Introduction

The climate is a set ofweather conditions specific to a place, consisting of the amount of precipitation and temperature whose action influences the existence ofbeings subject to it. The changes experienced by the climate on climate history in a region and that persists for an extended period are called climate change and is due to both natural and anthropogenic causes (^{Crowley and North, 1988}).

According to the Intergovernmental Panel on Climate Change (^{IPCC, 2013}) the occurring climate change will impact different regions of the world, the warming of the climate system is unequivocal and since the 1950's, many observed changes is unprecedented. For all scenarios considered representative concentration pathways (RCP), except for RCP2.6 scenario is likely to have a temperature higher than 2 °C increase by 2100.

Future estimates of the effects of climate change predict that in Latin America are significant, irreversibly affecting ecosystems and the services they provide (^{Vergara et al., 2007}). Figures from the World Bank (Bank) for disaster risk reduction indicate that Mexico is among the countries most vulnerable because its territory is highly exposed to the risk of direct adverse effects of climate change. Among the effects of climate change are reducing the availability ofwater, increased flooding, droughts, reduced agricultural yields and loss of biodiversity (^{Herran, 2012}).

In countries within Central and South America have been studies on the effect on climate change on life zones Holdridge (^{Mendoza et al., 2001}), with estimates reflected in his involvement on ecosystems. This is because in the living areas of Holdridge partnership as a natural unit proposed in which vegetation, animal activity and climate are all interrelated in a single recognized combination (^{Holdridge, 1996}).

It is important to consider that a life zone represents the climatic conditions that influence the potential vegetation and ecosystem functioning and not the state of vegetation cover in a given time. The variables used for classification are factors that represent ecophysiological restrictions on plant growth (^{Lugo et al, 1999}).

In our country there have been significant efforts in order to estimate the spatial distribution of climatic conditions under different models and scenarios developed by the IPCC (^{Roeckner et al, 1996}; ^{UNIATMOS, 2014}) where the general trends are evident of increases in temperature (^{Trejo et al., 2007}); however, information regarding studies on the vulnerability of ecosystems is quite low, usually focused on very particular plant or animal species.

One of the main constraints that exist, even in works where we have used the bioclimatic zoning system Holdridge experimental unit to the climate change scenarios, is the omission of the bioclimatic zones of transition, where ecosystems are particularly sensitive to climate change (^{Jiménez et al, 2010}). An ecosystem is the set of species in a given area interacting with each other and with their environment. Mexico has a land area of 1 964 375 km² therefore for analysis focused on the behaviour of ecosystems to changes in climate, it is convenient to define areas of study that yield meaningful information even with small variations of temperature increase and decrease rainfall.

In response to this need, the objective of this study is to perform a bioclimatic zoning based on model life zones Holdridge, defining the transition areas prone to warm-dry and warm which are particularly sensitive to increases in temperature and decreases in precipitation.

Materials and methods

A computer system bioclimatic zoning for the Mexican republic based on the methodology of ^{Holdridge (Holdridge, 1996}) was conducted. Biotemperature, potential evapotranspiration and the average annual precipitation was calculated. The estimation of climatic factors for zoning as a source of information was the data contained in the Quick Climatological Information Extraction (ERIC, III), container for the stations of the Mexican Institute of Water Technology (^{IMTA, 2013}).

A historical series of climatological data was processed 1961-2003 range and spatial distribution of monthly maximum temperature, monthly minimum temperatures and

total annual precipitation was estimated, the result was a set of raster files with spatial resolution of0.001665 degrees of units arc. Estimating the sequence of the living areas was performed as shown in Figure 1.

Figure 1 Diagram of the sequence descriptor estimation living areas (CU) regions of humidity (RH), latitudinal regions (RL) and altitudinal regions (RA). 

Biotemperature estimation, which is defined as the air temperature, about 0 °C and 30 °C, which determines the rate and intensity of the physiological processes of the plants (plant photosynthesis, respiration and transpiration are performed ) and the rate of direct evaporation of water contained in the soil and vegetation (^{Crivelli and Dzendoletas, 2002}).

To calculate the average monthly biotemperature (BMM), there are three cases using the average monthly temperature (TMM):

Where: BMM= monthly average biotemperature; TMaxM= maximum monthly temperature; and TMinM= minimum monthly temperatura

The mean annual bio-temperature (BMA) was estimated using the following equation.

3)

Where: BMA= annual average biotemperature; BMM= monthly average biotemperature; and n= number of months.

Potential evapotranspiration, which is the amount of water that can be evaporated directly from the soil and transpires natural vegetation in a stable state that is located on a soil of good characteristics and optimum moisture content was calculated (^{Samani, 2000}). It was estimated by the following equation.

4)

Where: EP= potential evapotranspiration; and BMA= annual average biotemperature.

The ratio of potential evapotranspiration is a function of biotemperature and precipitation, is an index ofthe humidity that reflects the availability of water for plant growth and ecological processes (^{Holdridge, 1996}; ^{Lugo et al., 1999}). It was estimated by the following equation.

5)

Where: REP= ratio of potential evapotranspiration; EP= potential evapotranspiration; and PMA= annual rainfall.

Once estimated each of the components required proceeded to use the nomogram "Holdridge" to identify bioclimatic zones. One of the main drawbacks of the classification system Holdridge is the use of logarithmic progressions in the nomogram, which limits its use practically only graphic interpretations. To correct this situation logarithmic nomogram units were transformed to linear units using the following equations:

6)

Where: Da= distance in linear scale; Vb value= transform; Li= lower limit ofeach range logarithmic scales; and 2/log2= constant associated with the spacing between the values of the logarithmic scales. 2 ensures that the distance between logarithmic graphs is 2 cm intervals.

7)

Where: Ci= corrected linear distance; Da= distance in linear scale; and Di= cumulative spacing intervals from the origin to the desired position.

The units conversion chart nomogram allowed to play in a Cartesian plane with linear units since its basic structures. The software used for this activity was the AutoCad®. Start assigning a coordinate (x, y) was possible to reconstruct each of the components of the nomogram in an environment that combines graphical and analytical tools (Figure 2).

Figure 2 Nomogram full Holdridge in AutoCAD®. 

Once plotted hexagons that make up the living areas and expressed in a Cartesian plane linear units was possible to obtain the centroids in x, y coordinates of each of them as well as the ranges that define each of the latitudinal regions altitudinal and moisture classification system.

A method to estimate the spatial location ofthe REP and PMA units developed coordinates x, y. For this it is first necessary to find the location of each value on its line of origin of the nomogram by equations.

8)

Where: x= X coordinate of the line of origin of the nomogram; 0= angle between the lines REP and PMA (60°); and Di= spacing intervals accumulated from the source to the desired position.

9)

Where: ya= Y coordinate of the line of origin of the nomogram; 0= angle between the lines REP and PMA (60°); and Di= spacing intervals accumulated from the source to the desired position.

We have that:

10)

Where: b= intercept m= slope of the line; and 0= ordinate of the origin of the nomogram.

Obtained values (xa, ya and b) for REP and PMA proceed to make use of the equation of the line for each of them.

11)

Where: y= value corresponding to the y-axis, x= X coordinate of the line of origin; nomogram; m= slope of the line; and b= intercept.

Finally, the equation system is solved and the result is a pair of coordinates (x, y) corresponding to a location within the nomogram.

Each of the hexagons of living areas has a centroid coordinates (x, y) therefore, the closest pair of coordinates resulting system of equations REP and PMA centroid will correspond to hex the living area that concerns. The altitudinal and latitudinal soils are well defined by the coordinate axis and within the grid while the moisture region is defined directly by the values of REP (Figure 3).

Figure 3 Modelling of a pair of coordinates that allow the location of a living area. 

One of the most important characteristics of the nomogram Holdridge is the ability to identify areas hexagons transitional living areas (Figure 4). The main lines of the hexagons are the limits of each area of life. The biotemperature guide, precipitation and potential evapotranspiration ratio, lines form six triangles in each hexagon. These triangles are the transition areas. Within each triangle, two of the three main factors correspond to the same region, the same province of moisture or precipitation band corresponding to the main body of the hexagon. The third factor relates to the region, girdle, province or precipitation regime of the neighbour hexagon (Jiménez, 1993).

Figure 4 Transition zones in a living area 

A software system written in C language, which performs the operations described above to pixel level, once we supply climate information in raster format was developed. This allows us to play the automated procedure being in a position to repeatedly test data both current and future scenarios of precipitation and temperature caused by climate change. In the analysis were not considered corrections for soil, water and atmospheric associations.

Validation of the model

In order to verify the veracity of the living areas, a comparison between the estimated and measured data areas directly in the field through the upheavals of the National Forest Inventory and Soil Project (INFyS) (^{CONAFOR, 2011}) was performed. 24 sampling sites for each information regarding geographic location, dominance and species richness were selected (Table 1). By using the geographic location of each site was removed from the map of life zones and grade accordingly proceeded to make an assessment of the correlation as shown in the Table 2.

Table 1 Data From field surveys INFyS 

Table 2 Evaluation of matching living areas estimated and observed by the INFyS. 

Concordance evaluation was performed by the Kappa coefficient (^{Cohen, 1960}), using equation 12.

12)

Where: K = Kappa coefficient, N = number of elements; Xij = sum of the diagonal; Xc = sum of columns; and Xl = sum of lines.

According to the evaluation of agreement made, a value of 0.95 was obtained. The theoretical Kappa coefficient takes values between 0 (total disagreement) to 1 (full agreement) thus obtained the degree of agreement is almost perfect (^{Landis and Koch, 1977}), demonstrating the validity of bioclimatic zoning.

Similarly, to assess the sensitivity of the transition zonez to climate change, we proceeded to make a comparison of the current status of bioclimatic zones regarding expected changes with temperature varations specified in the scenario for RCP2.6 period 2016-2035 the IPCC (^{IPCC, 2013})

Results and discussion

As a result of bioclimatic zoning a map was obtained with the areas of life that correspond to the Mexican republic, with other regions with humidity and latitudinal regions according to climatic characteristics.

According to the classification of areas of modern life, the classification forest dominates Mexico with 56.58% of the territory, followed by the thorny bush with 30.56%, 8.69% is desert scrub, 4.05% is made up ofdesert and finally 0.12% corresponds to steppe (Figure 5).

Figure 5 Areas of current life in Mexico 

The distribution of moisture regions of the country are estimated at 37.32% in the humid sub region; 33.61% is semiarid; 9.88% is the arid region; 4.01% is extremely arid and 0.5% is dried. Furthermore, 1.21% the country belongs to the humid region and only 0.0005% is super humid region (Figure 6).

Figure 6 Regions humidity of the Mexican Republic. 

The estimated latitudinal regions correspond to 21.96% of the country as tropical; 48.44% were classified as subtropical; 28.25% corresponds to the warm temperate region; 1.28% belongs to the cold temperate region and finally 0.07% correspond to boreal regions, subpolar and polar (Figure 7).

Figure 7 Latitudinal regions of the Mexican Republic. 

Using triangles correspond to areas of warm and dry-warm transition within areas of life, it was found that almost a third of the country (29.61%) is located in these transition zones; i.e. 581 613.86 km 2 of our country are particularly vulnerable to climate change, they consider small reductions in rainfall or temperature rises, will cause great changes in the composition of the ecosystems (Figure 8).

Figure 8 Location of surfaces in transition areas ofwarm and dry-warm. 

Result of the comparison ofthe current status ofbioclimatic zones regarding expected changes with temperature variations stipulated in the scenario RCP2.6 for the period 2016 to 2035 the IPCC are presented in Table 3. We can see the temperature increase of 0.3 °C will cause changes in current bioclimatic zones in 17.25% ofthe estimated surface as a transition zone, causing to locate its climatic latitudinal regions as warmer and drier regions of moisture. When the increase is 0.7 °C, changes in the transition surface increases to 34.65%. In Figures 9, 10 and 11, we can display the distribution of bioclimatic regions that would experience the Mexican republic, but these changes are more pronounced in the transition zones.

Table 3 Percentage ofchange experienced by transition zones in the presence ofsmall variations in temperature and precipitation. 

Figure 9 Life zones of the Mexican republic once increased 0.7 °C. 

Figure 10 Regions of moisture from the Mexican republic once increased 0.7 °C. 

Figure 11 Latitudinal regions of the Mexican republic once increased 0.7 °C. 

According to the above, sensitivity was observed for bioclimatic transition zones against small changes in temperature and precipitation, thus confirming the importance of its delimitation.

Conclusions

Bioclimatic zoning system under the methodology of Holdridge was developed. By zoning was obtained 29.61% of the land area of Mexico was located in transitional areas, which makes them particularly sensitive to climate variations. An increase of 0.7 °C can produce changes to 34.65% causing said surfaces located in warmer regions and regions latitudinal drier moisture. The demarcation of sensitive areas to climate changes provides valuable information for future research concerning the adaptive capacities of ecosystems and the effects that climate change may cause on a large-scale.