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).