446 A. T. Marques et al.
2006; Jorda et al., 2015) and avoids falsely attributing ex- planatory power to some variables (Smith et al., 2013). We assessed model performance using the explained deviance (as a percentage of the null deviance), correlation and area under the receiver operator characteristic curve (AUC), through cross-validated statistics (Buston & Elith, 2011). We estimated the relative importance of each individual
variable (as per cent contribution to the overall effect of all variables) in a model based on how often the predictor was selected and the improvement to the model as result of the selection (Buston & Elith, 2011). We used the function gbm. plot to build partial dependence plots and visualize the fitted functions from the boosted regression tree models. Important interactions between predictor variables were visualized using the
gbm.interaction function. Because of its stochasticity component, each boosted
regression trees run provides slightly different results. There- fore, we performed 100 runs of
gbm.step to estimate the minimum and maximum values for the fitted functions, the importance of variables and cross-validated measures of model performance (Fernandes et al., 2016). We used spline correlogram plots with 95% pointwise confidence intervals calculated with 1,000 bootstrap resam- ples to check for spatial autocorrelation in model residuals (Bjørnstad & Falck, 2001). We assumed that variable selec- tion and parameter estimation were unbiased if therewas no significant autocorrelation in model residuals (Rhodes et al., 2009). Correlograms were built with the function
spline.cor- relog from the R package ncf (Bjørnstad, 2016).
Results
A total of 156 bustard fatality events were recorded in Alentejo during 2003–2015, 59 of great and 97 of little bustards. Most (75%) fatality records were reported in two studies, one with a wide geographical range (42% of the total number of power line sections surveyed in the region) corresponding to 35% of the fatality events (Neves et al., 2005), and a local study with an intensive survey effort (surveys at 15-day intervals for 29 months) that reported 40% of the events (Marques et al., 2007).
Spatio-temporal collision patterns
Collision events of both species exhibited a clustered spatial pattern (Fig. 1c). Great bustard collisions were concentrated in 15 (10.4%) of the 144 power line sections, 12 of which also had little bustard fatalities. Little bustard collisions were more widely spread across the study area, occurring in a total of 42 sections (29.2%). The number of collision events varied throughout the
year (Supplementary Fig. 3). Most of the carcasses of great bustards were found inside Special Protected Areas (73%),
whereas little bustards were more frequently found outside (55%). Inside Special Protected Areas 65% of the collision records of great bustards occurred during the autumn (September–November), with a second peak in spring (18%, in April–May). Outside Special Protected Areas fa- talities were concentrated during August–October (50%). Little bustard collision events were registered all year. Inside Special Protected Areas fatalities peaked during the breeding season (c. 37%, March–May) and during the post- breeding period (12% in July, and 39% during October– December). However, outside Special Protected Areas 62% of little bustard collision events occurred during the dry months (July–September).
Factors influencing bustard collisions
The original (with unconstrained variables) boosted regres- sion trees model for the great bustard (Supplementary Fig. 2a) explained 20.4% of the total deviance (AUC: 0.85 ± SD 0.02; Pearson’s correlation: 0.42 ± SD 0.03). The pro- portion of open habitat was the most important predictor, with a trend for increased likelihood of collision for values $50%. Survey effort, i.e. accumulated surveyed distance in all sampling visits (larger survey effort correlates with a higher likelihood of collisions being recorded, with a marked increase at c. 120 km accumulated sampling dis- tance) and power line configuration (lower likelihood of collision in small configuration), ranked second and third, respectively. Wire marking and the dominant habitat in the close vicinity of the power line section had less influence on collision records. In the simpler model with the con- strained variables (explained deviance: 15 ± SD 2.1%; AUC: 0.77 ± SD 0.01; Pearson’s correlation: 0.45 ± SD 0.02) the order of variable importance was largely the same, although wire marking and dominant habitat near power lines were even less relevant (Fig. 2). Fitted functions of this model are shown in Fig. 2. The most important interactions be- tween variables (Supplementary Fig. 4) suggest that the risk of collision with power lines in a small configuration, compared to other configurations, was much lower in re- gions with higher open habitat availability, and the effect of survey effort was particularly important in line sections with a higher proportion of open habitat. For little bustard collisions, the boosted regression tree
model with unconstrained variables explained 15.5% of the total deviance (AUC: 0.778 ± SD 0.01; Pearson’s correlation: 0.46 ± SD 0.02; Supplementary Fig. 3b) and was similar to the model with the constrained variables (14.8 ± SD 1.5% of explained deviance; AUC: 0.774 ± SD 0.01; Pearson’s cor- relation: 0.46 ± SD 0.02). The proportion of open habitat was also the most important variable (although the shape of the fitted function suggested a continuously increasing ef- fect, rather than a threshold effect as for the great bustard),
Oryx, 2021, 55(3), 442–451 © The Author(s), 2020. Published by Cambridge University Press on behalf of Fauna & Flora International doi:10.1017/S0030605319000292
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