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Transect sampling means collecting data along a straight line (a transect) laid through a study area instead of surveying the whole area. Counting what lies on or beside the line gives a fraction of the area that can be scaled up to the whole. This guide covers the line and belt variants, the density formula used in distance sampling with every symbol explained, a worked calculation, and code to reproduce it.
What is transect sampling?
A transect is a path along which an observer records the objects of study: plants, animals, burrows, nests, litter, coral colonies. The transect is the sampling unit. Because the line crosses the habitat in a chosen direction, the method is common in ecology and wildlife biology, and it is one way of drawing a spatial sample. Where the lines sit at a fixed spacing from a random start, it behaves like systematic sampling; the wider family is described in sampling methods.
Line transect vs belt transect vs distance sampling
The three names describe what the observer records, not three different kinds of line. The table separates them as this guide uses the terms.
| Method | What is recorded | What you can estimate |
|---|---|---|
| Line (intercept) transect | Each organism or feature that touches or crosses the line, often at set points | Presence, cover along the line, which species occur at which position |
| Belt transect | Counts inside a strip of fixed width, often as quadrats placed along the line | Abundance per unit area within the strip |
| Line transect distance sampling | Counts plus the perpendicular distance from the line to each detection | Density, with a detection function correcting for missed individuals |
A belt transect assumes everything inside the strip is counted. Distance sampling drops that assumption: individuals far from the line are easier to miss, and the recorded distances are used to model how detection falls off.
Transect sampling formula: the density estimator D = n / 2wL
For conventional line transect distance sampling, density is estimated as (Morgan et al., 2024):
D = n / (2wL)
- D: estimated density, in individuals per unit area.
- n: number of individuals detected within the strip of length L and width 2w centred on the line.
- L: total transect length surveyed.
- w: the effective half-width, the distance at which the fitted detection function estimates the same number of animals as are detected inside it. The strip is 2w wide because it extends w on each side of the line.
The denominator 2wL is the effective area surveyed. L and w must use the same length unit, and D comes out in that unit squared.
Worked example: density from one survey
Suppose 48 animals are detected along 2,000 m of transect, and the detection function gives an effective half-width of 25 m.
- Effective area surveyed: 2wL = 2 × 25 m × 2,000 m = 100,000 m², which is 0.1 km².
- Density: D = n / 2wL = 48 / 100,000 m² = 0.00048 animals per m².
- Convert: 0.00048 × 1,000,000 m² per km² = 480 animals per km².
Check: 48 animals in 0.1 km² is 48 / 0.1 = 480 per km².
Interpreting the result
D is a point estimate for the surveyed area. How much it moves with its inputs is shown by changing one value at a time in the example above.
| Change | New D | Reading |
|---|---|---|
| Baseline: n = 48, L = 2,000 m, w = 25 m | 480 per km² | Reference estimate |
| w falls to 20 m (detection drops off faster) | 600 per km² | A narrower effective strip means each detection stands for more animals |
| L doubles to 4,000 m with the same n | 240 per km² | Same count over twice the effort means lower density |
A density from one set of transects has sampling error. Report an interval with it; see confidence interval.
Assumptions and common mistakes
The conventional estimator rests on these assumptions (Morgan et al., 2024):
- Objects are distributed independently of the lines. Lines laid along a path, ridge or stream, where animals may be more or less abundant, break this.
- Detection on the line is complete: detection probability g(0) = 1. Animals missed on the line bias D downward.
- Distances, angles and counts are measured correctly.
- Animals do not move before they are detected. Animals that move before they are detected bias the estimate.
Mistakes that follow from these: choosing line positions for convenience instead of by a random or systematic design, mixing metres and kilometres in L and w, counting animals seen beyond the truncation distance, and treating belt counts as if they corrected for missed animals. Recording errors by the observer are a form of observer bias.
How to report transect sampling results (APA)
State the design, the effort and the estimator inputs so a reader can recompute the result. An example sentence in APA 7th style:
Density was estimated by line transect distance sampling at 480 animals per km² (n = 48 detections along L = 2,000 m of transect; effective half-width w = 25 m).
Reference entry for the paper behind the estimator (APA 7th):
Morgan, D. G., Gibbens, J. R., Conway, E. T., Hepworth, G., & Clough, J. (2024). Wildlife density estimation by distance sampling: A novel technique with movement compensation. PLOS ONE, 19(10), Article e0310020. https://pmc.ncbi.nlm.nih.gov/articles/PMC11482707/
How to calculate transect density in Excel, R or Python
Excel
Put n in B1, L in B2 and w in B3 (L and w in metres), then:
=B1/(2*B3*B2)*1000000This returns animals per km². With the example values it gives 480.
R
n = 48; L = 2000; w = 25
D = n / (2 * w * L) # per m^2
D * 1e6 # per km^2: 480To estimate w from the distances instead of assuming it, the Distance package fits a detection function to line or point transect data. Its ds() function defaults to a half-normal key function (key = "hn"), also offers hazard-rate ("hr") and uniform ("unif"), and takes a truncation argument, which defaults to the largest observed distance (The Distance R package documentation, 2026):
library(Distance)
fit = ds(my.data, truncation = "10%", key = "hr", adjustment = NULL)
summary(fit)Python
n, L, w = 48, 2000, 25
D = n / (2 * w * L) # per m^2
print(D * 1e6) # 480.0 per km^2Transect sampling FAQ
What is the difference between a transect and a quadrat?
A transect is a line; a quadrat is a fixed-size frame. A belt transect combines them by placing quadrats along the line so that counts come from a strip of known width.
What is the density formula for line transect sampling?
D = n / 2wL, where n is the number of detections, L the total line length and w the effective half-width of the strip.
What does it mean if w is the effective half-width?
It is the distance at which the fitted detection function would have counted as many animals as were actually seen within it, so animals missed far from the line are accounted for.
Does transect sampling need random placement?
The method assumes objects are distributed independently of the lines, so line positions should come from a random or systematic design, not from where animals are expected.
Sources
- Morgan, D. G., Gibbens, J. R., Conway, E. T., Hepworth, G., & Clough, J. (2024). Wildlife density estimation by distance sampling: A novel technique with movement compensation. PLOS ONE, 19(10), e0310020. https://pmc.ncbi.nlm.nih.gov/articles/PMC11482707/ (checked 2026-10-29)
- Distance R package,
ds()reference. https://distancesampling.org/Distance/reference/ds.html (checked 2026-10-29)
