7.2: Nested Plots and Frequency Data Analyss

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Learning Guide

Using Nested Plots

One of the greatest shortcomings of assessing vegetation with frequency is that this measurement is completely dependent on quadrat sizeNested quadrats (Figure 1) are typically used when multiple quadrat sizes are needed to estimate frequency of different species.


Figure 1. Nested sampling is most commonly conducted using nested squares (a), nested circles (b), and open-ended square with marked dividers and rectangular partitions (c). An illustration of how these dividers are used to create the nested plots with different sizes and shapes is provided (d).


Ideally, we have pre-determined the appropriate quadrat size for each species, and then record the presence of each species in its “designated” quadrat. In order to make comparisons between years, it is important to consistently estimate the frequency of each species using the same “designated” quadrat size.


Please remember that the terms “plot” and “quadrat” are often used interchangeably. Both terms are used throughout this text and hold the same definition.

Overcoming Quadrat Size Issues

Problems may arise because we’ve made a few assumptions – how do we “pre-determine” the appropriate quadrat size for each species, and will that always be the best quadrat size?


Specific challenges with determining quadrat size include:

  • We need to select a plot size that estimates frequency between 20% and 80%. However, until you collect the data or conduct a pilot study, you do not know what the appropriate size should be.
  • Even if you select a quadrat size that works this year, the quadrat may become too big or too small as the vegetation community changes over time.
  • A quadrat that is “just” right for one plant may be too big or too small for another species of interest. (Sounds a bit like Goldilocks searching for the right chair).


To overcome this “right size” problem, rangeland scientists, (Smith, Bunting, and Hironaka 1986), proposed an approach to collect frequency data using nested frequency plots in which it isn’t necessary to have prior knowledge about the most appropriate quadrat size for each species.


With nested quadrats, all plants recorded in the smallest section of the nested quadrat are automatically known to occur in the larger quadrat sizes. As we examine the successively larger quadrats in the nested quadrat frame, new species are recorded as they occur. In the approach described by Smith et al. (1986), the smallest frame in which a species occurs is recorded. Figure 2 illustrates this approach in which nested quadrats with 3 plot sizes (1 = smallest (red plot), 2 = medium (blue plot), 3 = largest (purple plot) are used to record frequency of 4 plant species.


Figure 2. Four sets of nested quadrats (Sample A, B, C, D) show varying occurrence of four plant species (pink flower, grass, clover, and white flower). Each nested quadrat includes three plot sizes (Plot 1 -small, 2 -medium, 3 -large).


Table 1 shows how the frequency data from Figure 2 would be recorded. The smallest frame in which the plant species occurred was recorded.  Remember, the recorded number designates the plot size, not the number of times the species occurs in the plot.


Table 1. Frequency data collected from the 4 quadrats (Samples A, B, C, and D) in Figure 2. The values recorded indicate the smallest plot that included the plant species.


Next, we summarize the data to examine occurrence in each plot size (Table 2). Remember, if a species occurred in plot 1, then it also occurred in plots 2 and 3, we record the smallest plot size in which it occurred. “Hits” reflects how many times we found the plant in a plot of a certain size. In addition, “hits” are cumulative, so if a species occurred in plot 1, when we summarize the data we indicate that it also occurred in 2 and 3, etc.


Table 2. Data from Table 1 are summarized to give the total number of times that each species occurred in each plot size (Hits).  The “hits” are then divided by total number of samples (4) to obtain the percent frequency of each species in each plot size.


Let us examine the summary for clover. Clover occurred in the smallest plot (plot 1) for three of our samples (Sample A, Sample B, and Sample C), so we recorded 3 “hits” for plot 1. Plants found in plot 1 also occurred in plot 2, and since there were no new records of clover in plot 2, the number of hits for plot 2 remains at 3 + 0 = 3. We did record clover in plot 3 for Sample D, so we add that new occurrence to the 3 times we already have the plant recorded in plot 1 for a total of four “hits” in plot 3 (Table 2).


To calculate the percent frequency, we divide the number of hits by the total number of samples examined; in this case, n= 4.


For example, consider Plot A for Grass.   Hits = 3, total number of samples = 4;


Percent frequency = 3 hits ÷ 4 samples = 0.75 or 75%


Which Plot Size is Correct?

Using this approach, we can select the appropriate plot size for each species, and we can estimate frequency using the data that we collected. Recall that we want to use a plot that measures percent frequency between 20-80%. For the pink flower, we would select plot 1, because plot 2 and 3 are both outside that range. Of course, this example was based on a sample size of only 4 quadrats, and in practice we need at least 100 quadrats to estimate frequency (Despain et al. 1991).

Nested Frequency Method: Step-by-Step

Now let us review the frequency process as a whole.

  1. Create a nested quadrat that is a series of 3 to 5 quadrats nested within each other (Figure 1d). A common frame size for herbaceous plants is 50 x 50cm, with three smaller quadrat sizes nested within the frame (5 x 5 cm, 25 x 25 cm, 25 x 50 cm, and 50 x 50 cm).
  2. Examine the smallest quadrat first. Record that quadrat size for the species that occur there. Then, examine each successively larger quadrat and record each new species that has not already been recorded as occurring in smaller quadrats.
  3. Remember, presence of a species in a smaller quadrat means that it automatically occurs in larger quadrats.
  4. Estimate frequency for each species in each quadrat size (small to large separately):

  1. Examine the data to see which plot size most appropriately estimates each important species. Recall that a good plot size would yield a frequency between 20 and 80%. The advantage of this technique is that one does not need to determine in advance which plot size is going to best represent each species.  You simply record occurrence in all quadrats and decide later which is best for each species of interest.
  2. Finally, be SURE to clearly document the quadrat size that was ultimately used in the frequency estimate. This is VERY IMPORTANT because in order to compare frequency between years we need to ensure that we compare frequency that was estimated in quadrats with exactly the same size and shape.


Example Calculations In the following example (Figure 3), a nested quadrat using 4 sizes of quadrats (1, 2, 3, and 4) were used to estimate frequency (n=15). Idaho fescue (FEID) occurred in 12 of the 15 samples (single placement of the nested quadrat), and was recorded at least once in each of the 4 quadrat sizes. The frequency of each species in each of the quadrat sizes is summarized on the right side of the data sheet (Figure 3)


Figure 3. Data sheet on which frequency data were recorded using the nested plot approach described in the text. The smallest quadrat size in which a species occurred was recorded on the left half of the data sheet.  The frequency summaries were subsequently calculated on the right side of the data sheet (frequency values for each quadrat size are written in red).


Idaho fescue would be best sampled with a medium (size 2) or large (size 3) plot.  The smallest plot (size 1) is too small because frequency should be > 20% and the largest plot (size 4) is too big because frequency should be less than 80%. For bottlebrush squirreltail (SIHY), the large and largest plots (sizes 3 and 4) are the only plots that are large enough to properly measure frequency.  Lupine (LUPIN), has frequencies between 20-80% for the small, medium and large plots (sizes 1, 2, and 3), but the largest plot (size 4) has a frequency greater than 80% so it could not be selected.


Ideally, we want to select the smallest size of plot that has a frequency fitting the selected percent range (in this case 20-80%). In the case of lupine, this would mean we would select the plot size 1. However, if we discover that we are able to measure all species with one plot size, then we would need to select the plot size 3 as it would accommodate all three species.


Using nested quadrats is particularly relevant when you are monitoring an area after vegetation treatments and want to determine the response of target species, such as invasive plants, as well as the response of the native plant community to those treatments. For example, Turner (1969) used nested frequency plots to monitor five herbicide treatments on plant communities in Eastern Oregon that had been invaded by two exotic annual grasses, medusahead (Taeniatherum caput-medusae) and cheatgrass (Bromus tectorum).  Nested quadrats ranging in size from small (4 in2), medium (36 in2) and large (144 in2) were used to measure the frequency of medusahead, cheatgrass, and native perennial grass species. A nested quadrat design was selected to accommodate the different sizes of the species being monitored.

Basics of Frequency Analysis and Interpretation

The second challenge of assessing frequency is to analyze the data using statistics in order to interpret their implications. We use frequency data to compare:

  • Changes in a site over years, or
  • Differences between sites

In most cases we want to know if repeated measurements from within a site are “significantly different”. Similarly, we may want to compare the frequency of individual species between sites.  This statistical comparison of frequency data is usually conducted with a Chi Square Analysis (pg 241-243, Elzinga et al. 1998) or by calculating binomial confidence intervals (Despain et al. 1991).

Using Chi-Square Analysis to Compare Frequency Data

For example, assume we examined 150 plots on bunchgrass sites (Figure 4) with south-facing slopes in Idaho and Oregon. On these sites we calculated a frequency of 36% (present in 54 of 150 plots) for Indian paintbrush (Castilleja linariifolia) using a 1 m2 plot. Then, we also examined 150 plots on sites with north-facing aspects and we found that the frequency of Indian paintbrush was 48% (present in 72 of 150 plots). What we really want to know is – does a difference of 12% indicate a real, or significant, difference in the frequency of Indian paintbrush on north and south facing slopes. A Chi Square Analysis can give us a way to judge if the sites are really “different.”



Figure 4. A bunchgrass community and Indian paintbrush within the bunchgrass community.


  • Data are arranged in rows of what was observed and columns of the treatment we want to examine.   In this case our “treatment” is south- versus north-facing slopes.
  • Data from field = “Observed” either present or absent in the plots examined.
  • The number “Expected” is based on an equation to estimate the value you would expect if there was no treatment effect.


Expected= Total occurrences of “Observed” for both treatments × total plots in one treatment ÷ Total plots examined on both sites.


Easily calculated in a table as Expected Value = (Row Total × Column Total÷ Grand Total




Thus, from the example above:


A calculated  statistic of 4.4 can then be compared to a critical, or table,statistic to determine if the values in the comparison are different. In other words, is thestatistic that we generated large enough to be “significant”?
Evaluating aStatistic:

Look in a Chi Square Table to determine the appropriate. To find a value in a chi-square table you must determine the degrees of freedom (represented as either df or n-1) for your comparison:


df = (number of rows in comparison – 1) (number of columns – 1)


In our example, for a 2 x 2 comparison, df = (2-1)(2-1) = 1

  • If we use a P-threshold (or α) of 0.10, the critical value (from the table) is 2.706.
  • The  statistic calculated for these data was 4.4.
  • The null hypothesis is that there is no difference between or among samples in the comparison. (In other words, the null hypothesis in this example is that there is no difference in the frequency of Indian paintbrush on north- and south-facing slopes).
  • If the calculated statistic is greater than the critical  value, we reject the null hypothesis.
  • In this example, 4.4 is greater than 2.7 so we reject the null hypothesis, and conclude that the frequency of Indian paintbrush is different between north- and south-facing slopes.

**Note on Chi-Square Tables – 1) Excel also has a function to calculate chi-square (check the help button in Excel)