Local Convex Hull (LoCoH) — Fixed Sphere

Summary

Estimates an animal's home range and utilization distribution by the fixed-sphere-of-influence (r-) Local Convex Hull method of Getz et al. (2007): every location's local hull is the convex hull of that point and all points within a sphere of influence of radius r. The hulls are sorted by point count, most points first (ties going to the smaller hull), and merged cumulatively into density isopleths. Outputs are the dissolved cumulative isopleths — each carrying its within-sphere point count and point density alongside the area and point statistics — and, optionally, the individual hulls.

How the radius shapes the hulls

Where the Standard variant counts neighbors and the Adaptive variant spends a distance budget, the Fixed Sphere variant asks a simpler question: who is within r of me? Every point inside the focal point's sphere of influence joins its hull — many points in dense country, few in sparse — and at least the focal point's two nearest neighbors are always included, so every hull forms a polygon. The neighborhood has a fixed spatial scale, which is this variant's reason to exist: when a biologically meaningful distance should set the scale of “local” — a perception range, a daily movement radius, a territory-defense distance — r states it directly, rather than letting the data's own density decide. Because the sphere holds more points where use is dense, each hull also carries a point count and density, making r-LoCoH the variant whose hulls read most directly as a density surface. Larger r gives larger, smoother hulls; smaller r gives tighter, more fragmented ones.

Choosing r. Getz et al. (2007) suggest starting with r equal to half the maximum nearest-neighbor distance — the tool's automatic option — then refining by the minimum spurious hole covering rule, watching isopleth areas across a range of values as the T-LoCoH package recommends (Lyons, Turner and Getz 2013). Expect the automatic radius to look sparse: Getz et al. report that their own r₁ rule generally lands below the optimum — by as much as a factor of three in their trials — so treat it as a deliberate floor to refine upward from, not as a best guess (they trust the Adaptive method's a₁ heuristic considerably more). The LoCoH Parameter Explorer window runs that whole sweep for you and charts the result — its help page shows a Fixed Sphere sweep picking out two usable plateaus on one dataset, a tight radius for core areas and a generous one for the general home range, both read straight off the curves. When you specify the radius yourself it may be entered in any linear unit and is converted to meters internally; the radius used is recorded in the output metadata. Screen out obvious location errors first; LoCoH is sensitive to outliers.

What you get

The primary output holds the dissolved cumulative isopleths: each feature stores its dissolved area (Area), enclosed point count (Point_Count), point proportion (Point_Proportion), the number of points within the sphere (Sphere_Point_Count), and point density in points per square kilometer (Pts_per_SqKm). The optional second output holds the individual local hulls with their own areas, point counts, proportions, within-sphere counts, and densities. Geographic inputs use Haversine distances and WGS84 spheroidal areas; projected inputs use planar measures. Area is in square meters for geographic inputs and in square map units for projected inputs. The Output Coordinate System environment is honored for the final polygons.

A tour of the dialog

A run needs the points, a choice for the radius — the automatic half-maximum-nearest-neighbor-distance heuristic, or a radius you specify — and an output name; the individual hulls are one optional output more.

ModelBuilder

Both outputs chain onward in a model — the isopleth polygons feed clip, overlay, or reporting steps directly, and a Select on Point_Proportion pulls the 95% or 50% isopleth out of the stack for the next tool.

Parameters

Python

A fixed-sphere LoCoH using the automatic radius, with both outputs:

import arcpy
arcpy.ImportToolbox(r"C:\path\to\JennessEnterprisesTools.pyt")  # your install path
arcpy.jenness.LoCoHFixedSphere(
    in_features=r"D:\data\telemetry.gdb\owl_fixes",
    r_method="Automatic (half the maximum nearest-neighbor distance)",
    out_isopleths=r"D:\data\telemetry.gdb\owl_isopleths_r",
    out_hulls=r"D:\data\telemetry.gdb\owl_hulls_r")

Recommended citation

Credits and references

By Jeff Jenness, Jenness Enterprises (www.jennessent.com), implementing the r-LoCoH method of Getz and colleagues. Full references on the About LoCoH page.

• Getz, W. M., S. Fortmann-Roe, P. C. Cross, A. J. Lyons, S. J. Ryan, and C. C. Wilmers. 2007. LoCoH: nonparametric kernel methods for constructing home ranges and utilization distributions. PLoS ONE 2(2):e207. doi.org/10.1371/journal.pone.0000207
• Lyons, A. J., W. C. Turner, and W. M. Getz. 2013. Home range plus: a space-time characterization of movement over real landscapes. Movement Ecology 1:2. doi.org/10.1186/2051-3933-1-2

Licensing information

Works at every ArcGIS Pro license level (Basic, Standard, Advanced). No extension licenses are required.

Related tools and pages

• About LoCoH home-range analysis — the shared theory.
• LoCoH (Standard) — a fixed neighbor count; the original, and the easiest knob to reason about.
• LoCoH (Adaptive) — a cumulative distance budget instead of a fixed radius; adapts best when fix density varies strongly.
• LoCoH Parameter Explorer — sweep the parameter and chart the leveling-off curves before committing to a value.
• Concave Hull — one clean footprint polygon instead of a utilization distribution.