Introduction

In Mexico between 1998 and 2014, there were 8,500 fires on average with an estimated damage of 300,000 ha·year^-1 (^{Comisión Nacional Forestal [CONAFOR], 2014}). The greatest percentage of fires (98 %) was attributed to human activities, and the rest drived from natural causes such as electrical discharges and volcanic eruptions (^{Ressl & Cruz, 2012}). Although it is apparent that human beings have favored the occurrence and frequency of fires due to their domestication, it is also evident that there have been modifications in fire regimes, to which some ecological systems have adapted (ecosystems with natural-anthropic regimes) (^{Pyne, 1995}; ^{Rodríguez, 2014}). Therefore, and in accordance to fire response, ecosystems are classified as follows: 1) dependent, 2) sensible, 3) independent, and 4) influenced (^{Hardesty, Myers, & Fulks, 2005}).

The fire dependent ecosystems require this ecological factor in order to survive in the landscape; in Mexico, these ecosystems are dominated by Pinus hartwegii Lindl. The ecosystems of this species present a natural-anthropic fire regime. The regime is characterized by high frequency (every five years on average), low intensity (^{Rodríguez, 2001}; ^{Rodríguez & Fulé, 2003}) defined by speed, flame height, and longitude (^{Willson & Sorenson, 1979}), and low to moderate severity (^{Jardel, Alvarado, Morfín, Castillo, & Flores, 2009}) characterized by tree mortality, biomass consumption, and basal area and canopy reduction with the subsequent modification of stand composition and structure (^{Fulé & Covington, 1997}; ^{Glitzenstein, Streng & Wade, 2003}; ^{Regelbrugge & Conrad, 1993}).

Pinus hartwegii is a species with adaptations to fire such as: thick bark, grass stage, basal sprouts, recovery of burned canopy, natural prune, and capacity to be regenerated in burned areas (^{Rodríguez & Fulé, 2003}). However, poor fire management strategies as fire suppression, as well as the large human contribution to these disturbances, have resulted in the high frequency or lack of fire management. Such causes have modified the fire regime in P. hartwegii ecosystems, which are associated with high mortality indices of young trees (^{Rodríguez, Martínez, & Ortega, 2004}). It has been indicated that the resistance of a tree to fire-caused mortality depends primarily on the useful morphological characteristics to protect its vital tissues (which increase with age), the ability to recover from injuries, and the season in which the events occur (^{Regelbrugge & Conard, 1993}). In the case of annual species, fires are less severe before the opening of the buds, mainly due to the existing carbohydrate reserve in the trees (^{Van Wagner, 1973}).

The importance of predicting tree mortality resides in that it is a planning tool for carrying out operations such as tree regeneration or prescribed burnings (^{Regelbrugge & Conard, 1993}). When modeling the mortality or survival of trees, the dependent variable is a binomial character (i. e., a tree is alive or dead after a period of time); therefore, the logistic regression is the most utilized mathematical expression (^{Hosmer & Lemeshow, 2000}). The tree mortality models must include variables that reflect the severity of the fire damages, in this case, proportion of crown damage is one of the most used characteristics (^{Hood, McHugh, Ryan, Reinhardt, & Smith, 2007}; ^{Van Wagner, 1973}). Likewise, the inclusion of the cambium damage reflects the increase in the probability of mortality for a given crown damage level (^{Hood et al., 2007}; ^{Peterson, 1983}).

This paper seeks to contribute to the understanding of fire as a natural process that frequently operates as an integral part of the ecosystem where it occurs and therefore, fire can be utilized as a tool for the integral management of the dependent ecological systems. The objective was to evaluate and model the P. hartwegii trees probability of mortality in seedling and sapling stage development, under a low intensity prescribed burning and to a medium to high fire intensity, in a forest under conservation conditions. The main hypothesis considers that the individual probability of mortality is greater when there is a larger proportion of crown damage, greater fire scar height, and lower bark diameter.

Materials and methods

Area of study

The area of study is located in the Iztaccíhuatl-Popocatépetl National Park, found in the eastern central part of the Trans-Mexican Volcanic Belt in central Mexico. The site is known as Telapón hill and is found between the extreme coordinates 19º 22’ 8.4” -19° 22’ 44” LN and 98º 42’ 32.40” - 98º 43’ 1.2” LO, at an average altitude of 3,800 m (Figure 1). The climate is temperate, sub-humid, with rain in the summer and an annual average temperature of 15 °C (^{García, 1988}). The soil is Andosol with a sandy-loam texture, a dark brown to black color, and with 2 to 8 % organic matter (^{Secretaría de Medio Ambiente y Recursos Naturales [SEMARNAT], 2013}). The dominant vegetation is the P. hartwegii forest and among the most common species in the undergrowth are Lupinus montanus Kunth, Muhlenbergia quadridentata (Kunth) Trin., Festuca spp., Calamagrostis spp. and Acaena elongate L. (^{Rzedowski, 1978}).

Figure 1 Location of the area of study for the probability of mortality evaluation of Pinus hartwegii in the Izta- Popo National Park. 

Treatments

On March 3, 2013, a fire occurred affecting 59 ha of the study area. Subsequently, on March 15 of the same year, preliminary observations were made of the percentage of trees cown damage, which served as the basis to choice the area of evaluation. The main assumption was that with a greater percentage of crown damaged in the trees of this area, a better contrast would be obtained in comparison with prescribed burning, and that by utilizing the trees of the two zones in the survival modeling, a higher response interval would be obtained for different crown damage ratios. On the same date, the appropriate sites were determined to carry out the prescribed burning and for the establishment of the control area; the location of the forest roads was a priority. A clinometer (Suunto® PM5/1520, Finland) and a compass were utilized for the homogenization of the areas with regard to gradient and exposure. The preselected locations were georeferenced using a GPS (Garmin GPSMAP® 78, USA) with a maximum precision of 3 m for their subsequent location in the map. The points located in the field were verified with the program ArcGIS 9.3® (^{Environmental Systems Research Institute [ESRI], 2009}) and then proceeded to the selection of the previously standardized areas. A digital elevation model was utilized for the area of study at a 1:50,000 scale (^{Instituto Nacional de Estadística y Geografía [INEGI], 2013}), with which gradient (30 to 40 %), exposure (E-SE), and altitude (3,780 to 3,900 m) maps were obtained.

Finally, according to previous obtained values, the optimal surfaces for the delimitation of the burned area, the establishment of the prescribed burning and the control area were determined using the algebraic map technique (^{De Mers, 2002}). Figure 2 shows the three selected areas.

Figure 2 Delimitation of the areas of study for the probability of mortality evaluation of Pinus hartwegii in the Izta-Popo National Park. The numbered points represent the sampling sites.  

Four ha were delimited of the total burned area, The preliminary evaluation showed that in this area wind and slope favors the fire, with an average flame height of 2.5 m. The flame height was calculated through random sampling from the scar height of 50 trees in the evaluated area. The prescribed burning was carried out on April 13, 2013, with drip torches as a mean of ignition and backing strips as the burning technique. The wind speed at medium flame was 10 km·h^-1, average relative humidity of 34 %, average temperature of 13 °C, and fire speed was 5 m·min^-1. The activity finished when wind gusts reached 15 km·h^-1, the relative humidity decreased to 29 %, the temperature increased to 16 °C, and the flame height reached 1 m, resulting in a treated surface area of 1 ha. The burning was done based on the standard established in the NOM- 015-SEMARNAT/SAGARPA-2007 (^{SEMARNAT, 2007}) and with the collaboration of specialized fire workers (Universidad Autónoma Chapingo, Comisión Nacional Forestal (CONAFOR) and the Comisión Nacional de Áreas Naturales Protegidas (CONANP) crews), as well as two community crews (Figure 3). The flame height for the prescribed burning and wild fire were the fire intensity indicators (^{Willson & Sorenson, 1979}). The control area remained delimited to 3.5 ha.

Figure 3 Prescribed burning for the probability of mortality evaluation of Pinus hartwegii: a) start of the prescribed burning (ignition of belt one), b) fire behavior, c) ignition of belt two, d) experimental site moments after the prescribed burning.  

Results and discussion

In general, low mortality indices were shown for P. hartwegii in the three treatments. Mean mortality was 28 % in the fire area, 13 % in the prescribed burning, and 3 % in the control.

The low mortality in the fire area is attributed to a short residence time at high or lethal temperatures fires a characteristic related to fire adaptation P. hartwegii (^{Rodríguez et al., 2004}), and to the temporality in which the fire occurred. ^{Vera and Rodríguez (2007)} evaluated the same species in the Ajusco zone in the Distrito Federal and reported lower mortality indices for high intensity fires that occurred in the March (13.9 %) compared to those that occurred on May (52 %) two years after treatments application.

The high mortality presented in the prescribed burning probably was due to the application timing (April). ^{Vera and Rodríguez (2007)} reported a mortality of 67 % for a high intensity prescribed treatment (that emulated wild fire), 4.4 % for a low intensity burning, and 4.2 % for the control area in treatments established in March. The differences between the study by Vera and Rodríguez and this paper could be attributed to the variability in the fire behavior and to the temporality in which this factor presented itself (^{Ryan & Reinhardt, 1988}; ^{Vera & Rodríguez, 2007}). ^{Vera and Rodríguez (2007)} also report that the low intensity prescribed burnings in the month of May can reach up to 14.5 % mortality, due to the accumulated dryness during the fire season (evaluation carried out two years after applying the treatments). Other influencing factors are the tree vigor before the prescribed burning (^{Ryan & Reinhardt, 1988}) and the seasonality of bud growth (^{Wagener, 1961}). Both of them, can be important and defining factors, given that in the study area, dwarf mistletoe (Arceuthobium sp.) is present; furthermore, it was visually confirmed that the beginning of bud elongation coincided with the application of prescribed burning, exposing the sapling buds to the fire effects.

The probability of mortality models were adjusted from a final basis of 549 trees, obtaining six models in accordance with the parsimony and significance of parameters (Ӽ² P < 0.05). None of the generated models include the unit inside the Wald confidence interval and, in general, all of them showed good concordance between the percentage of the predicted probabilities and the observed probabilities. It can be seen in Table 2 that the minimum concordance values are close to 60 % and that the models structured from PCD showed greater concordance to the prediction with regard to the appearance of the mortality event. The most consistent explicative variables in the models of the sapling category (1.3 to 6.0 m) were PCD and DNCC, although this latter variable was only consistent in the case of the total modeling. In the case of the seedlings, the probability of mortality was explained in a greater percentage due to the scar height and, finally, for the general model, the most explicative variables were both the PCD and the scar height (Table 2).

Figure 4 shows the mortality behavior of P. hartwegii in each of the generated logistic models. Based on the models, the maximum probability of mortality of seedlings with a scar height of 1.29 m is 44 % (Figure 4a). In the sapling category, the DNCC and PCD were the most important explicative variables. According to this, the maximum individual probability of mortality estimated with the total model on the individuals with DNCC of 1 cm was 13 % (Figure 4b). Regarding the PCD, the young trees showed a maximum probability of mortality of 52 % in the total model, whereas the maximum values in the prescribed burning and conflagration were 43 and 57 %, respectively (Figure 4c). Finally, the general model was determined by the PCD and ACtz, variables that favored the probability of mortality as the values increased (Figure 4d).

Figure 4 Individual probability of mortality of the Pinus hartwegii trees in function of: a) scar height in saplings, b) normal bark diameter in stem exclusion, c) damaged canopy by treatment and total in stem exclusion, and d) damaged canopy and scar height for all trees.  

The probabilities of mortality of P. hartwegii obtained with the generated models correspond to those reported by other authors. In general, the probability of mortality increases when the measure of the trees is smaller, in this case trees less than 1.3 m in height, due to the damages caused to the cambium (^{Peterson & Ryan, 1986}), independent of the quantity of the damaged canopy. This is basically due to the younger trees having a tendency to have thinner bark (^{Costa, Oliveira, Viexas, & Neto, 1991}; ^{Regelbrugge & Conard, 1993}). ^{Wyant, Omi, and Laven (1986)} determined that the damage to the cambium is correlated to the ACtz. In this study, the ACtz was the characteristic that showed the best results in predicting mortality in saplings; as this variable increases, the individual probability of mortality is greater (Figure 4a).

In the case of trees greater than 1.29 m in height, mortality is influenced mainly by the PCD and DNCC (Table 2). The DNCC-mortality relation is notably inverse (Figure 4b), which coincides with the results of ^{Vera and Rodríguez (2007)}. The PCD is one of the indicators most utilized in determining mortality (^{Hood et al., 2007}; ^{Peterson, 1985}; ^{Ryan, Peterson, & Reinhart, 1988}). The models generated in our study show that at a greater PCD there is a greater probability of mortality, which coincides to that established for Pinus ponderosa Dougl. ex Laws (^{Wyant et al., 1986}) and P. lambertiana Dougl. (^{Mutch & Pearson, 1998}). The mortality of these species is influenced mainly by the substantial crown reduction (^{Wyant et al., 1986}) and, therefore, a decrease in the production of photosynthates. Figure 4c shows that in the sapling category, the model predicts the least probability of mortality in the area with prescribed burning when there is 100 % damaged canopy, in comparison with fire or the total model. ^{Vera and Rodríguez (2007)} also found that P. hartwegii mortality in prescribed burnings in comparison to forest fires is much less during fire season. The inflexion points (around 70 % damaged canopy) of the curves defined by the PCD models coincide with those generated by ^{Stephens and Finney (2002)} for P. ponderosa. This suggests that the deficit in the production of photosynthates behaves in an exponential way after the loss of three fourths of the canopy. The general model shows the combined effect of PCD and damage to the cambium, represented by the ACtz (Figure 4d); it is observed that tree mortality increases when damage to the canopy is accompanied by damage to the conductive tissue.

Conclusions

The probability of mortality increases with a greater percentage of crown damage and thinner bark diameter in trees classified as saplings; in the case of the seedlings, the probability increases with a greater scar height. Therefore, the probability of mortality in trees of 0.3 to 6.0 m increases by the interaction of a greater scar height and percentage of damaged canopy. The mortality was less in prescribed burning than in the fire area, which is attributed to a greater fire intensity in the later. The prescribed burning presented 54 % less mortality than the fire area, but four times high mortality than the control area, due mainly to the tree vigor before the burning and to the timing treatment. Prescribed burnings are a viable tool in the management of fire dependent ecosystems (i.e. P. hartwegii); however, it is recommended that future studies evaluate the characteristics of the behavior and temporality of fire, as well as the physiology of the trees, with the purpose of providing more elements to the forest managers such as when and how to implement this tool and the possible responses of the species to the stress of fire.