The study area was continental Chile. This territory extends from 17.5° to 56° S latitude, with an elevation range from sea level to over 6000 m. Its topography may be divided into four characteristic zones, roughly from east to west: the Andes Range, the Intermediate Depression, the Coast Range and the littoral flatlands, thus this territory includes a broad range of climates and vegetation. It is divided into 15 administrative regions.

We used only climatic grids for this study, which were downloaded from the WorldClim database ( http://www.worldclim.org) at a spatial resolution of 2.5 arc-min, about 4.63 km at the equator (Fourcade et al., 2014). This continuous grid format must be transformed to ASCII format in the ArcGis 10 software (ESRI, 2012) to use it in Maxent. Variables such as altitude, slope and exposition were not used for the model, since the layers of Worldclim (Hijmans et al., 2005) were constructed using altitude, thus avoiding the problem of spatial autocorrelation (Legendre, 1993). Ayerza (2009) suggested that the length of the growth cycle was related to temperature and not to altitude, and Martínez et al. (2012) indicated that the areas closest to sea level are the warmest, and temperature decreases with increase in elevation.

We used the environmental layers of extreme temperatures (maximum and minimum of the coldest and warmest months) and the mean annual precipitation from the Worldclim project (Hijmans et al., 2005) to calculate the main climatic requirements. We selected variables from the 19 bioclimatic variables of Worldclim (Hijmans et al., 2005) for the models that produced the aptitude map; these are the most often used predefined bioclimatic variables available in the Worldclim global database of climate surfaces (Hijmans et al., 2005; Pliscoff & Fuentes, 2011; Duarte et al., 2014; Peña et al., 2014). These variables are: annual mean temperature (Bio1); mean monthly temperature range (Bio2); isothermality (Bio3); temperature seasonality (Bio4); maximum temperature of warmest month (Bio5); minimum temperature of coldest month (Bio6); temperature annual range (Bio7); mean temperature of wettest quarter (Bio8), mean temperature of driest quarter (Bio9), mean temperature of warmest quarter (Bio10); mean temperature of coldest quarter (Bio11); annual precipitation (Bio12); precipitation in wettest month (Bio13); precipitation in driest month (Bio14); precipitation seasonality (Bio15); precipitation in wettest quarter (Bio16); precipitation in driest quarter (Bio17); precipitation in warmest quarter (Bio18) and precipitation in coldest quarter (Bio19). The variable selection was made using the Pearson correlation matrix in the ENMTools software version 1.3 (Warren et al., 2008), considering as significant those variables with r>0.65, as recommended by Phillips et al. (2006). This selection was made to avoid spatial autocorrelation (Legendre, 1993) and to avoid overfitting errors in the model.

After eliminating duplicated points, occurrences were selected so that there was no more than one point in each pixel of the environmental layer grid, thus avoiding spatial autocorrelation (Legendre, 1993). These filtering processes were performed using Microsoft Excel and ArcGis 10 (ESRI, 2012). We compiled 78 records of presence (occurrence) of chia around the world to perform the modeling. Sixty of these points were located in its native range and were obtained from GBIF (2015); the other 18 points were locations where it is grown without irrigation outside its native range, and were obtained from the studies of Ayerza and Coates (Coates & Ayerza, 1996, 1998; Ayerza & Coates, 2004; Ayerza, 2009, 2010, 2013), the Virtual Herbarium of Australia (AVH, 2015) and GBIF (2015) (Fig. 1).

The spatial modeling of the SDM was generated with the Maxent version 3.3.3k software (Phillips et al., 2006), which creates a statistical model that estimates the probability distribution of maximum entropy. The result is interpreted as the environmental suitability of an area for a species to develop, which has also been called the probability of presence. For every scenario we always generated a pair of species distribution models with the same 2.5 arc min spatial resolution but different extension, the native range and the world range, in order to search for greater niche breadth in the model. The background of the native range model was limited to the territory of the countries of Mexico, Guatemala, Belize, El Salvador, Honduras, Nicaragua and Costa Rica. The occurrence points were divided randomly, 75% to create the model and 25% to validate it. The mean of each model was estimated with 50 bootstrap replicates. Although Phillips et al. (2006) recommended leaving the default quantity of pseudo-absences, we modified them in this study since different ranges were used for the models. For the native range model we tested 600 (10 x presences), 2000, 5000 and 10,000 pseudo-absences, and for the world range we tested with 780 (10 x presences), 2000, 5000 and 10,000 pseudo-absences. The number of pseudo-absences was calibrated for each model using two evaluation criteria, the area under the ROC (receiver operating characteristic) curve, called area under the curve (AUC), and the omission test. We used the AUC because it is the one most used by other authors, in spite of the criticisms it has received. One of the problems associated with the use of ROC curves is that there must be true absence data, which generates an error since the abscissa of the graph would only be the proportion of area predicted by the model. Another problem is that the method assigns the same weight to errors of omission and commission; however, omission errors are more important because they are areas that the model is incapable of predicting, which might be important for the survival of the species (Mateo et al., 2011). The value of the AUC is among the results of Maxent for each model and it was interpreted using the recommendation of Swets (1988): < 0.6 bad; 0.6-0.7 poor; 0.7-0.8 acceptable; 0.8-0.9 good, >0.9 excellent. The omission test was performed using the 10% cutoff point returned by Maxent with the ArcGis 10 software (ESRI, 2012). The rest of the configuration used the default values as recommended by its authors (Phillips et al., 2006).

The climatic requirements of the crop were defined using performance curves, which indicate the performance of a species according to each environmental variable considered; these are analogous to thermal performance curves (Schulte et al., 2011). They identify the range of values for each variable in which the species can survive and the range in which it develops ideally, as Ecocrop (2007) has determined for more than 2300 plant species. This may also be interpreted as the search for the tolerance of the species to different environmental variables, since these tolerance limits define the spatial limits of distribution. Growth and reproduction are limited when the abiotic variables are near the tolerance limit, which is directly related to the abundance and production yield of the species (Richards & Janes, 2011). Performance may be measured in different ways, including survival, reproductive success and fitness (Pianka, 2011), however these are empirical measures. Performance is optimized in the optimal range, between the minimum and maximum optimal values (On and Ox), while it declines to 0 at the critical minimum and maximum values (Cn and Cx) which define the tolerance range (Fig. 2A).

The Maxent software generates response curves after creating an SDM, which are associated with the performance curves of a species. As response curves are a priori estimations, they substitute performance for probability of presence (Morales et al., 2015). The performance curves were defined for two variables, temperature and precipitation, similar to the Ecocrop (2007) definition and considering the dependence of crops on these variables. Temperature determines the overall effect on growth (Fernández & Johnston, 2006); the growth and development of a plant occurs within a framework of temperatures in which below the minimum it does not grow, it grows at a maximum rate with the optimal temperature and does not grow and may die at above the maximum temperature (Salisbury & Ross, 2000; Vidal, 2009). Water is fundamental for plant growth, since without it there is no photosynthesis or nutrient transport. Scarcity of water decreases both yield and the quantity and quality of production, while an excess does not allow the roots to respire (Martínez et al., 2012).

Using the response curves returned by Maxent we calculated the values for each environmental variable independently of the others, using the value of 0.5 for probability of presence (PP). Since Maxent returned probability values less than 1 even within its native area, the values were normalized by the maximum value, thus the current rule was applied to the adjusted probabilities. Using these criteria, we defined analysis parameters a-e from properties of the curve (Fig. 2B): a is the variable value with 0.5 PP adjusted and before maximum; b is the variable value with 0.5 PP before the maximum; c is the value of the variable at maximum probability of presence; d is the value of the variable with 0.5 PP above the maximum and e is value of the variable with 0.5 PP adjusted and above the maximum. With these five values we obtained the mean between the analogous pairs according to the two extension models. For the temperature variables we calculated the mean of the values a and b, and the mean of d and e. Finally, the performance curves were defined using these ranges.

Using the selected bioclimatic layers along with the described occurrences and the Maxent configuration described we generated 2 SDM scenarios; scenario A with precipitation and temperature layers and scenario B with only temperature layers, both worldwide. Scenario A corresponds to cultivation without irrigation, and scenario B to cultivation with irrigation so precipitation is not a limiting factor. To extend the models to Chile we configured the software with a projection to the Chilean territory, with the layers also entered in ASCII format with 2.5 arc min resolution and processed in ArcGis 10 (ESRI, 2012). The importance of the model variables was tested using Tukey's jackknife (Phillips et al., 2011). Once the model was chosen based on the parameter calibration, the suitability values returned by Maxent were classified for the Chilean territory analogously with the aptitude classes of the Agro-Ecological Zoning of crops (AEZ) proposed by FAO (1996), which are: 0-0.2 "not suitable”; 0.2-0.4 "marginally suitable”; 0.4-0.6 "moderately suitable”; 0.6-0.8 "suitable”; 0.8-1 "very suitable”. Finally, we generated the corresponding maps in the ArcGis 10 software (ESRI, 2012).

Calibration and evaluation of the models. To obtain the response curves from Maxent we produced two models of different extension, the native range and worldwide. The number of pseudo-absences was defined as 50,000 for the worldwide model and 5000 for the native model, according to the results of the AUC and the omission test. The best AUC (0.977) was given for the world model, considered as an excellent model, with 8.9% omission (7 points). The chosen native model had an AUC of 0.928, also considered excellent, with 11.7% omission (7 points).

Precipitation performance curve. The maximum probability of presence for annual precipitation was 0.6 for both models according to the response curves, which corresponds to approximately 1000 mm/yr ( c analysis value). The critical and optimal values for annual precipitation were obtained directly from the proposed analysis values, in which a generated the value C _n, 660 mm/yr, b produced the value O _n with 780 mm/yr, d generated the value O _x with 1560 mm/yr and e produced Cx with 2130 mm/yr (Fig. 3A).

Temperature performance curve. The maximum probability of presence for the four variables was between 0.6 and 0.7, for both the native and world models. The minimum temperature of the coldest month (Tnc) was excluded from the results because it included very low values, incompatible with the intolerance of the species to frosts. The critical and optimal values were thus defined with the a-b and d-e means of the variables maximum temperature of the coldest month (Txc), minimum temperature of the warmest month (Tnw) and maximum temperature of the warmest month (Txw). The temperature value of Cn was defined with the a-b mean of Txc and was 10° C. O _n was defined with the d-e mean of Txc; it coincided with the a-b means of Tnw and Txw, which confirmed the value of O _n. Thus the minimum optimum (O _n) was estimated to be 18 °C. The O _x value for chia was defined as the d-e mean of Tnw, which was 26 °C. The maximum critical temperature was estimated as the d-e mean of Txw, which was 29 °C (Fig. 3BCDE).

Scenario definitions. The bioclimatic variables to generate the SDM of chia were selected as the least correlated variables; these were Bio1 (annual mean temperature), Bio2 (mean diurnal range), Bio4 (temperature seasonality), Bio 12 (annual precipitation) and Bio15 (precipitation seasonality). Thus scenario A was composed of these five variables, while scenario B considered only the temperature variables Bio1, Bio2 and Bio4.

Evaluation and calibration of the models. Models of scenarios A and B were both classified as excellent with an AUC of 0.97, while the omission test indicated 8.9% of the points omitted (7 points) for both models. Pseudo-absences were established as 50,000 according to the AUC obtained. The jackknife test of the SDM of scenario A showed that annual mean temperature (Bio1) was the variable that contributed most. The order of the contribution of the other variables was Bio4, Bio12, Bio15; the variable that contributed least was Bio2. However, the set of variables produced a much better model than any variable by itself. The same order of contribution of the temperature variables was found for scenario B.

World SDM. The climate envelope for scenario A shows aptitude zones in equivalent latitudes for both hemispheres, located at or near the Tropics of Cancer and Capricorn (23° 26' 14'' in both hemispheres). This confirms the exclusively tropical nature of the species. It also shows that the potential distribution according to this realized niche model is quite restricted, which explains why the species is not found globally. The model showed a maximum presence probability of 0.94 (Fig. 4A). It must be noted that for this scenario there are other countries besides Guatemala and Mexico that have a high presence probability of the species (>0.6), including Bolivia, Peru, Ecuador, Colombia, Kenya, Angola, Zambia, Zimbabwe, Congo, Ruanda, Burundi, Malawi, Madagascar and particularly Ethiopia, where the presence probabilities are greater than 0.8. In all these countries chia could be grown as a rainfed crop.

Since the precipitation variables were excluded for irrigated cultivation (scenario B), the geographic distribution of the niche covered a wider range than in scenario A, expanding to areas near the tropics in both hemispheres. Model B had a maximum probability of presence of 0.92 (Fig. 4B). The areas with greatest presence probability (>0.6) are places where the species could be cultivated and included the following additional countries: Chile, Venezuela, Brazil, Panama, Costa Rica, Dominican Republic, Honduras, Namibia, South Africa, Tanzania, Democratic Republic of Congo, Uganda, Yemen, Indonesia, Papua New Guinea, India, Vietnam and Kenya, all with presence probabilities above 0.8.

Zoning of climatic suitability in Chile. The projection of the model for scenario A indicated that Chile is not a plausible niche for chia, since in addition to the low probability of presence obtained, the layer of winter precipitation that was included enabled areas where precipitation occurs in winter while temperatures are too low for the plant to develop; this result indicates that rainfed cultivation is not feasible in mainland Chile. The highest climate category was "moderately suitable”, mostly in the Maule region; however, this area has frosts, which would impede its development (Fig. 5A).

The zoning for scenario B showed favorable results for agriculture under irrigation. According to this scenario the Chilean territory had a "very suitable"area of 11556.76 km ², mostly in the Antofagasta region but also including Atacama. The "suitable"category included an area of 58545.82 km ², located in the Arica y Parinacota, Tarapacá, Antofagasta, Atacama and Valparaíso regions. The "moderately suitable"area additionally included the coastal areas of Coquimbo and a large part of Valparaíso region. Table 1 shows the total areas by category of climatic aptitude with irrigation. Note that the category "marginally suitable"was present in 13 of the 15 regions of the country.

Figure 5B shows the map of climatic zoning for chia in Chile with irrigation. Most of the suitable area is located in the littoral plains and intermediate depression of Antofagasta, followed by the Arica y Parinacota and Atacama regions. The Andes Range zone was completely excluded, given the low temperatures in the higher altitude zone. The areas in the "very suitable"and "suitable"categories are mostly located in the northernmost part of Chile, which include the highest temperatures in continental Chile that fulfill the temperature requirements of the species. The "suitable"category also includes a small area in the Valparaíso region, while the "moderately suitable"category includes the entire coastal edge and intermediate depression of the northern part of the country, along with two small areas in the Metropolitan region and two regions farther south, Maule and Bío-Bío.