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The study area is represented by the Canton Ticino (Switzerland) (Fig. 1) a mountainous Swiss canton that ranges from 200 m to 3,400 m a.s.l. Summers are wet and warm and winters dry and mild (‘Insubrian’ climate). The mean annual precipitation ranges from 1,660 to 2,600 mm and is mostly concentrated between June and September while the mean annual temperature ranges from 3 to 12°C (source: MeteoSwiss climatic norm values 1981–2010).
Figure data removed from full text. Figure identifier and caption: 10.1371/journal.pone.0116875.g001 The study area of Canton Ticino (Switzerland) with the meteorological station of Locarno/Monti. The climate is often influenced by a dry foehn wind from the north, which occurs occasionally in the main valleys of the study area causing significant drops in the relative air humidity (down to 20%) [35]. About 50% of the total surface of Canton Ticino is covered by heterogeneous structured forest with the species composition that reflects the altitudinal gradient. The early introduced Sweet chestnuts (Castanea sativa) at low elevations [36], with an occasional mixture by other broadleaved species such as, deciduous oak (Quercus spp. ), small-leaved lime (Tilia cordata), wild cherry (Prunus avium), black alder (Alnus glutinosa), maple (Acer spp. ), and ash (Fraxinus spp.). The slopes at medium elevations (900–1,400 m a.s.l.) are dominated by European beech (Fagus sylvatica) forests, followed by Norway spruce (Picea abies) stands [37] intermixed with European silver fir (Abies alba), pine species (Pinus spp. ), and European larch (Larix decidua). Forest fire data and current fire regimes: Fire data has been collected in Ticino by the Forest Service since 1900, and geo-referenced perimeters of the burnt area exist for most forest fires since 1969 [38]. According to Pezzatti et al. [10], a significant shift in burnt area took place—starting in the 1980s—as a result of a major fire brigade reorganisation (1978) and of the start of the systematic use of helicopters for both the transport of fire fighters and aerial fire fighting. Concerning fire frequency, a relevant drop in anthropogenic induced fire ignitions without a corresponding change in the precipitation regime occurred in 1990 as a consequence of two preventative legal acts [36], [10]: the prohibition of burning garden debris in the open (Cantonal decree approved on October 21, 1987, but operational with the corresponding penalties since January 1, 1989) and the prohibition against fireworks and celebration fires on the Swiss National Day of August 1st in case of high fire ignition danger (Cantonal decrees of July 11, 1990). Present pyrologic conditions have existed therefore since 1980 concerning burnt areas and since 1990 concerning the anthropogenic fire ignitions [10]. The current monthly distribution of fires highlights the existence of three fire regime patterns (Fig. 2). During vegetation rest (December to April, hereafter called winter) fire events mostly consist of rapid spreading (surface) fires of anthropogenic origin with a major peak in March-April. During the vegetation season (May-November hereafter called summer) and in the summer months of July-August in particular, a mixed pattern consisting of slow spreading fires of both natural (lightning-induced) and anthropogenic origin (hereafter called summer natural and summer anthropogenic respectively) dominates. According to Conedera et al. [39], summer fires also have two distinct geographic distributions: lightning-induced fires are concentrated in the coniferous forests at higher altitudes and on steeper slopes than human-caused events.
Figure data removed from full text. Figure identifier and caption: 10.1371/journal.pone.0116875.g002 Monthly fire distribution of Canton Ticino.Monthly values refer to the same database used for the analysis: the winter fires from 1991 to 2012 (light grey), the summer anthropogenic fires from 1991 to 2012 (grey) and the summer natural fires from 1981 to 2012 (dark grey). In the present study, homogeneous fire regime conditions in the study area refer to the period 1991–2012 for both winter (w) and summer anthropogenic fires (sa) and 1981–2012 for natural summer fires (sn) (Fig. 2). Extending the period of the natural forest fire regime back to 1981 represents a compromise between the consistency (homogeneity) and the representativeness (quantity) of the data, since lightning-induced fire ignitions are not influenced by preventive legislation.
Meteorological data and fire weather indices: Daily meteorological data was gathered from the MeteoSwiss meteorological station of Locarno-Monti, which is considered to be representative for the whole study area (Fig. 1). The daily meteorological variables used are: Air Temperature in Celsius degree (T), Air Humidity in percentage value (H), Wind velocity in m/s (U), Precipitation in mm (P), coverage of sky in ratio between 0 and 1 (CloudCover) and coverage of snow expressed as snow presence or absence (SnowCover). From the original data, we also derived some cumulative meteorological parameters to be used as model input variables: total rainfall over the last seven days (WeekRain), the days since the last rainfall (DaysSinceRain), the sum of the last rainfall (consecutive days with rain) (LastRainSum), the dew point temperature (Tdew), that is the temperature to which air needs to be cooled to make air water vapour saturated [40] and the vapour pressure deficit (VPD) that is the difference between the saturation vapour pressure and the actual vapour pressure at a particular temperature. The meteorological variables were used as input for the Fire Weather Indices Calculator software, developed in the frame of the ALPFFIRS project by WSL (www.wsl.ch), in order to calculate fire weather indices for each day of the time interval considered (Table 1). In this study, we retained 15 of the most well-known fire indices used to assess forest fire hazards in several parts of the world (see Table 1 for more details).
Table data removed from full text. Table identifier and caption: 10.1371/journal.pone.0116875.t001 Fire indices used in this study and related input variables, meteorological data and site parameters used for calculations. When a variable is retained, the units are in square brackets. (*) single indices used as input for logistic models for the comparison with the best Maxent models (see Fig. 4 and Table 4).
In order to consider all existing fire regimes, meteorological and fire data were split according to the three fire regimes: winter (w), summer anthropogenic (sa) and summer natural (sn). Within the three fire regimes we defined the days with at least a fire ignition of the correspondent origin (anthropogenic or natural) as “fire days”, and the ratio between fire days and the total number of the days considered as “prevalence” (hereafter called background, see Table 2).
Table data removed from full text. Table identifier and caption: 10.1371/journal.pone.0116875.t002 The total number of fire days (days with at least one fire ignition corresponding to presence in the niche models) and background (the total number of the days) in the time interval considered and the prevalence value calculated as the ratio between the two previous numbers for each fire regime. Three different sets of input variables were then defined: the meteorological variables (hereafter called meteo), the fire weather indices (hereafter called indices), and the combination of a subset of both (hereafter called mixed).We decided to test also the combination of climatic variables and indices, in order to take into account both the linear information of the single meteorological variables and the complex, non-linear or cumulative information that the same variable may reflect within the complex algorithm of a fire index. To avoid redundancy, however, we retained only the combinations with all pairwise Spearman correlations among the variables lower than 0.9. See input variables in Table 3 for more details.
Table data removed from full text. Table identifier and caption: 10.1371/journal.pone.0116875.t003 Selected variables and model performances for the input variable combinations and fire regimes considered. Considered unselected (○) and selected variables (●) for the best Maxent models are shown.
As term of reference we used the logistic model. It is a particular case of the generalized linear model (GLM—[41]), also widely used in species distribution modelling because of its strong statistical foundation and ability to realistically describe ecological relationships [42], [30]. Generalized linear models are extensions of linear regression models that can handle non—normal distributions such as binomial distributions (e.g. presence-absence data; [43], [44]). GLMs are based on an assumed relationship, called a link function, between the mean of the response variable and the linear combination of the explanatory variables [43]. In our case, the link function is the “logit” function of the binary response data, and therefore the appropriate GLM is a logistic model. Each day of the study period and of the corresponding fire regime represents a binary response variable for which we considered the days with at least one fire ignition (fire days) as presence and the days without fire ignitions as absence. Among existing niche modelling approaches, Maxent is a machine learning method that uses the principle of maximum entropy on presence data to estimate a set of functions that relate environmental variables and habitat suitability, so that it approximates the species’ niche and potential geographical distribution [29]. The principle of maximum entropy is used to seek a marginal suitability function for each variable that matches the empirical data and is maximally uninformative elsewhere [45]. The functions of the environmental variables are called features [29] and may be linear, product, quadratic, hinge, threshold or categorical. The use of these functions makes it possible to consider the complexity and potential non-linearity of the species’ response to environmental factors [42]. An increasing number of features building the model is treated as a penalty to avoid creating complex and over-fitted models. In order to avoid over-fitting [45], Maxent software uses a regularization process that allows model distributions to lie in a range around empirical data. Widely used for many purposes such as biogeography and ecology, Maxent has recently been applied to wildfires to model fire occurrence in India’s Ghats Mountains [46] and fire ignition and distribution in the US [47], [34]. In the present study, we test the efficiency of Maxent in considering daily meteorological conditions as environmental variables. More precisely, for each fire regime considered, fire days represent the presences, whereas all days of the study period are the background. Daily values of the selected weather variable groups (meteo, indices, mixed) represent the explanatory environmental variables. All model analyses were performed with the R statistical package, version 3.0.2 [48]. For the Maxent model, we used the ‘dismo’ R package (version 0.8–17) with the Maxent default settings.
Model performances were evaluated with the widely-used metric AUC, which is the area under the ROC (relative operating characteristic) curve. The ROC graph is a way to depict classifiers’ ability (performance) to distinguish between correct and false classifications. ROC performances are frequently reduced to the single one-dimensional value Area Under the Curve (AUC), in order to enable a direct comparison among classifiers [49], [50], even if the single AUC value does not often communicate the rich information that the entire ROC curve can reveal [51]. The AUC is widely considered to be a very useful index (however, see [52] for a contrasting view) because it provides a single measure of overall accuracy that is not dependent upon a particular threshold [53], [54], [55]. The AUC value is obtained by calculating the area under the ROC curve derived by plotting the true positive fraction on the y-axis and the false positive fraction on the x-axis. It ranges from 0 to 1, where the 1 score indicates perfect discrimination, a 0.5 score implies predictive discrimination that is no better than a random guess, and values lower than 0.5 indicate performance worse than random. AUC is interpretable as the probability that a model discriminates correctly between presence and absence [56]. Where no reliable absence data is available, the AUC is calculated by distinguishing presence from the whole background (AUC.bg), or a random sub-sample, rather than presence from absence. This implies that the maximum possible AUC.bg will always be less than unity [57], [29]. If the species’ distribution covers a fraction p of the background (prevalence, see Table 2), then the prevalence-based theoretical maximum achievable AUC can be shown to be exactly 1 − p/2 [29] (see theoretical Maximum AUC.bg in Table 3). According to these assumptions, the AUC.bg is only suitable when comparing models trained on the same dataset. Our dataset consists of a reliable and small background allowing us to use the whole data for both modelling approaches. A preliminary comparative test on the presence-absence logistic approach allowed us to show that the values resulting from the traditional AUC and from the AUC.bg were very similar (S1 Fig.). We therefore opted to use the AUC.bg to evaluate and make both the Maxent and logistic models comparable.
To evaluate the robustness of the selected models, a k-fold cross-validation [58], [59] was used in order to make the validation more meaningful and reliable [60]. The k-fold cross-validation consists in randomly splitting the whole original data into k subsets of equal size. Of the obtained k subsets, each one is used in turn for testing and the remaining k-1 subsets for training. In the splitting process, we paid particular attention to form folds (sub-periods) of two entire and consecutive years, obtaining 11 folds for w and sa (1991–2012) and 16 folds for sn (1981–2012) fire regimes. The mean k-folds performances of the test cases were retained and used to compare the two model approaches. The differences between the classical logistic approach and Maxent were statistically verified using the non-parametric paired Wilcoxon Signed-rank test. We first tested the best models of the two modelling approaches, successively comparing the performance of both methods when applied to single indices. All statistical tests were run using the R statistical packages version 3.0.2 [48].
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