The statistical models were developed using  MaxEnt (Phillips and Dudik 2008, Elith et al. 2011), a map-based modeling software that is frequently used for species distribution modeling, but has been successfully used for modeling fire risk and ignitions (e.g.,Syphard et al. 2012, Bar Massada et al. 2012).  Through iterative contrasts between fire occurrence locations and background locations distributed across the entire study area, the model uses a machine-learning approach to find the best distribution pattern, i.e., the one with maximum entropy.  The output of the model is an exponential function that assigns a probability of fire occurrence to every cell across the gridded map.  Therefore, the maps here should be interpreted as the relative likelihood of fire occurrence across the given landscape.  Because of the stochastic nature of fire, these maps are not predictive and should be evaluated probabilistically.

We used two sources of fire data to train the model.  One database included spatial coordinates obtained from federal agencies who own land in the region (including NPS, BIA, BLM, USFWS, and USFS) from 1970 – 2010, and the other included spatial coordinates for fires on non-federal lands from 1992 – 2013 (Fire Program Analysis, Fire-Occurrence Database (FPA FOD) (Short 2014)).  All data included the date and size of the fire.  We selected predictor variables based on hypothesized relationships with fire distribution patterns, and descriptions are in the table below.

For each map, we ran three cross-validated model runs using ten thousand random background points.  This resulted in a total of 2841 presence records for training and 1421 for testing for the all fire dataset and 219/110 for large fires. We used hinge features, linear, and quadratic, with an increase in regularization with a beta of 2.5, to reduce model overfitting (Elith et al. 2011).  Finally, we estimated explanatory variable importance with jackknife tests.

The maps and results presented here represent the average across the three replicates.  The average AUC for the cross-validated replicate runs was 0.75 for all fires 0.81 for large fires.