Sampling Trees Using the Point-quarter Method


Ecologists often need to estimate the number of  individuals present in a population or community. If there are a few, large individuals, this can be done directly by counting each individual. If there are many individuals, the community is large, or the individuals are small, it may be impractical to count all of the individuals. In these cases it is easier to take samples of the community and then estimate density the population size based on the samples. For example, suppose that you wanted to know how many sugar maple trees are in the Adirondack Park. It would be impossible to count every tree in the 2.4 million hectare (6,000,000 acre) park. Instead, randomly-located samples can be taken. Suppose that 100 one-hectare samples were taken at random locations in the park and in each of these samples, the number of Maple trees was counted.  The average number of maples per one-hectare sample was 500. From this we can estimate the number of maples in the entire park by multiplying 500 X 2,400,000.

Plot sampling as described above may be difficult for sampling trees, particularly if a large area is to be sampled. It may be easiest to sample trees using a plotless technique. Plotless techniques are best used with stationary organisms because they involve measuring distances to organisms.

The point-quarter technique is perhaps the most popular of the plotless sampling techniques.  Each sample is taken at a random location in the area to be sampled.  This is frequently done by choosing random points along a transect but any randomization technique may be used. The area near each random point (sample point) is divided into four imaginary quadrants as indicated below.  Within each quadrant, the distance from the random point to center of the nearest individual is measured.  There are four quadrants, so you will measure a total of four trees at each sample point. In the diagram below, point A represents a random point (sample point) and the letters b through h represent trees.  The distance from A to the center of b, d, e, and h would be measured.  For each individual (b, d, e, and h), the species name and its basal area or area of coverage are also recorded.  Basal area is the area of a cross section of the stem.

For trees, the basal area can be calculated by measuring the circumference or the diameter at 4 ft above the ground (called DBH or diameter at breast height) and converting these measurements to area.  For smaller plants, the total area of coverage by the entire plant is frequently used.


The diagram of a hypothetical forest below will be used to explain the rationale for density calculations. Each dot in the diagram represents a tree. The distance between each tree is 5 meters.

If you were to draw a square around each tree, the sides of each square would also be 5 meters (see diagram). The area occupied by each tree is therefore 5 m X 5 m (or 52) sq. m = 25 sq. m. This gives you the number of square meters per tree. We want to calculate density, which is the number of trees per square meter. Density is therefore the inverse. Density = 1/(distance between trees)2.

In nature, organisms are seldom distributed in such a regular pattern. The distance between each tree in a forest, for example varies. The formula for density calculations given above can still be used if we use the average (mean) distance between each tree.

To calculate the density of all species, it is necessary to sum the point-to-organism distances for all species and calculate a mean.  The square of this number is equal to the mean area occupied per organism.

Mean area per organism = mean point-to-plant distance2

Density is equal to the inverse of the area per organism as shown below.

Density (all species) = 



Mean point-to-plant distance2

   Equation #1


Note that the above formula computes the density of all species combined.  The unit of density is the same unit as the mean point-to-organism.  For example, if the point-to-organism distance is in meters and you want density calculated in individuals per square meter, then use the equation given above.  If you want to know the number of individuals per 100 sq. meters, then D = 100/mean point-to-plant distance2.  In our samples, we will measure distance in meters but calculate the number of individuals per hectare.  The numerator in the equation becomes 10,000 because there are 10,000 square meters in one hectare.

The equations below show calculations for relative density, dominance, relative dominance frequency, relative frequency, and importance value.

Relative Density

# individuals of a species


Total # of individuals (all species)

  X  100   Equation #2



Relative density of a species



  X  Density ( all species)   Equation #3

The units for density will be the same units that you used for measuring the distance from the sample points to the trees. For example, if you measured these distances in meters, the calculation for density will be trees per square meter. If you measured these distances in centimeters, density will be given as trees per square centimeter. It is usually to convert these measurements to trees per hectare. There are 10,000 square meters in one hectare.

Dominance = density for a species X average basal area for species   Equation #4


Relative Dominance



Total dominance of all species

  X  100   Equation #5


Frequency = number of sample points at which species occurs*    Equation #6

*Important- This is not equal to the number of individuals in your samples. There are 4 measurements taken (4 trees measured) at each sample point. Regardless of how many times a species occurs at that point (1, 2, 3, or 4), it's frequency for that point is still 1. For example, if you sampled 5 points (20 trees), there may have been 6 maples. If these maples occurred at two sample points, the frequency for maple is 2.

If your samples are obtained from 5 sample points, the maximum value that a species can have for frequency is 5.


Relative Frequency



Total frequency of all species

  X  100   Equation #7


Importance Value = Relative Density + Relative Dominance + Relative Ffrequency

Equation #8

Materials Needed

A 10 foot (or 3 meter) tape measure. Some of the distances that you measure in this lab are likely to be longer than 10 feet but a 10-foot measure can be used to measure these if you do not have a longer tape measure.


We will use this technique to sample a woodlot. Most wooded areas will have several different tree species. Choose a woodlot that has at least 3 tree species. This should not be a problem unless you choose to sample a tree plantation that has only one species. Your samples should include at least 3 species of trees.

1.   One  method of determining the location of sample points in a field is to first obtain two two-digit random numbers that are less than 50 from a table of random numbers.  If you do not know how to use a table of random numbers, see the instructions for using a table of random numbers. These numbers are used to determine the coordinates of a sample point.  For example, if these numbers were 22 and 12, you would pace 22 steps along one border and then turn 90 degrees and pace off another 12 paces into the area to be sampled.  For our purposes, we will simply walk in a straight line through a woodlot.  The number of paces will be determined by selecting a two-digit random number that is less than 50.  If you reach the end of the woodlot before obtaining 5 sample points, turn 90 degrees and walk along the edge for a few paces and then turn another 90 degrees and walk in a line parallel to the one you just sampled as is indicated in the diagram.  The distance between the two lines could be determined by a single random digit.

2.   At each sample point, measure the distance to the center of the nearest tree in each quadrant and record this measure along with the name of the species in the raw data table. You should have four trees per sample point. Next, record the circumference in he raw data table. Record all of your measurements in meters to the nearest 0.01 m. For example 5.61m. If your measurements are in inches, you will later need to convert them to meters. This can be done by dividing by 39.4. If you do not know the name of the species, use numbers. For example, species #1, species #2, etc. It might be helpful to briefly describe the species so that if you see it again in later samples, you will know what number you gave it.

3.   Repeat this procedure until data for 5 sample points (20 trees) have been recorded. A sample size of 5 sample points is adequate for our purposes but if you were interested in more accurate estimates, you should collect data from more points.

4.   Table 2 can be used to help organize your data for performing the calculations discussed below. This table will also be useful for entering the data into the spreadsheets.

Lab Report

Online Students: Go to the document "Point-quarter Method Questions" in Angel to submit your data and answer questions about this exercise.

Campus Students: Answer the Point-quarter Method Questions.