Range sizes¶

for analyses that require only range sizes, not full-fledged range maps, there are alternative, much faster techniques that can be used to estimate range size:

bounding-circle¶

1. calculate centroid of occurrence points for the species
2. determine each point's radius: the distance from it to the centroid
3. remove outliers using box plot of radii¹
4. calculate the standard deviation of the radii
5. calculate the bounding-circle radius: use 1x the standard deviation, because we want this to also be a good estimator for long, narrow ranges
   • this includes 70% of the points in the area estimate
6. calculate the bounding-circle area, which is an estimate for the convex-hull/maxent range size

¹ needed because standard deviation is a mean, not a median, and therefore sensitive to outliers
.

linear regression¶

1. fit a line to the points to determine what axis, if any, they may be distributed along
2. rotate the points so the axis is completely vertical or completely horizontal
3. remove x- and y-outliers using box plots
4. calculate width and height of the bounding box (x_max - x_min, etc.)
5. calculate the area of an ellipse which fills the bounding box, which is an estimate for the convex-hull/maxent range size

• note that this doesn't work as well for v-shaped distributions, but a convex hull won't, either
• for circular distributions, this includes more points than the bounding-circle method because it uses the x/y-range instead of the standard deviation