)} predicted the distribution of 11 species of barkers in Mexico, with support in the BIOCLIM algorithm; however, they do not show the fit of such predictions that allows to formulate a discussion on the adjustment of the model generated for bark beetles in this work, although no information is presented about a particular type of barker.

Potential distribution of forest pests

Borers. The states with the largest area of potential distribution for borers (probability ≥ 0.85) were Chihuahua (23 %), Durango (16.9 %) and Oaxaca (10.2 %) of the 270 402.35 km² (Figure 1), while in San Pedro Mártir Sierra (Baja California) where ^{Díaz (1988)} has described borers of the genus Cydia on Pinus jeffreyi Balf. and P. ponderosa Douglas ex C. Lawson, the model predicts probability of presence up to 0.88. Likewise, ^{Galindo et al. (2011)} made the first record of the Megastimus genus which causes significant damage to seeds of Abies religiosa (Kunth) Schltdl. et Cham. and A. hickeli Flous & Gaussen in Cofre de Perote (Veracruz), where the probability of presence of 0.51 is predicted. This suggests that borers may exist in the sites indicated by the model, while the fact that they have not been recorded or described only indicates the deficiency in field studies. Some areas of discontinuous distribution are also observed in the Trans-Mexican Volcanic Axis, as in Chiapas, Coahuila and Nuevo León (Figure 1A).

Defoliators. MaxEnt estimated that there are 315 305.72 km² in Mexico (Figure 1B) that combine favorable climatic and forest mensuration conditions for the presence of defoliators, where the highest probability occurs in the forests of the center and south of the country (Figure 1B). The largest area is found in Chihuahua (66 367.47 km²) where ^{Castro (1981)} registered defoliators of the Neodiprion genus in Pinus arizonica forests Engelm. in Bocoyna municipality, Chihuahua, where the model predicted high probabilities (> 0.90, Figure 1B). Other states with ample favorable zone for defoliators are Durango (51 655.29 km²), Oaxaca (32 351.08 km²) and Chiapas, Guerrero and Michoacán with about 19 801.3 km², on average, for each one (Figure 1B).

Barking beetles. ^{López et al. (2015)} identified barking beetles in Abies religiosa forests in the Monarch Butterfly Biosphere Reserve; like ^{Rodríguez et al. (2013)}, mention Dendroctonus adjuntus in ejido Los Pescados, Veracruz, where the model predicts 0.68 probability of occurrence, on average, for both zones, although in areas surrounding the last locality it is predicted up to 0.99. Chihuahua and Durango are the states with the broadest potential area for barking beetles of the Dendroctonus genus (20.96 and 16.56 % of the national total) mainly since they have the greatest extension of forests and the highest diversity of species of this genus (^{Salinas et al., 2010}). However, in the Trans-Mexican Volcanic Axis the problem increases (Figure 1D), which could be due to the fact that in this mountainous system a high percentage of Pinus colonized by barking beetles is concentrated (^{Salinas et al., 2010}).

Mistletoe. The highest number of mistletoe records was observed in Durango and Chihuahua (601 and 452), where the largest extension of their potential distribution is verified (65 986.49 and 51 617.97 km²); in contrast, Aguascalientes and Baja California Sur have the lowest potential area, with 27.7 and 161.01 km² (Figure 2C), mainly due to the limited coniferous forests in these states. 308 539.29 km²were predicted with the right characteristics for the proliferation of some species of mistletoe. These organisms have been consigned by ^{Ramírez and Porcayo (2010)} in the Nevado de Toluca National Park on Pinus hartwegii Lindl. and P. montezumae Lamb. where the maximum probabilities of 0.60 were determined (Figure 1C).

In general, the potential area for each type of pest was greater than 270 thousand km², the smallest of which corresponds to the borers and the opposite for defoliators (Figure 1). Durango has the largest wooded area under optimal conditions for defoliators, bark beetles and mistletoe, followed by Chihuahua, while for other states such as Nuevo León, Coahuila and Nayarit the highest susceptibility is found for barking beetles, and for borers in forests of Mexico City (Figure 2).

B01 = Annual average temperature (°C); B03 = Isotermality of temperature; B04 = Seasonality of temperature; B06 = Average minimum temperature of the coldest period (°C); B08 = Average temperature of the wettest annual quarter (°C); B10 = Average temperature of the warmest annual quarter (°C); B12 = Annual precipitation (mm); B14 = Precipitation of the driest period (mm); B15 = Seasonality of precipitation (mm); B18 = Precipitation of the warmest annual quarter (mm); B19 = Precipitation of the coldest annual quarter (mm); Aba = Basimetric area ha^-1; Arb = Number of trees ha^-1; Dnp = Average annual diameter ha^-1; Nsp = Number of species.

A = Borers; B = Defoliators; C = Barking beetles; d = Mistletoes

Figure 2 Importance of the variables (Jackknife test) in models of the potential distribution of pests that affect the conifer forest of Mexico. 

Given the high risk that their forests are infested, in the states of Oaxaca, Guerrero and Chiapas (for defoliators); Estado de México, Michoacán and Nuevo León (for barking beetles); Chihuahua and Durango (for mistletoe and borers) attention should be focused and the design of monitoring systems for the timely detection of outbreaks of some pest (Figure 1).

Important environmental variables

The environmental variables that did not present a correlation higher than 0.6 were five bioclimatic (variables for each TP) and four of forest mensuration (Figure 3). According to the results of the Jackknife test, those that decrease the gain of the model when they are excluded (light gray bar of Figure 2) are as important as those that provide the greatest gain when modeled individually (white bar of Figure 2); in this sense, the most relevant parameter in the prediction of the distribution of borers, defoliators and mistletoes was the number of species (Nsp), while for barking beetles, it was the basimetric area (Aba) (Figure 2D).

Of the climatic variables, isothermality (B03) was more relevant for the defoliators, the average annual temperature (B01) for borers, and for mistletoe, the average minimum temperature of the coldest period (B06) of the year (Figure 2). In general, those associated with temperature are the most significant for the four types of pest (Figure 2), which may be due to conditions such as evapotranspiration or the severity of drought, which keep the tree under stress and make it vulnerable to attack by insects (^{Raffa et al., 2008}, ^{Del Val and Sáenz, 2017}).

Specifically for bark beetles, low temperatures (B08: average temperature of the wettest annual quarter of the year (Figure 2), represent an important element in their distribution, as well as other direct effects on insects, by promoting the mortality of adults and larvae and the alteration of the time required to complete a generation (^{Raffa et al., 2008}), which has an impact on their population dynamics (^{Bentz et al., 2010}). However, due to climate change and the increase in temperature, the limiting relationship to insects could gradually decrease and cause a population explosion (^{Hernández et al., 2017}).

In general, the prospect for temperate forests in Mexico is not very encouraging in the context of pests. On the one hand, bark beetles are positively influenced by rising temperatures (^{Del Val and Sáenz, 2017}), which leads to an increase in the number of generations per year (^{Bentz et al., 2010}); with this, their possibilities of adapting to the new environmental conditions multiply. Trees, on the other hand, do not have the same ability to adjust to the changes implied by the massive presence of insects or those of their environment.

Ecological-climatic profile of forest pests

The contribution percentage of the climatic and forest mensuration variables in the distribution models was not constant for the four types of pest. For borers and mistletoes, the forest mensuration variables contributed more than 50 % to the model, while the climatic variables contributed more than 70 % to the construction of the models for barking beetles and defoliators. According to the Jackknife test, the most important variables (Figure 3) were also those that had the highest contribution percentage in the construction of the models (Table 1).

^{Gan (2004)} indicates that the risk of infestation of Dendroctonus frontalis increases when temperatures range from 8.79 to 14.87 °C, whereas in this investigation the average temperature range is wider for bark beetles (Table 1); this is mainly due to the fact that the Mexican forests are at a lower latitude than the region mentioned by the author, and that this study did not work at the species level.

^{Mendoza et al. (2011)} assert that the average temperature contributed with 30.1 % and precipitation with 10.5 % in the distribution of Dendroctonus rizophagus in the Sierra Madre Occidental, while in this work the same behavior is presented (54.9 % for temperatures and 20.26 % for precipitation). (Table 1), which indicates that the distribution of bark bees is largely governed by temperature (Figure 3D). However, not only the distribution of insects is affected by temperature, but also its population explosion (^{Raffa et al., 2008}), mortality (^{Bentz et al., 2010}) and physiology (^{Hernández et al., 2017}).

According to ^{Cuellar et al. (2012)}, in the northeast of Mexico, the precipitation and the temperature (average and maximum) monthly do not determine the abundance of Dendroctonus mexicanus, which in turn would show that in some regions, the distribution and abundance of bark beetles are not conditioned to monthly changes in the climate, but to seasonal or even annual variations (^{Mendoza et al., 2011}).

In Mexico, ^{Queijeiro and Cano (2015)} observed that the incidence of mistletoe (Arceuthobium vaginatum Humb. & Bonpl. ex Willd. J. Presl. and Arceuthobium globosum Hawksw. & Wiens) is more linked to stochastic processes such as fires or tree felling; however, in this work the information was not handled at the species level nor were variables that represent some type of disturbance included. The analysis indicates that the average minimum temperature of the coldest period (B06) of the year was one of the most important in the model (Figure 2D, Table 1), which is confirmed by the results of ^{Brandt et al. (2005)} that mention that low temperatures reduce by 95 % the dispersal ability of dwarf mistletoe seed (Arceathobium americanum Nutt ex Engelm.).

Forests and forest pests

According to INFyS data, the observation of forest pests in Mexican forests has occurred in sites with less than 15 m² of basimetric area per hectare (Figure 3B, F, J, N) and less than three species (Figure 3D, H, L, O).

A – D = Borers; E – H = Defoliators; I – L = Barking beetles; M – O = Mistletoe Frecuencia = Frequency; Área basal = Basimetric area; Número de árboles = Number of trees; Diámetro normal = Normal diameter; Número de especies = Number of species

Figure 3 Distribution of pests presence records; with respect to forest mensuration variables. 

The homogeneity in structure and age of the forests are determinant for the incidence of bark beetles (^{Raffa et al., 2008}); unfortunately, in this study the variability between sites with this type of pest was not analyzed to corroborate this hypothesis, although with the available data it has been observed that the sites with small diameter categories are preferred by borers and mistletoes (Figure 3C and Ñ), while defoliators and barking beetles are found in more mature forests (Figure 3G and K), which could be due to a lower resistance of the trees to be attacked, especially by insects of the second sort.

The high densities of the trees do not seem to be the favorite sites for the types of pest studied here (Figure 3B, F, J, N), since most of the presence of bark beetles has been observed in sites with densities under 30 m² ha^-1 and 500 individuals (conifers) ha^-1 (Figures 3 I and J), as mentioned by ^{Íñiguez (1999)} who analyzed the density of trees in healthy and infested sites in Nuevo León and recorded an average density of 455 trees ha^-1; concluded that there are no significant differences in the density of both sites. Contrary to the above, ^{Cuellar et al. (2013)} established that the higher density of trees increased the risk of attack by bark beetles in the south of the state.

The contradiction with the results found in this work can be explained, mainly, because the INFyS data collection is not done in sites where these beetles exist as pests, since they are a natural element of the forests (^{Salinas et al., 2010}). In the INFyS only the presence or absence of insects is recorded and no data on their demography are specified; therefore, it would be convenient to do studies in places where there is certainty of a massive infestation of forest pests.

The analysis of the data used in this work does not provide information on any species of forest pest in particular, which expands the area of opportunity to develop further studies and which at the same time represents a limitation of this study. However, in the absence of distribution studies on the majority of forest pests and the inclusion of forest parameters, this work offers an approximation of forest areas that should receive more attention from the corresponding entities.