Biological databases

The data of 1 138 georeferenced sampling sites, corresponding to the database of the National Inventory of Forestry and Soils (INFyS) of the Comisión Nacional Forestal (Conafor) (^{Conafor, 2016}).

Databases and geographic information system

Raster images of precipitation and temperature for the 1960 - 1990 (reference climatology), 2041-2060 and 2061-2080 periods were utilized; these were obtained from the ^{WorldClim Global Climate Data website (2017)} and processed using raster and ASCII images with a resolution of 30 arc seconds; furthermore, the soil texture raster of the National Institute of Statistics and Geography of Mexico (Inegi) was used for the 2041-2060 and 2061-2080 climatologies (^{Inegi, 2009}), and the MGC (for its acronym in Spanish): GFDL-CM3, which is part of the climate modeling developed by the Coupled Model Intercomparison Project Phase 5 (CMIP5) was considered under the RCPs 4.5 and 8.5 (^{Walton et al., 2013}). The RCPs refer to the global radiation of energy expressed in W m^-2 and they assume that this radiation varies as the greenhouse gases (GHG) increase.

A series of additional variables were derived from the basic climate variables mentioned above in order to carry out the MaxEnt analysis of potential distribution niches, under the conditions of the 1960-1990 climatology, as well as of the 2041-2060 and 2061-2080 climatologies. The utilized variables were: maximum mean annual temperature, maximum May-October temperature, maximum November-April temperature, mean annual temperature, mean May-October temperature, mean November-April temperature, mean temperature of the warmest month, mean temperature of the coldest month, minimum mean annual temperature, minimum May-October temperature, minimum November-April temperature, annual accumulated precipitation, May-October accumulated precipitation, November-April accumulated precipitation, precipitation of the driest month, precipitation of the wettest month, annual thermal oscillation, average May-October photoperiod, and soil texture (tex).

Those parameters were implemented, and their respective raster images were generated using the Idrisi Selva system (^{Eastman, 2012}). The variables are those normally used for the territorial potentiality of vegetal species (^{Costa et al., 2010}; ^{Moreno et al., 2011}).

Ecological niche model

The Maximum Entropy (MaxEnt) software, in its desktop version 3.4.1, was utilized for modeling the ecological niche and predicting the current and future distribution of the taxon (^{Steven et al., 2017}). The MaxEnt model establishes species distribution predictions based on information of the presence data (Phillip et al., 2006) and based on the most significant environmental conditions (^{Moreno et al., 2011}). The pixels where there is a certainty that the species studied herein occur are the sampling points, and the characteristics are the climate, edaphic variables and other functions of these. The purpose of the model is to predict the aptitude of the environment for taxa in terms of environmental variables (^{Phillips et al., 2006}).

Based on the coverage of the parameters and presence data of the species, distribution niches were modeled for the 1960-1990, 2041-2060 and 2061-2080 periods; for this purpose, 75 % of the registered of presence were used as training points, and 25 %, 50 replications and 500 iterations were used as validation points (^{Sánchez et al., 2018}). The AUC (area under curve) index was used to evaluate the statistical model, as this index is one of the most widely used to measure the quality of the models (^{Moreno et al., 2011}). The complexity of the model is controlled through the choice of the variables; furthermore, the MaxEnt model includes in its configuration an operator known as “parameter regulation” which helps prevent the superimposition of variables, and, therefore, its potential harmful effect on the prediction (^{Phillips and Dudík, 2008}).

The values of the obtained points represent relative aptitude for the presence of the species and constitute the basis of a potential distribution model. The resulting images of the MaxEnt niche distribution modeling were recovered in the ArcGis system (^{ESRI, 2010}) and edited in the map format.

Fit of the model

Through the ecological niche model, the MaxEnt model predicts the relative occurrence rate (ROC curve) of the species, as a function of the environmental predictors in each locality (^{Merow et al., 2013}); in turn, the area under the curve (AUC) is interpreted as the adjustment of the model, in which a value of 1.0 would be a perfect classifier and a random classifier would have a value of 0.5 (^{Phillips et al., 2006}), and therefore, those that are close to 1.0 show a better fit of the model to the data.

The MaxEnt results include images with potential areas of distribution of the species, where each cell has a prediction value; on the other hand, a large number of researches require fixating a threshold value for estimating the areas with environmental aptitude for each taxon (^{Liu et al., 2016}), for which purpose the MaxEnt model incorporates a file with the most frequently utilized threshold values. The present study utilized the fixed cumulative value 10 as a logistic threshold.

Potential distribution niche model

The results of the application of the Receiver Operating Characteritic (ROC) technique showed that the model is good, as the value of the area under the curve was 0.948 for the training data of the current scenario (red line), and 0.95 for the future scenarios (Figure 1). This indicates that the model for classifying the presence of L. leucocephala was satisfactory (^{Parolo et al., 2008}).

Figure 1 Operational or Roc curve for Leucaena leucocephala (Lam.) de Wit. 

In general, an AUC value above 0.7 is considered to have a good fit (^{Hanley and McNeil, 1982}; ^{Elith, 2006}). The environmental variables that accounted for 74 % of the distribution of the species were: the photoperiod, the precipitation of the wettest month, the mean temperature of the coldest month, the accumulated precipitation of the May-October period, and the mean temperature of the November- April period.

Ecological descriptors

Table 1 summarizes the parameters of the ecological descriptors of the environmental variables that accounted to a larger extent for the distribution of L. leucocephala. The environmental distribution intervals were observed to be wide for the variables related to temperature or precipitation. This fact proves a broad rusticity of the species, a characteristic which may be favorable in environments where climate change manifests more aggressively (^{Heuzé and Tran, 2015}).

Based on the information of Table 1, L. leucocephala is distributed in regions where the photoperiod of the November-April season lasts 11.2 to 11.6 hours; this condition agrees with the information reported by ^{Heuzé and Tran (2015)}, according to whom it is a short-day species whose flowering and reproduction are stimulated by a photoperiod of less than 12 hours. However, ^{Whitesell and Parrotta (2008)} indicates that the common varieties of L. leucocephala blooms the whole year. Another important variable is the mean temperature of the coldest month, which is distributed in sites with a temperature of 11 to 28 °C, a condition that corresponds to areas with temperate to very warm areas (^{Medina et al., 1998}). Thus, temperature does not appear to be a very restrictive factor for the distribution of the species.

Another important variable was the precipitation of the wettest month. Table 1 shows that L. leucocephala thrives in places with values of 60 and 640 mm, which exist in semiarid to humid areas and which exhibit relative moisture values ranging from low to high in the wettest month of the year. This agrees with the statement of ^{Petit et al. (2010)} in the sense that L. leucocephala has a natural distribution in areas where the relative moisture in the month of September (generally the wettest month) is up to 85 %.

Leucaena leucocephala areas with environmental aptitude

The environmental aptitude during the 1960-1990 period (Figure 2) proved to be favorable for the species under study as a result of their broad environmental intervals (^{Heuzé and Tran, 2015}). The surface area with environmental aptitude was notorious in a large part of the center and south of Mexico, which proves that the tropical and subtropical conditions correspond better to the climate needs of the species (^{Zarate, 1999}; ^{Heuzé and Tran, 2015}).

Figure 2 Areas with environmental aptitude for Leucaena leucocephala (Lam.) de Wit in the 1960-1990 period. 

The largest presence of the populations was concentrated in the Southern Sierra Madre, in the coastal plains of the Gulf of Mexico and in a large portion of the Yucatán Peninsula; this is consistent with the information cited by ^{Loya et al. (2014)} in the sense that L. leucocephala grows in a wide variety of environments, as it has a broad range of climatic adaptation.

Figure 2 shows that the surface area with environmental aptitude of 251 134 km²,is located, mainly, in the coastal areas in the Gulf of Mexico, the Eastern Sierra Madre, the Western Sierra Madre, the Southern Sierra Madre and the Northern Sierra of Puebla, the Isthmus of Tehuantepec and a large portion of the Yucatán Peninsula. This information agrees with the data recorded by ^{Loya et al. (2014)} and ^{Heuzé and Tran (2015)}, according to which this legume has a broad distribution in Mexico and spreads in tropical and subtropical climates at altitudes ranging from sea level to 1 500 masl. This altitude interval of the species may expand due to the pressure of the increase in the temperature of the studied periods, and therefore L. leucocephala will migrate toward higher altitudes.

Environmental aptitude for Leucaena Leucocephala in climate change scenarios

The delimitation of areas for the species and its territorial dynamics, in terms of climate changes, determine in what sense they will impact the increase, reduction or maintenance of the areas of distribution.

The maps of Figure 3 show the territorial dynamics that the areas with environmental aptitude for L. leucocephala will have; in this regard, the prediction of the MCG predicts a favorable dispersion of the surface in the two climate periods and in the two representative GHG concentration routes (Table 2), although it is accentuated with the RCP 4.5 for both periods. As for the 2041-2060 period, the area with environmental aptitude will increase by 72 %, and by 61 % for the 2061-2080 scenario (Figure 4); this agrees with what has been pointed out by Gutiérrez and Trejo (2014), according to whom the effect of the climate change on the ecosystems will reflect on the alteration of the distribution and abundance of the species, or on the direct disappearance of certain taxa and populations.

Figure 3 Areas with environmental aptitude for two time periods and two RCPs with the GCM GFDL-CM3 for Leucaena leucocephala (Lam.) de Wit. 

Figure 4 Percentage of expansion of the areas with environmental aptitude (in dark gray) with respect to the reference climate in the 2041-2060 and 2061-2080 periods for two RCPs (4.5 and 8.5). 

Figure 3 shows small new areas with environmental aptitude for L. leucocephala, located in the Western Sierra Madre, specifically in the states of Sonora, Sinaloa, Chihuahua, Durango and Nayarit; in the Eastern Sierra Madre, in Nuevo León and Tamaulipas. Also, the model predicts greater increases in the Southern Sierra Madre, the Isthmus of Tehuantepec, and the Yucatán Peninsula; this agrees with the prognosis cited by ^{Hu et al. (2015)}, according to whom the climate change rates will drastically affect the groups of community and the biodiversity in the tropical areas of the Earth.

Although the RCPs agree with the tendency of the variations in the environmental aptitude surface area, they differ as to their magnitude (Table 2). This is due mainly to the variations of the precipitation, as the RCP 8.5 estimates lower annual precipitation volumes in the two future climate periods.

The above shows that the areas with environmental aptitude are sensitive to the climate simulation variations of the RCPs, even in the models that are considered to be similar in the prediction of the climate change for Mexico (^{Conde et al., 2006}).

Likewise, certain potential dynamic areas with environmental aptitude that respond to the climate change (Figure 3) occur in the central and northern regions of Mexico and exhibit changes in the cropping patterns due to the climate change (^{Ramírez et al., 2011}; ^{Santillán-Espinoza et al., 2011}).

The differences in the projections of the surface area with environmental aptitude for L. leucocephala, in the trajectories of GHG concentration of the general circulation model utilized agree with the findings of ^{Beaumont et al. (2008)}, according to whom, regardless of the model used to estimate the loss of biodiversity as the trajectories of the emissions of greenhouse gas change, the results obtained can be contrasting.

Figure 3 also shows small areas with environmental aptitude which L. leucocephala will lose in the future scenarios, mainly located, for the four RCPs, in the states of Jalisco, Michoacán, Hidalgo, Querétaro, San Luis Potosí, Guerrero, Oaxaca, Chiapas, Puebla, Morelos, Veracruz, Tabasco and the Yucatán Peninsula. This information agrees with that cited by ^{Uribe (2015)}, in the sense that the climate change predicted for the year 2050 will have serious impacts on the biodiversity of the Mexican territory.