Overview
How much space does a single mammal use? That question has been at the center of wildlife biology for decades — and answering it requires exactly what you've been doing in this track: recording where individual animals show up, repeatedly, across a defined area.
Home range analysis is the spatial counterpart to population analysis. Instead of asking "how many animals are here?" you ask "where does this particular animal go?" The answer shapes conservation decisions: minimum wildlife corridor width, reserve size, road crossing placement, urban habitat planning.
In this project you'll take your sign data from the track, plot the locations, draw the simplest standard home range estimator — a minimum convex polygon — and calculate the approximate area. Then you'll compare it to what biologists have documented for your species using radio telemetry and GPS collar data.
What You'll Learn
- What home range means in mammal biology — and how it differs from territory
- How to construct a minimum convex polygon (MCP) home range estimate from point location data
- How to calculate polygon area using the grid-square counting method (and the shoelace formula for 13+)
- Why MCP is the standard baseline method and what its limitations are compared to kernel density estimation
- How to compare a field estimate to published radio telemetry data and interpret the difference
Background
HOME RANGE: The area an individual animal uses regularly during its normal activities. Not the same as territory — an animal defends its territory; it merely uses its home range. Many home ranges overlap between individuals of the same species. Home range size varies enormously: a meadow vole's home range may be 0.1 hectares; a mountain lion's may be 300+ square kilometers.
MINIMUM CONVEX POLYGON (MCP): The simplest way to estimate home range from a set of location data. Draw the smallest convex polygon that encloses all your data points — like stretching a rubber band around the outermost points. The area of that polygon is your MCP home range estimate.
MCP is a baseline method, not a sophisticated one. Its weakness: it includes large areas of habitat the animal may never use, simply because those areas fall inside the polygon boundary. Modern biologists use kernel density estimation (KDE) which models the probability distribution of locations and produces a more accurate home range that reflects the actual usage pattern — smaller "core areas" of high use surrounded by larger "peripheral areas" of occasional use.
For this project, MCP is the right method: it's understandable, calculable by hand, and still used as a standard comparison baseline in published research.
CALCULATING MCP AREA: Once you've drawn the polygon on graph paper, count the number of graph squares inside the polygon. Multiply by the real-world area each square represents (based on your map scale). This gives you area in square meters or hectares.
For learners 13 and up: the shoelace formula calculates exact polygon area from vertex coordinates:
Area = ½ |Σ(xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ)|
where the sum is taken over all vertices in order.
Materials
Everything on this list is either free or available at a dollar store. No lab equipment required.
Step-by-Step Procedure
-
1
Compile Your Location Data
Gather all your mammal sign records from the Sign Survey Transect and Track Story projects. For each sign record, you need two things:
• The approximate location — distance along the transect (0m, 15m, 40m, etc.) and the rough distance to the left or right of the transect centerline
• The suspected speciesIf you have sign from multiple species, choose one species for your analysis — the one with the most records. Write that species at the top of your data page.
List all sign locations for that species, numbered 1 through N.
💡If you only have transect data from one session, use all of it. If you have data from multiple sessions or locations, combine them — more points make a more meaningful polygon.
-
2
Build Your Map
On graph paper, draw your transect as a horizontal line. Choose a scale: let each graph square = a real-world distance that fits your data on the page. For a 100m transect with signs up to 10m off center, a scale of 1 square = 5m works well.
Plot each sign location:
• The transect position = horizontal distance from the left end
• The offset = vertical distance above or below the transect line (left = above, right = below)Label each point with its record number. Use a dot or small X for each location. When all points are plotted, label the transect line, write the scale in the corner, and add a north arrow if you know orientation.
💡If your sign locations are only along the transect itself (no offset recorded), plot them along a single line and note that your MCP will be elongated — this is a limitation of a single linear transect design.
-
3
Draw the Minimum Convex Polygon
Find the outermost points in your data set — the points that form the outer boundary when you imagine a rubber band stretched around all the dots.
Connect them with straight lines to form the smallest convex polygon that contains all your points. A convex polygon has no interior angles greater than 180° — every corner points outward, none inward.
To check: from any point on the polygon boundary, you should be able to see all other points without the line of sight crossing outside the polygon.
Shade the interior lightly. This is your MCP home range estimate.
💡If two or more of your outermost points are nearly in line, include all of them as vertices — a polygon with more vertices is still valid, just more precisely fitted.
-
4
Calculate the Area
METHOD 1 — Grid counting (ages 8+):
Count every graph square completely inside your polygon. Count squares that are more than half inside as full squares; squares less than half inside, skip. Total squares × real-world area per square = your MCP area estimate.Convert to hectares if useful: 1 hectare = 10,000 square meters.
METHOD 2 — Shoelace formula (ages 13+):
Number your polygon vertices 1 through N going clockwise. Record the (x, y) coordinates of each vertex from your graph paper. Apply:Area = ½ |Σᵢ(xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ)|
where vertex N+1 = vertex 1 (the formula wraps around).
Multiply the result in graph-square units by your scale factor squared to get real-world area.
-
5
Compare and Reflect
Look up published home range data for your species. Searches to try:
• "[species name] home range hectares"
• "[species name] home range size study"
• IUCN species profile (often includes home range data)Published home range estimates for common North American species:
• White-tailed deer: 40–200 ha (varies by season and habitat)
• Raccoon: 4–200 ha (males much larger than females)
• Eastern cottontail: 1–4 ha
• Coyote: 10–50 km² (much larger — note km² vs. ha)
• Red fox: 2–50 km²Answer in writing:
• How does your MCP estimate compare to the published range for your species?
• If your estimate is much smaller: what explains this? (Your data covers only part of the animal's actual range, from one transect, on limited visits.)
• If your estimate is larger: what might explain this? (Multiple individuals? Misidentified species?)
• What would you need to do to get a more accurate home range estimate? (More sessions, larger area, individual ID via camera trap or unique marking)
• What conservation decision could home range data inform — road crossing design, urban green corridor width, park boundary planning?
Expected Results
Learners who have completed the Sign Survey Transect and Track Story projects will have 8–20 sign locations across a defined area. With those plotted, a minimum convex polygon and area estimate are achievable in one 45-minute session. Comparing the result to published home range data for the most likely species produces an interesting and meaningful comparison, regardless of whether the numbers match.
Your results may differ — and that's valuable data, not a mistake. Document what you actually observed, not what you expected.
Going Further
GPS Collar Data
Modern home range studies use GPS collars that record an animal's location every 15 minutes, 24 hours a day. Look up a published study using GPS collar data for any mammal species — the supplementary data in ecology papers is often freely available and includes mapped location points. Count how many GPS fixes are in a single week of tracking for one individual. How does that compare to your data set? What patterns are visible in the GPS data that would be invisible in a transect survey?
Kernel Density Estimation
Kernel density estimation (KDE) is how modern biologists model home range from GPS data. Instead of drawing a polygon around the outermost points, KDE places a probability "kernel" (a smooth curve) at each location and sums all the kernels to produce a probability surface — showing not just where the animal went, but how intensively it used each part of its range. The 95% contour of this surface is the standard home range; the 50% contour is the "core area." Look up a graphic explanation of KDE home range analysis — how does the core area compare to the overall 95% range?
Connectivity and Corridors
Home range data is used directly in wildlife corridor design. If a mountain lion requires 300 km² and the remaining natural habitat in a region is fragmented into 50 km² patches, the lion cannot persist unless there are corridors connecting patches into a functional landscape. Research the Wallis Annenberg Wildlife Crossing being built over the 101 Freeway near Los Angeles — what home range data drove the decision to build it? What species will it serve?
Nature Path
Submit your home range map to Nature Path along with your most complete sign record from this track. A mapped home range estimate is one of the richest possible sighting submissions — it moves beyond "I saw this animal here" to "here is the spatial footprint of this individual's activity."
