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.