Human-caused wildfires are often regarded as unpredictable, but usually occur in patterns aggregated over space and time. We analysed the spatio-temporal configuration of 7790 anthropogenic wildfires (2007)(2008)(2009)(2010)(2011)(2012)(2013) in nine study areas distributed throughout Peninsular Spain by using the Ripley's K-function. We also related these aggregation patterns to weather, population density, and landscape structure descriptors of each study area. Our results provide statistical

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... evidence for spatio-temporal structures around a maximum of 4 km and six months. These aggregations lose strength when the spatial and temporal distances increase. At short time lags after a wildfire (<1 month), the probability of another fire occurrence is high at any distance in the range of 0-16 km. When considering larger time lags (up to two years), the probability of fire occurrence is high only at short distances (>3 km). These aggregated patterns vary depending on location in Spain. Wildfires seem to aggregate within fewer days (heat waves) in warm and dry Mediterranean regions than in milder Atlantic areas (bimodal fire season). Wildfires aggregate spatially over shorter distances in diverse, fragmented landscapes with many small and complex patches. Urban interfaces seem to spatially concentrate fire occurrence, while wildland-agriculture interfaces correlate with larger aggregates. Forests 2016, 7, 185 2 of 15 anticipate high-risk wildfire conditions and take preventive actions, or to pre-position firefighting resources in advance, can reduce the damages and optimize the use of the suppression resources [7, 9] . A number of previous studies have focused on the spatial and/or temporal distribution of wildland fires. For instance, [10] identified the most significant spatial variables for analysing human-caused wildfire occurrences using non-spatially explicit models (autoregressive Poisson and logit processes). Other studies have used spatially explicit models to explain patterns of fire occurrence, for instance, geographically weighted regression models [11] , ignition density estimates [12] , log-Gaussian Cox processes [13, 14] , scan statistics permutation [15] , or Ripley's K-function [16] [17] [18] . A few studies have focused on the temporal pattern of fire ignitions; [19] found temporal aggregations using temporal trajectory metrics of wildfire ignition densities, while [20] found temporal aggregations when analysing the fire weather indices of summer fire ignitions in Finland. In addition, time series of the fire occurrence models of [6] included temporal and spatio-temporal lags lasting up to 2-3 days. Wildfire occurrences have also been analysed as points placed within a spatio-temporal region using point process statistical tools. These tools include, for instance, analysis of inhomogeneous spatio-temporal structures of wildfire ignitions [21] , cluster analysis [15, 22] , modelling of fire locations by spatio-temporal Cox point processes [23] , and spatio-temporal analysis of fire ignition points combined with geographical and environmental variables [2] . For instance, [21] analysed space-time configuration of forest fires assuming spatial tools for each year of study separately, and they did not consider a continuous space-time approach for the fire occurrence. Here we consider inhomogeneous spatio-temporal point processes to analyse the point pattern configuration of human-caused wildfire ignition points of several data sets in Spain. We applied the inhomogeneous spatio-temporal counterpart version of Ripley's K-function proposed by Gabriel & Diggle [24]. This approach was adopted because of the apparent inhomogeneous structure of the spatio-temporal point patterns suggested by the analysis of available official fire reports from the Spanish Ministry of Environment. The analysis of these point configurations would be valuable for interpreting the space-time dependencies of fire ignition points in order to understand wildfire dynamics. The expected spatial and temporal aggregation patterns of HCFs should be related to the underlying fire risk factors [10] found in previous work such as weather or population. Land use has been used often as a proxy variable for distribution of vegetation/fuels and the presence and activity of human sources of ignition [25, 26] . However, the spatial structure of the land mosaic is rarely considered [26], although its composition, configuration, and length of land use interfaces should be of special interest in spatial processes like this. Advances in landscape ecology provide abundant indices to measure mosaic characteristics [27] . Consequently, we also test linear correlations between spatial and temporal parameters derived from the fire patterns and relevant spatial variables linked to the structure of the fire environment with the Pearson product-moment correlation coefficient [28]. Materials and Methods Study Area This study analysed nine regions in windows of 40 km × 40 km distributed over forested areas (at least >20% forest area) in Peninsular Spain (Figure 1 ). These study areas comprise a wide range of forest environments with different landscape structures, but all have fire use levels conducive to significant fire occurrence (at least 100 fires over the study period). Most of peninsular Spain is dominated by a Mediterranean climate, and only 15% of the land area, located in the north, has an Atlantic climate. These climatic zones and the complex topography combined with human socio-economic development over millennia have given way to a very uneven spatial distribution of the vegetation, combining the presence of medium-scale farming areas, areas with scarce natural vegetation cover (grasses, rangelands), extensive shrub-lands, park-like open forest structures (dehesas) with undergrowth, and high forests of variable densities [29] . Tables 1