PLOTLESS SAMPLING: The Point-Quarter Method

It is easiest to sample some types of vegetation using plotless techniques.  Plotless sampling is generally faster than plot (quadrat) sampling when sampling large organisms or large areas.

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 point is divided into four imaginary quadrants as indicated below.  In each quadrant, the distance from the center of the nearest individual to the random point is measured.  In the diagram below, point A represents a random 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 plant is frequently used.

Calculations

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.

1

DENSITY (all species) =                                       Equation #1

Mean point-to-organism dist.2

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.

DOMINANCE and FREQUENCY should next be calculated.  As with the plot sampling technique, an importance value can be obtained for each species by summing the RELATIVE DENSITY, RELATIVE DOMINANCE, and RELATIVE FREQUENCY values.

# individuals of a species

RELATIVE DENSITY =       X 100                                 Equation #2

Total # individuals (all species)

Relative density of a species

DENSITY =   X total density (all species, equation 1)            Equation #3

100

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

Dominance

RELATIVE DOMINANCE =           X 100                     Equation #5

Total dominance for all species

FREQUENCY = number of points at which species occurs                                     Equation #6

Frequency for a species

RELATIVE FREQUENCY =