Extended derivation. The Local Convex Hull (LoCoH) family was developed by Getz & Wilmers (2004) and refined by Getz et al. (2007). For each fix P_i with n relocations, a neighbourhood N_i is built using one of three rules:

• k-LoCoH: N_i = the (k − 1) Euclidean-nearest neighbors of P_i.
• r-LoCoH: N_i = all points within radius r of P_i.
• a-LoCoH: N_i = the largest set whose summed distances from P_i remain ≤ a.

A convex hull H_i = ConvexHull({P_i} ∪ N_i) is constructed for every fix using the Andrew monotone chain algorithm. Hulls are sorted in ascending area, then merged sequentially until the cumulative area reaches the chosen isopleth percent. The 95% isopleth is the home range; the 50% isopleth is the core area.

Assumptions. (1) Fixes are independent samples of space use. (2) The animal's range is approximately stationary during the sampling window. (3) The chosen parameter (k, a, or r) is appropriate for the local point density. (4) Coordinates are projected on a metric coordinate system before area computation — this tool projects WGS84 to a local meter grid at the centroid latitude.

Limitations. LoCoH can fragment ranges if k is too small; it can grossly over-estimate if k is too large (similar to MCP). Always plot the area-vs-k inflection curve and choose k near the elbow. LoCoH cannot, by itself, distinguish habitat selection or seasonal range shifts — pair with resource selection or step-selection analyses.

Decision Checklist

• You have at least 30 GPS or VHF relocations from one individual
• Your study area has hard boundaries (cliffs, water, roads) that MCP would over-fly
• You want a non-parametric, distribution-free home range estimator
• You need a method that converges to the true range with more data
• Do NOT use if you have fewer than 30 fixes — use MCP with caution instead
• Do NOT use if your fixes are extremely autocorrelated (sub-minute fix rate on a stationary animal)

Real-world examples (USA)

• Wildlife monitoring: Yellowstone wolf packs — LoCoH home ranges around den sites with multiple river crossings.
• Game management: Wisconsin white-tailed deer winter yard fidelity, where MCP would include unused agricultural fields.
• Predator ecology: Florida panther daily ranges with hard barriers from interstate highways.
• Avian telemetry: Chesapeake Bay bald eagle foraging ranges that exclude open water the bird never used.

Related metrics — when to pick which:

• Need a quick, classical estimate → MCP (Minimum Convex Polygon)
• Need a smooth probability surface → KDE (Kernel Density Estimation)
• Need an adaptive, sample-size-robust polygon → LoCoH (this tool)
• Need to compare ranges across treatments → run all three and report jointly

1. Enter your data. Paste comma-separated latitudes and longitudes, upload a CSV/Excel from your collar manufacturer, or type rows manually.
2. Choose a sample dataset. Five USA wildlife datasets are pre-loaded; Deer #07 — Yellowstone NP is the default.
3. Set the group/individual name. The name flows into all reports, citations, and the conclusion automatically.
4. Pick the LoCoH method. a-LoCoH is recommended for most field studies because it adapts to point density.
5. Set the parameter (k, a, or r). For k-LoCoH a good starting point is √n where n is your number of fixes.
6. Choose the isopleth percent. 95% = home range, 50% = core area. Most papers report both.
7. Click Calculate. The tool projects WGS84 to meters, builds local hulls, and merges them.
8. Read the summary cards. Green = ample sample size and stable estimate; amber = borderline; red = under-sampled.
9. Examine the four charts. Look at the isopleth curve elbow — that is your defensible parameter choice.
10. Export. Download the .txt for sharing, the PDF for archiving, and copy the journal-style template into your manuscript.