Empirical data
There are large holes in the geographic range of the American black bear, such as the Great Basin of the western United States and a large part of eastern Canada (Fig. 3A). Although the mosaic hull fills in some gaps (Fig. 3A), it emphasises these two. Squares drawn around the mosaic lines also illustrate them well (Fig. 3B). By contrast, the IUCN website depicts a solid historical range extending throughout almost the entirety of North America (https://www.iucnredlist.org/species/41687/114251609).
Mosaic area estimates for individual five-year historical intervals show some random scatter, but no definite trend, and good consistency with the overall estimate of 602.8 equal-area degree cells (Fig. 4). By contrast, the overall estimate based on a convex hull is 1853.9 degree cells, not only much higher than most of the individual mosaic areas but much higher than convex hull areas for the same intervals. These patterns reinforce the point that the hull areas are doubly biased: they are too low when a data set is small (curve vs. upper line), but they are too high when a distribution has gaps (upper line).