6.2: Counting Methods

Video Presentation

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Learning  Guide


Density is defined as the number of individuals or counting units within a unit area. Since the measurement units of density (number/area) are based on area, counting the number of individuals within a specified area is the most common approach to estimating density. Counting methods are always done in a quadrat or plot. A variety of decisions about sampling design elements need to be made when we develop a sampling design to estimate density.

  • Counting Unit
  • Quadrat/Plot Dimensions
  • Ground Rules for Counting

Counting Units

When measuring density we most often consider that individuals serve as the counting units. However, for certain species such as sod-forming grasses or other clonal plants, it may be difficult to clearly identify individuals. In those cases, we often define the counting units as plant parts that are easily distinguished, such as grass tillers or culms. Similarly, when the research or management objectives focus on reproductive potential, the counting units may be defined as individual flowers or inflorescences, or individual fruits or infructescences. In essence the definition of the counting unit is determined by research or management objectives, and ensuring that the counting unit can be easily discerned by field personnel.

Quadrat/Plot Dimensions

The dimensions of the sampling unit can have a large influence on the precision of density estimates, so decisions about the size and shape of quadrats and plots are very important. The same decision rules apply to both quadrats and plots, but it’s worth taking a minute to define these two terms:


Quadrat: a sampling unit of a specific area and shape in which measurements are taken. A quadrat is a frame, constructed out of a resilient but lightweight material such as plastic or PVC pipe, metal rod or rebar, or occasionally wood. Quadrats are solid frames that are carried into the field and placed flat on the ground, over the vegetation. Due to practical considerations for transporting them, they tend to be relatively small, usually ≤ 1m2, but occasionally as large as 1.5 – 2.0 m2 (Figure 1a). The terms quadrats and plots are often used interchangeably.


Plot: a general term for a specified area in which measurements are taken. Plots also have a specific area and shape. Plots are larger than quadrat frames, although the term may be applied to small areas. In general, plots do not have a solid edge, but are designated by four corners (for squares and rectangles) or a center point and radius (for circles). Sometime we use transect tapes to temporarily delineate one edge of a plot while we take measurements (Figure 1b). Since plots don’t have permanent edges, they can represent large areas, such as 1m wide by 50m long, etc.


Figure 1. Comparison of quadrats and plots: a) quadrats frames in various sizes and shapes, and b) plots delineated by pin flags at the corners, with a transect tape running along one side.


The appropriate size (area) and shape of quadrats and plots is determined by the spatial arrangement of the vegetation and by the average size of individual plants.  Is the vegetation relatively homogeneous, or evenly distributed across the landscape, or are plants clumped or patchy (heterogeneous distribution)? Does vegetation occur in linear strips, clumps, and what average area does one individual occupy? These factors influence our decisions about quadrat and plot dimensions.

Quadrat Size

In selecting an appropriate quadrat size, we need to ensure that the quadrats are big enough to contain at least one plant of interest. Conversely, the quadrat needs to be small enough that the attribute can be measured in a reasonable amount of time. For example, if small seedlings are plentiful, it will be more efficient to count them in smaller quadrats (Figure 2a). Larger plots will be needed for larger individuals such as shrubs or trees (Figure 2b).


Figure 2. Comparison of plot sizes for different sized plants. a) smaller quadrats are appropriate for small, plentiful plants; b) larger plot size is needed for larger individuals.


General guidelines concerning quadrat size
  • Select the size of quadrat based on the species of greatest interest.
  • Quadrat is too large if the 2 most abundant species are found in every plot.
  • Quadrat is too small if the most abundant species are not found in the majority of plots.
  • Increase plot size if the number of empty plots (zero plants) is greater than the number of plots with 1 plant.
  • The plot should be larger than the average-size plant and larger than the average space between plants.
  • Sparse vegetation requires larger quadrats or plots than dense vegetation.
  • Uniform vegetation requires smaller quadrats than patchy and heterogeneously distributed vegetation.
  • Avoid using quadrats that are larger than necessary, in order to increase efficiency and to avoid counting errors.

Quadrat Shape

The choice of quadrat shape generally depends on how the vegetation is distributed.

  • Square or rectangular quadrats are used most often to measure density; circular plots are less commonly used.
  • Square plots work well in dense, herbaceous vegetation.
  • Rectangles are more likely to cut across plants or clumps of plants in “patchy” vegetation (Figure 3).
  • Extremely elongated rectangles, belt transects, are used in highly diverse vegetation, especially when species of interest include larger individuals such as trees and large shrubs.


Figure 3. Rectangular quadrats (b) and belt transects (d) tend to cut across patchy vegetation better than square (a) and circular quadrats (c).


Since rectangles and belt transects have higher perimeter:area ratios than squares, the need to make boundary decisions (i.e., decide when to count plant “in” or “out” of the plot) increases. Ground rules for edge or boundary decisions are discussed below.

Case Studies

Let’s examine a few case studies in which density was measured in different communities to illustrate the importance of selecting plot size and shape.


In each example, the size and shape of quadrat or plot was determined based on the average size of the species of interest, as well as the spatial distribution of the vegetation.

Ground Rules for Counting Methods

Certain ground rules must be considered when using counting methods to estimate density.

  • Boundary Decisions
  • Nested Quadrats


Boundary Decisions

In general, plants need to be rooted in plots to be “counted”. It is necessary to establish ground rules for boundary decisions to prevent bias when plant bases touch or are intersected by the edge of quadrats or plots (Figure 4).


Figure 4. Schematic diagram showing various scenarios where boundary decisions may apply. Boundary decisions do not apply if the plant base does not touch the plot edge (a and b). In all other cases where the plant base touches the plot edge (c, g, and h) or if the plant base is partially rooted inside the plot boundary (d, e, and f), a boundary rule needs to be applied. (Adapted from Figure 8.3 in Elzinga et al. 1998).


Two types of boundary rules may be applied:

  1. Two Sides “In”, Two Sides “Out” Rule: Pre-define certain sides of the quadrat as “always in” or “always out”. For example, decisions for plants at the top and right sides of a quadrat could always be counted “in”, and decisions for plants at the bottom and left sides of the quadrat could always be counted “out”.
  2. Alternative Decision Rule: Boundary decisions, to count plants “in” or “out” are alternated throughout sampling.  To apply this “every other” approach, you must keep track of the boundary decision that have been made. In this case, if the first boundary decision was to count the plant as “in”, the next decision would count the plant “out”.
  3. 50:50 Rule: Each decision is made on an individual basis, based on a visual estimation of whether half of the plant base is “in” or “out”. This method is not recommended because of the potential to introduce bias at each decision. Quadrats with a smaller perimeter to area ratio have less opportunity for plants to intersect the boundary. The shape of the quadrat and its corresponding perimeter to area ratio becomes important when deciding when a plant is actually “in” a quadrat. For most cases, plants are counted “in” the quadrat if they are rooted within the quadrat.


Nested Quadrats

We can encounter difficulties when we want to determine density for multiple species that exhibit different sizes or different distributions on the landscape, because the different species will be more efficiently measured with different quadrat sizes or shapes. In this case, we can use nested quadrats.

Nested quadrats include multiple sizes of quadrats positioned together so that measurements can be made at multiple scales using a single placement of the quadrat or plot. More abundant species are measured in smaller quadrats, and less abundant or larger species can be measured in larger quadrats. Pilot sampling is conducted to measure plant density of all species in each division of the nested quadrat (Figure 5).









Figure 5. Diagram of a nested quadrat that includes three quadrat sizes (small, medium, and large). Density of each species was measured in each of the quadrats to determine the most appropriate size for density estimations of each species.

The quadrat size that most efficiently estimates density for each species is then determined, and each species is only measured in the one quadrat size/shape.  In the example above (Figure 5), the small quadrat would be selected to measure grass density, and the large quadrat would be selected to measure density of the yellow dandelion and pink flower.


Once the appropriate quadrat size has been determined, it is important to clearly document the quadrat dimensions that are associated with each species, since density calculations (explained below) require knowledge of the quadrat or plot area. Nested quadrats are also used extensively for frequency measurements.

Density Calculations

Density is reported as the number of plants (or counting units) per unit area. Since density measurements are often taken in quadrats that vary in size or area, we usually report density in units of the number of plants per square meter (m2) or per hectare (ha).


Density measurements should be converted to standard units prior to analyzing the data. This is especially important when nested quadrats were used, because density measurements were not made with a uniform quadrat or plot area for all species.


Example 1:   Assume 2 plants were counted in a 25 cm X 25 cm (0.25 m2) quadrat.  The number counted is divided by the size of the quadrat.


Example 2: Assume 2 plants were counted in a 2 m X 25 m (50 m2) plot. Again, the number counted is divided by the size of the quadrat.


It is difficult to envision what 0.04 plants per m2 would look like, so in this case we would want to report density in units of the number of plants per hectare. To do this, we need to multiply the number of plants per m2 by 10,000 because there are 10,000 m2 per hectare.  In this example, density = 400 plants/ha.