Quadrat sampling: how to count plants on the edge, how many quadrats you need, and how to estimate the population

The quadrat method in five steps

Quadrat sampling estimates a population by counting every individual inside a few frames of known area, placed at random, and scaling the average up to the whole site. It suits plants and animals that stay put while you count. The US Bureau of Land Management's field manual, Sampling Vegetation Attributes (Technical Reference 1734-4, 1996, revised 1999), sets out the density method in this order:

1. Mark out the area and lay two tapes at right angles along two of its sides as axes.
2. Pick random coordinates, one number for each tape, for every quadrat. Each pair marks a quadrat's lower left corner.
3. Count the individuals rooted inside each quadrat, applying one edge rule throughout and counting seedlings separately if they matter.
4. Average: total plants divided by the number of quadrats. The manual's example is 177 plants in 40 quadrats, 4.4 per quadrat.
5. Scale up: the mean per quadrat times the number of quadrats that would fit in the area. In the manual, a 40 × 80 m plot holds 200 quadrats of 1 × 16 m, so 4.4 × 200 = 880 plants.

Dividing the mean by the quadrat's area gives the same result as density per square metre, and multiplying that density by the site's area gives the population. The number on its own is only half the answer. The other half, how far it could be out, is covered under how many quadrats.

Counting plants on the edge of the quadrat

Count a plant touching two adjacent sides of the frame as in, and a plant touching the other two sides as out, and tell everyone on the team which sides are which. This is the rule the BLM's Measuring and Monitoring Plant Populations (Elzinga, Salzer and Willoughby, Technical Reference 1730-1, 1998) calls "the recommended approach for reducing boundary bias". The vegetation manual gives the same rule as top and left in, bottom and right out.

Revision notes give different rules, and the manual explains what each one does to the count:

Why does touching the frame inflate the count? Counting every plant that touches the line, the manual explains, effectively makes the quadrat larger by the width of a plant on every side. The two-sides rule works because a plant on the shared edge of two neighbouring quadrats is counted in exactly one of them, so nothing is counted twice and nothing is lost. On a rectangular quadrat, the "in" sides should be one long side and one short side, so the in and out halves of the perimeter are equal.

What counts as one plant

For most species the counting unit is a plant rooted inside the quadrat, decided at ground level, not by where its leaves spread. Both BLM manuals say so, and both warn that the unit has to be written down before counting, because many plants are not tidy individuals:

• Rooted, not overhanging. A plant whose leaves lean into the frame but whose base is outside does not count. Using the canopy outline makes the count change with how vigorous the plants are.
• Clumps and mats. For rhizomatous grasses the vegetation manual suggests counting each culm group, and for mat-forming plants that break into fragments, each separate fragment.
• Life stages. Count seedlings separately from mature plants. Elzinga and colleagues show a quadrat where the total fell only from 39 to 37 plants in a year while flowering plants fell from 14 to 4.

The same manual warns that the most common counting errors come from "high speed" counts that miss small individuals, and suggests a minimum search time per quadrat.

Worked example: daisies on a 30 × 20 m field

A class surveys daisies on a 30 × 20 m field, 600 m², with a 0.5 × 0.5 m quadrat (0.25 m²) at 10 random coordinates, counting with the two-sides rule. The counts are made up for the example; the arithmetic is the method above.

1. Total and mean. 37 daisies in 10 quadrats: 3.7 per quadrat.
2. Density. 3.7 ÷ 0.25 m² = 14.8 daisies per m².
3. Population. 14.8 × 600 m² = 8,880. As a check, 600 ÷ 0.25 = 2,400 quadrats would tile the field, and 3.7 × 2,400 = 8,880 as well.
4. Round it. Report about 8,900, not 8,880: ten quadrats cannot support four significant figures.
5. Frequency. Daisies were in 8 of the 10 quadrats, a frequency of 80%.

The counts also say something about the daisies. Their variance is 9.3 against a mean of 3.7. If the plants were scattered at random, counts would follow a Poisson distribution, in which the variance equals the mean, so a variance well above the mean is the sign of a clumped population. Elzinga and colleagues note that very few plant populations are randomly distributed; most are clumped, and that decides both the number of quadrats and their shape.

How many quadrats do you need?

Enough that the estimate's confidence interval is as narrow as your purpose needs; ten is a classroom minimum, and for a clumped plant it leaves a wide margin. The daisy example shows it. The ten counts have a standard deviation of 3.06 and a standard error of 0.97 (3.06 ÷ √10), so the 95% confidence interval for the mean is 3.7 ± 2.262 × 0.97, or 1.5 to 5.9 daisies per quadrat (2.262 is the t value for nine degrees of freedom). Scaled to the field, that is 3,600 to 14,100 daisies: the honest answer to "how many daisies?" from ten quadrats.

The sample size equation the field manuals use

Elzinga and colleagues' sample size equation #1 (Appendix 7) gives the number of quadrats for a chosen precision: n = Z² × s² ÷ B², where s is the standard deviation from a pilot sample, Z is 1.96 for 95% confidence and B is the margin you will accept, in plants per quadrat. Because the equation underestimates, the manual then looks the result up in a correction table, and applies a finite population correction when quadrats cover more than 5% of the area.

The finite population correction is n ÷ (1 + n ÷ N), where N is the number of quadrats that would fit in the area; the survey sample size guide explains the same correction for questionnaires. The lesson of the table is that the spread of the counts, not the size of the field, sets the number of quadrats.

The running mean check

Without the formula, use the BLM vegetation manual's sequential sampling check: after each quadrat, recalculate the mean and standard deviation and plot them against the number of quadrats. Keep going until both lines flatten. In the manual's example, 1 × 5 m quadrats in a 50 × 100 m area, the curves settled after about 30 to 35 quadrats, and the manual adds "There are no hard and fast rules." A mean still swinging after ten quadrats is the sign you need more.

Quadrat size and shape

Choose a quadrat small enough to count accurately and large enough that few quadrats come back empty; for a clumped plant, a long thin rectangle beats a square of the same area. The UK's National Vegetation Classification users' handbook (Rodwell, JNCC 2006) sets sizes by the scale of the vegetation, for recording which species are present and their cover:

For counting individuals, shape matters as much as size. Rectangles are more likely to take in part of a clump, so fewer quadrats come back with zero or with a huge count, and the counts vary less. In Elzinga and colleagues' example population of 4,000 clumped plants, the same precision needed 416 quadrats of 0.25 × 1 m or 10 quadrats of 4 × 50 m (Table 7.1). The manual's advice is to make the long side longer than the distance between clumps and to run it along the gradient the plants respond to: up a slope rather than along the contour, across a stream rather than beside it. The cost of a long quadrat is more edge, which is why the edge rule matters.

Density, frequency and percentage cover

Density counts individuals, frequency records whether the species is present at all, and percentage cover measures how much ground its leaves hide; use cover when individuals cannot be told apart. Grasses, mosses and creeping plants are scored by cover because "one plant" has no clear meaning.

Frequency is the cheapest, but the vegetation manual warns that it is "highly influenced by the size and shape of the quadrats used", so two frequencies are comparable only when the quadrats were the same. Daisies found in 80% of 0.25 m² quadrats would be found in a higher share of 1 m² quadrats, never a lower one, because every larger quadrat contains a smaller one.

Three ways to score cover

• Grid squares. A frame divided into a grid: Elzinga and colleagues cite a 50 × 50 cm frame of 25 squares of 10 × 10 cm, each worth 4%, with partly filled squares grouped together. In that study it gave more consistent results between observers than 50 pins per frame, in half the time.
• Cover classes. Each quadrat gets a class, and the class midpoints are averaged. Daubenmire's six classes are 0-5%, 5-25%, 25-50%, 50-75%, 75-95% and 95-100%, with midpoints 2.5, 15, 37.5, 62.5, 85 and 97.5 in the BLM manual. The NVC uses the 10-point Domin scale (1 to 3 for under 4%, by how many individuals; 4 for 4-10%; up to 10 for 91-100%), and never the DAFOR scale, which it says "has no agreed quantitative meaning".
• Point intercept. Lower pins at fixed points and record a hit or a miss: cover is hits divided by points, 5 of 9 in the manual's illustration, 55.6%. It is the least biased method but misses rare species; the manual cites an estimate of about 2,000 points to measure a species at 8% cover to within ±10%.

A Daubenmire worked example: of ten quadrats, four score class 1 (2.5%), three class 2 (15%), two class 3 (37.5%) and one class 4 (62.5%). (4 × 2.5 + 3 × 15 + 2 × 37.5 + 62.5) ÷ 10 = 192.5 ÷ 10 = 19% cover. Add the classes for every species and the total can exceed 100%, because leaves overlap. Visual scores need care: one study the manual cites found cover estimates in 25 × 25 cm plots varying tenfold between observers.

Placing quadrats at random

Use random numbers as coordinates along two tapes at right angles, reject any pair that falls outside the area, and spread the quadrats across the whole site. Elzinga and colleagues are blunt: statistical analysis depends on knowing each quadrat's chance of selection, and "Preferential sampling, the practice of subjectively selecting sampling units, should be avoided at all costs." Both manuals also warn against putting every quadrat along one or a few lines, even randomly placed ones, because the sample will not represent the area.

Random coordinates suit square quadrats best. For long rectangles, the manual prefers a grid of cells, one quadrat per randomly chosen cell, because a random compass bearing either pushes the sample towards the middle or, if quadrats are bounced back off the edge, towards the edges. Tossing a frame over your shoulder is not on either manual's list of methods: where it lands depends on where you stood and how you threw.

A transect is different. To show how a species changes across a gradient, such as from a path into a meadow, quadrats go at fixed intervals along a line. That describes the change; it does not estimate the total population.

Counting without losing your place

Work through each quadrat in strips, one species at a time, and record the count against the quadrat number before moving the frame. Elzinga and colleagues suggest subdividing large square quadrats so no part is searched twice, and note that long, narrow ones are easier to search from one end.

Simple Online Counter is a free, browser-based set of counters that keeps its counts in your browser's own storage. The tally counter takes one tap per plant, with undo for a double tap. The multi counter keeps a named counter for each species or for mature plants and seedlings, side by side, and exports them as a CSV. Neither identifies plants: the edge rule and the counting unit stay your decisions. The mean count per quadrat can go straight into the average calculator, and a paper tally sheet works the same way, as the tally marks guide shows. For animals that move, quadrats do not apply; a large flock is estimated in blocks instead.

Mistakes the revision notes repeat

What this guide does not cover

This guide covers counting sessile organisms in quadrats and turning the counts into density, population, frequency and cover estimates. It does not cover distance sampling, plotless methods such as point-centred quarter for trees, or permanent-plot change detection, where the manuals add paired tests and their own sample-size equations. Animals that move need other methods, such as mark and recapture. If your course, survey protocol or agency standard names a quadrat size, edge rule or number of quadrats, it overrides the general guidance here.

The sources are field manuals from 1996 to 2006. Sampling Vegetation Attributes is an interagency reference of the BLM, the US Forest Service and the Natural Resources Conservation Service, and the NVC handbook is JNCC's guide to the standard vegetation classification of Great Britain.