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Distribution Modelling Overview

The maximum entropy (Maxent) method (Phillips et al. 2006 , Phillips & Dudik, 2008 ) was used to develop species distribution models for boreal bird species during the breeding season.  Maxent is a powerful machine-learning algorithm with demonstrated high predictive accuracy compared to other species distribution modelling methods (Elith et al. 2006 ). Although Maxent was developed for presence-only data (e.g., museum records), it is also appropriate for datasets compiled from disparate sources with varying levels of effort, such that information on species absences varies across spatial units. Although the resulting predictions cannot be interpreted as occurrence probabilities, they are robust representations of relative habitat suitability. Locations with high Maxent values are on average better habitats for the modelled species. The power of Maxent lies in its ability to describe complex functional relationships (e.g., non-linear, threshold, multiplicative) between species and environmental covariates. 

The key step in developing Maxent models, as with traditional resource selection functions (Manly 1993 ), is the selection of appropriate "background" data (Phillips et al. 2009 ). Biased samples lead to biased predictions. Following recommended practice, we constrained our background to surveyed locations. Due to the high spatial aggregation of survey locations and the resulting potential for bias, we aggregated occurrence records at the level of 4-km by 4-km grid cells corresponding to the resolution of our climate data.  A species was considered present in a grid cell if at least one individual had been counted over all point-count surveys contained in the grid cell. The model background was thus defined as all cells having at least one survey location (n = 29,059).