What is Camera Trap Distance Sampling (CTDS)?

CTDS is a wildlife density estimation method that combines camera trap photography with distance sampling theory. It measures the distance from each camera to each detected animal, fits a detection function to those distances, and produces an absolute density estimate in animals per square kilometre for unmarked populations (Howe et al., 2017).

What formula does CTDS use to calculate density?

The standard CTDS density formula is D = (n × Eg) / (e × a × p), where n is the number of detections, Eg is the mean group size, e is total sampling effort in independent snapshot moments (camera-seconds divided by snapshot interval), a is the area of the camera viewshed sector calculated as theta times w squared divided by 2, and p is the estimated detection probability from the fitted detection function.

How is CTDS different from RAI (Relative Abundance Index)?

RAI gives a relative, unitless count rate (detections per 100 trap nights) that cannot be compared across studies or species. CTDS produces absolute density in animals per square kilometre with confidence intervals, and the estimates are directly comparable across sites, species, and studies.

How many detections do I need for CTDS?

Buckland et al. (2015) recommend a minimum of 60 to 80 detections per species for stable detection function fits. With fewer detections, you can pool similar species (for example all medium-sized ungulates) or use a model-averaged detection function.

What detection function should I use for CTDS?

This tool offers 9 options: four key functions (half-normal, hazard-rate, uniform, negative exponential), four key plus cosine or Hermite series adjustments, and an automatic AIC-based selection that fits all eight models and picks the lowest AIC. Half-normal is the recommended default for camera trap data; use Auto-Select when unsure.

What is the truncation distance (w) in CTDS?

It is the maximum distance beyond which detections are discarded. A typical rule is to truncate at the distance where detection probability drops to roughly 0.10 to 0.15, often around 2.4 times sigma for a half-normal model. Truncation improves model fit by removing unreliable far-distance observations.

How do I measure animal-to-camera distance in CTDS?

The standard field protocol places visible distance markers (such as flagged vegetation, painted rocks, or PVC pipes) at known distances (commonly 1, 2, 5, 10, and 15 m) directly in the camera's field of view. Each photograph is then scored by visually estimating the animal's position relative to those markers.

Can I use CTDS for individually identifiable species?

You can, but spatial capture-recapture (SCR) is usually preferred for identifiable species because it produces both density and home-range size estimates. CTDS is most valuable for unmarked species where SCR is impossible.

What snapshot interval should I use for CTDS?

For large fast-moving mammals (deer, wolves), use 1 to 2 seconds. For slow species (bears foraging, tortoises), 5 to 10 seconds is fine. The snapshot interval is the time step at which the camera is treated as a point-transect moment.

Can CTDS estimate density for multiple species at once?

Yes, and that is one of its strengths. Each species gets its own detection function (because body size affects detection distance), and densities are then directly comparable. This tool supports multi-species CTDS via the Analysis Mode toggle.

How precise should my CTDS density estimate be?

A coefficient of variation (CV) under 20 percent is considered good; 20 to 30 percent is acceptable; over 30 percent suggests undersampling. To reduce CV, increase the number of cameras or extend the deployment period. Doubling effort typically reduces CV by about 30 percent.

Camera Trap Distance Sampling Calculator (CTDS)

📐 Camera Trap Distance Sampling — Geometry & Measurements

The diagram below shows the geometric setup of one camera trap and how each measurement contributes to the density estimate. It updates automatically when you change the truncation distance w or camera viewshed angle θ in the Analysis Configuration panel.

Top-down view of one camera's detection zone. The animal is detected at distance r, measured using vegetation distance markers placed at known intervals (1, 2, 5, 10 m). The shaded green sector is the viewshed of area a = ½ × θ × w².

📥 1. Data Input

📊 Sample Dataset:

🦌 Analysis Mode:

Group / Species Name (editable): Detection Distances (meters) — comma-separated:

0 valid distances detected

Upload CSV or Excel file:

Supports .csv, .txt, .xlsx, .xls — headers detected automatically. Column picker appears below.

🦌 Analysis Mode for Upload:

Single species: choose one distance column. Multi-species: pick one column per species (header text becomes the species name).

Manual Entry Table (Distance in meters):

#	Distance (m)

⚙️ 2. Analysis Configuration

🏞️ Study Area / Site Name (optional):

🎥 Number of Cameras:

📅 Camera Days (per camera, mean):

⏱️ Snapshot Interval (seconds):

Independent-event window in seconds (typical: 60–300 s). Defines what counts as a separate detection.

🕐 Active Hours per Day:

📐 Camera Viewshed Angle θ (degrees):

📏 Truncation Distance w (m):

🐾 Mean Group / Cluster Size Ē(g):

Average number of animals per detection event. Use 1 for solitary species (e.g., panther, leopard, lone bear). Use the observed mean (e.g., 2.4 for elk, 1.8 for white-tailed deer, 3.0 for bighorn sheep) for group-living species. CTDS counts groups, so Ē(g) scales the result to individuals via the formula D̂ = (n × Ē(g)) / (e × a × p̂).

📈 Detection Function Model:

Half-Normal is the default for camera trap data. Auto-Select fits all models and picks the lowest AIC.

📐 Output Area Unit (for density):

Density estimate (D̂) will be reported in this unit throughout the results, charts, and downloads.

CTDS Density Equation (Howe et al., 2017)

The Camera Trap Distance Sampling density estimator is:

\[ \hat{D} = \frac{n \cdot \bar{E}(g)}{e \cdot a \cdot \hat{p}} \quad\text{where}\quad a = \pi w^2 \cdot \frac{\theta}{2\pi} = \frac{\theta w^2}{2} \]

D̂: Density (D̂) - Animals/km² (the estimated population density)
n: Number of detections within truncation distance w
Ē(g): Mean group (cluster) size
e: Total sampling effort (number of independent snapshot moments = total camera-seconds ÷ snapshot interval)
a: Area of camera viewshed sector (km²) at truncation distance
w: Truncation distance (m) — max distance retained
θ: Camera horizontal field-of-view angle (radians)
p̂: Estimated detection probability from the detection function

📊 Visualizations

1. Distance Histogram & Detection Function

2. Density Estimate with 95% Confidence Interval

3. Detection Probability vs. Distance Curve

4. Per-Species Density Comparison

📋 Detailed Results Table

🔬 3. Methodology

🧠 4. Plain-Language Interpretation

▸ Interpretation Results

▸ How to Write Your Results in Research

▸ Research Poster Panel

🔬 Technical Notes — Formula Derivation, Assumptions & Limitations

📌 When to Use CTDS — Decision Checklist & Examples

🔍 Conclusion

▶ Run the analysis above to generate a personalised conclusion for your dataset.

❓ Frequently Asked Questions

📖 How to Use This CTDS Calculator — Step by Step

📚 References

The following references support the statistical and ecological methods used in this Camera Trap Distance Sampling (CTDS) calculator, covering wildlife density estimation, detection function modelling, and best practices in camera trap survey design.