Database

Data from 62 sampling sites were considered. The database was obtained from two sources: the National Forest and Soil Inventory (INFyS) from the National Forestry Commission (CONAFOR) and from the site: http://www.tropicos.org/.

Potential areas of distribution

The Maximum Entropy approach (^{Phillips et al., 2009}) was used in this research, to model the ecological niche and predict the most likely geographic distribution of M. alba. The result of the model expresses the most suitable value for habitat potential in terms of environmental variables used. Maximum Entropy has been used widely to estimate potential distributions of plants and animals species with high accuracy (^{Sobek et al., 2012}), and predict or infer species distribution based on the most significant environmental conditions, using only data of species presence (^{Moreno et al., 2011}).

Environmental databases and geographical information system

Monthly, seasonal and annual precipitation, maximum temperature, minimum temperature, average temperature and thermal oscillation data from the periods 2041-2060, 2061- 2080 and ~1950-2000 (reference climatology) were used. These climate data was obtained from the Global Climate Data website WorldClim and processed by raster images and ascii, at a resolution of 2.5 arcmin. For 2041-2060 and 2061- 2080 climatologies the GCM was considered: HadGEM2-ES under two representative concentration pathways (RCPs) of greenhouse gases (GEI): rcp4.5 and rcp8.5. The GCM used, is part of climate modeling developed by the Coupled Model Intercomparison Project Phase 5 (CMIP5) (^{Walton et al., 2013}). Altitude layer was obtained from the Environmental Information System (SIAN), from the National Institute of Agricultural Livestock and Forestry Research (^{Diaz et al., 2012}).

From the basic climate variables mentioned a number of additional variables derived to perform the MaxEnt analysis of potential distribution niches for both reference climatology conditions and for 2041-2060 and 2061-2080 climatologies. The total number of variables used were: height above sea level (m), slope (%), annual maximum average temperature (°C), maximum temperature from May to October (°C), maximum temperature from November to April (°C) , maximum temperature from the warmest month (°C), mean annual temperature from the coldest month (°C), mean minimum annual temperature (°C), minimum temperatures from May to October (°C), minimum temperature from November toApril (°C), minimum temperature from the coldest month (°C), annual accumulated precipitation (mm), accumulated rainfall from May to October (mm), accumulated rainfall from November to April (mm), precipitation from the driest month (mm), precipitation from the wettest month (mm) annual thermal oscillation (°C), thermal oscillation from May to October (°C) and thermal oscillation from November to April (°C).

Using covers from the parameters and presence of species data, niche distribution for the climate scenarios were modeled, using 75% of presence records as training points and 25% as validation points. The AUC index (area under the curve) was used to assess the statistical model, as this index is one of the most used to measure the quality of the models (^{Moreno et al., 2011}).

Areas with probability of environmental fitness

The prediction model for the distribution of M. alba was obtained with MaxEnt and examined with the IDRISI 17.0 (^{Eastman, 2012}) system, a map with threshold values corresponding to 20^th percentile was generated (^{Escalante et al., 2013}). To calculate the potential distribution surface of the species, the areas occupied by water bodies and urban centers were not considered. These thematic layers were obtained through land use and vegetation maps (^{INEGI, 2009}).

Ecological descriptors

The ecological descriptors for M. alba were determined based on the environmental derivatives intervals from site characterization for presence of species. This was made through IDRISI 17, raster images of each environmental variable and the geographic coordinates of each presence site.

Distribution of niche models

Figure 1, shows the operational curve or ROC curve that represents the fitness of the sampling data; in this analysis, the obtained value was 0.955 for training points and 0.897 for validation points; indicating that the ability of the models to classify the presence of the species was successful (^{Parolo et al., 2008}).

Figure 1 Graph of operational curve or ROC curve for M. alba. 

From this analysis it was determined that potential niche distribution model to describe the distribution of M. alba is high, as only two models environmental variables explained 87.6% of the spatial distribution of the species (Table 1). The variables that showed a higher level of contribution were precipitation from the wettest month (September) and mean temperature of the coldest month (January).

Table 1 Ecological descriptior from environmental variables that condition the geographical distribution of M. alba. 

Figure 2 shows the current geographical potential distribution of M. alba. Their presence is located from the Yucatan Peninsula to the north of the country, except for a large area in Baja California and part of the northern region of Sonora, Chihuahua, Durango, Zacatecas and San Luis Potosi.

Figure 2 Environmental fitness for the period ~1950-2000 of M. alba in Mexico. 

The highest presence of M. alba populations are concentrated in the southern and northeastern regions of Mexico; This presence is in line with the claim that M. alba grows in a variety of environments and latitudes. From tropical and subtropical regions which characterizes it by having a wide range of adaptation (^{Loya et al., 2014}).

The ecological descriptors for M. alba and environmental variables that contribute to the construction of niche distribution can be observed in Table1. According to these results, precipitation of the wettest month (September) is the variable that most contributes (72.7%) in the potential distribution of the species in Mexico. The Morus alba descriptor for this variable points to a range of 77 to 409 mm of precipitation. These results are consistent with those reported by ^{Loya et al. (2014)}, in the sense that this species grows well in a wide range of precipitation that can vary from 600 to 2 500 mm of annual precipitation.

The second ecological descriptor that most contributes is the average temperature of the coldest month with a range of 10 to 24 °C. M. alba also demonstrates a wide temperature range; it can be inferred that this species is able to explore and colonize thermally extreme environments.

The results regarding potential niches for M. alba for climate change scenarios are shown in Figure 3. The maps from this figure show the presence of environmental fitness areas and areas with increased and decreased surface for the species under study. In all future scenarios appear surface increases and decrease; showing the possible dynamics of suitable areas, depending on future climate changes.

Figure 3 Accessions and areas with environmental fitness of M. alba; under the general circulation model HadGEM2-ES with four scenarios of climate change a). 2041-2060 rcp 4.5; b). 2041-2060 rcp8.5; c). 2061- 2070 rcp4.5; and d). 2061-2080 rcp8.5. 

The logistics threshold of the 20th percentile forecast for reference climatology an optimal area of 80.8% of the total land area. After averaging increase areas and retractions under climate change climatologies (Figure 4), it was established that areas with environmental fitness decreased to 80.66%, 79.14% and 80.67% of the total area of Mexico, in the scenarios 2041- 2060 rcp4.5, 2041-2060 rcp8.5 and 2061-2080 rcp8.5 respectively; and an increase to 82.28% for scenario 2061-2080 rcp4.5.

Figure 4 Percentage of areas with environmental fitness for M. alba in Mexico. Under climate scenarios, light-colored bars indicate currently fitness areas and in the future (stable), while the darker bars indicate new fitness areas in the future (expansion areas). 

These results show that future climate changes apparently will be harmful for M. alba in the three climate change scenarios. Given that the most significant variables in niche distribution are precipitation from wettest month and mean temperature of the coldest month; it could be inferred that combinations of these parameters under climate change scenarios would be unfavorable to M. alba.

^{Hoffman and Sgro (2011)} noted that some species show retraction and expansion in spatial distribution areas by effects of climate change, in function to their evolutionary adaptation. The expansion of fitness areas due to climate change has been reported for other species such as Leucospermum hypophyllo carpodendron subsp. Hpophyllo carpodendron (^{Pearson et al., 2006}).

Most studies on the effects of climate change on the distribution of species report negative effects, i.e. retraction areas are larger than expansion areas (^{Sork et al., 2010}). In the present study one scenario presented the contrary, that is, the expansion areas are greater than retraction areas.

As shown in Figure 3, these two types of areas have a geographic pattern; retraction areas are mainly concentrated in the north and center part of the country, while the expansion areas locate mainly in the peninsula of Baja California and part of northern Sonora and southern Chihuahua. This fact points to a region of the country, where future weather patterns will be different to current weather conditions, and therefore differ in the adaptation level of M. alba. This situation has already manifested for the region where the recorded retraction areas; there have been reports of crop patterns as result of regional climate changes (^{Ramirez et al., 2011}; ^{Santillán et al., 2011}).

The maps in Figure 3 show that no population of M. alba is affected by the retraction of environmental fitness. However, in the event that some populations of M. alba were near retraction areas of fitness in the coming years, it would have to consider that these populations will have only two options for survival: a) migrate to more favorable environments; or b) adapt to new weather conditions (^{Morueta-Holme et al., 2010}), which largely depends on the genetic diversity of the species (^{Mercer and Perales, 2010}). For the present study, the environmental fitness will lose a little more area due to climate change, and this, apparently, could promote further loss of M. alba spreading to new areas. However, it is also important to consider the potential capabilities of this species to compete with other species in the ecosystem or invasive species which threaten the stability of the ecosystem (^{Mainka and Howard, 2010}).

Moreover, it is important to note that the conservation of M. alba in the future will also depend on its ability to adapt to climate change (^{Alsos et al., 2009}), which is a function of its ability to colonize new areas or, when necessary, of its ability to apply physiological changes to adapt to the new environment (^{Chown et al., 2010}).

According to previous statements, forecast climate change for both periods will have a negative effect on environmental fitness of M. alba (Figure 4), which would allow in the future its possible contraction in territorial coverage. However, it is clear that these unfavorable environmental conditions that will be caused by future climate change, it will be favorable for other species, perhaps in the context of competition with M. alba. Under such scenario, the wide range of ecological descriptors of M. alba (Table 1) could be an advantageous characteristic, especially if the species is considered of broad genetic diversity of other parts of the world, which could increase the adaptation and colonization capacity of M. alba (^{Burke et al., 2009}; ^{Ruiz et al., 2013}).

Even when the current and future climate scenarios seem to be unfavorable for M. alba, conservation measures could be taken to preserve current populations, in order to ensure their presence in their natural environment.