DISCUSSION
Quantifying range areas is not only important across ecology and evolutionary biology, but societally important. Specifically, because the IUCN uses this information to determine the status of threatened species (IUCN Standards and Petitions Committee 2019), the issue of accuracy is no small matter. In light of this fact, one would hope that the IUCN would reconsider its focus on simple extents and areas of occupation and also embrace more current methods of area inference.
On this point, mosaic area estimation has several crucial advantages. Unlike convex hulls, which are the basis of the extent of occupation criterion, mosaics are independent of sample size and have a built-in routine for handing outliers. Unlike counts of occupied cells, which are interpreted as areas of occupation, they are independent of scale in addition to sample size. Unlike KDE and hypervolume calculations, mosaic areas are not upwards biased when shapes are solid, even when sample sizes are small (Fig. 5A). Unlike those methods, mosaic calculation has no flexible parameters and assumes nothing about the underlying shape of the distribution. And unlike all the other methods discussed here, mosaic area computation is explicitly formulated to handle the problem of irregular and non-random point distributions, with even strong patterning having little effect (Figs. 5C, 6). Autocorrelation is a major concern in this field (Noonan et al. 2019).
Much more needs to be done with range area estimation. For one thing, more in-depth testing of a broader range of methods would be desirable. Papers proposing and testing methods, especially those related to KDEs, are numerous, and there is no space even to summarise them: see Walteret al. (2015), Junker et al. (2016), Qiao et al.(2016), Jarvis et al. (2019), and Noonan et al. (2019) for recent examples. I put forth, however, that based on the current results, even the more complex methods are unlikely to outperform mosaic area estimation by a large margin. For this hypothesis to be disproven, conventional 95% KDEs and hypervolumes would have to be shown to be quite poor estimators because they are already substantially worse than mosaic areas. If there really is a much better parametric method, then the most likely candidate might be another kernel density estimator of some kind (Noonan et al. 2019).
Another possibility is that a better mosaic-related method might be found. For example, perhaps one could allow for denser connectivity of points or more complex weighting of edges in area calculations. Also, the algorithm for selecting edges might perhaps be further optimised without imposing a heavy computational burden. Advantages of altering the graph theory are unclear, and even if possible, further optimisation may not be particularly helpful.
Finally, mosaic area estimation is fundamentally non-parametric and depends on deduction from fundamental graph theory and geometry. Some will see this as a disadvantage. This matter touches on a deep paradigm conflict in statistics that concerns a simple question: should every method be model-based and fall within the domain of maximum likelihood or Bayesianism? Strong assumptions and flexible options come with model-based methods, and full objectivity comes with this one – in addition to high performance. Thus, in a field bursting with methods of many kinds, there may be room for a different approach to the deep problem of determining the areas of unknown shapes.