## Frequency Mean densityMean cover

True value :

none

{(4x0.1) + (38x0.01) + (15x0.005) / 144} x 100% = 0.6%

Fig. 10.5. The effect of quadrat size on estimates of a population's density, cover and frequency. There is no frequency value for a 'true' population density of common species. Various measures of abundance will be affected by quadrat size in different ways (Krebs, 1999). Frequency is more dependent on quadrat size than other measures of abundance: large quadrats will result in more species having 100% frequency, whereas in small quadrats many frequencies will be zero (Fig. 10.5). The smaller the quadrat, the more likely you are to 'miss' individuals.

In some cases, we need to adjust how we collect random samples to ensure that they are representative. For example, if there is an environmental gradient, we might want to change the sampling protocol. Transects are lines, often arranged in a rectangular or square grid, to help determine where to locate quadrats to test for changes along environmental gradients. The random placement of quadrats along transects means that an ecologist is likely to be able to detect patterns. For example, we might be interested in how a weed's distribution responds to changes in environmental variable like soil moisture. If quadrats were randomly placed throughout the site, some areas might be missed; for example, there may be no quadrats in wet soils. To accommodate environmental gradients, researchers can use a combination of regularly spaced quadrats along randomly placed transects (Fig. 10.6). The main advantage to this is that it allows ecologists to sample randomly (using transects) to reduce bias yet still maintain a systematic, representative sample (Zar, 1999).

The spatial arrangement of individuals within a population can affect estimates of abundance. Quadrat sampling assumes that individuals are randomly distributed and the environment is relatively homogeneous. In fact, this is rarely the case. Figure 10.7 shows estimates of the density, frequency and cover of three populations (calculated using randomly placed quadrats). Estimates are different even though the true values of the three populations are the same. Therefore, under some circumstances, mean density, frequency and cover may be of limited value because of sampling bias. There are ways to sample populations that are highly non-random, but this requires the use

Gradient of increasing soil moisture -►

Fig. 10.6. Placement of regularly placed quadrats along randomly placed transects to accommodate an environmental gradient.

of advanced statistics (Cardina et al., 1996; Dieleman and Mortensen, 1999; Gibson, 2002).

### Plotless sampling

Sometimes it is not possible or appropriate to use plots for sampling. This is especially true for large plants. Several plotless methods have been developed to accommodate this (Brower et al., 1998; Krebs, 1999). For example, in the point-quarter method, a random point is located (usually along a transect) and from this point four equal quadrants (not quadrat) are established (Fig. 10.8). In each quadrant, the tree (>10 cm in diameter) nearest to the point is identified, and its diameter at breast height (dbh) and the distance are recorded. The same process can be repeated for saplings (2.5-10 cm in diameter). This process is repeated at multiple points, and a variety of statistics can be calculated using these data (Table 10.2) (Engeman et al., 1994). For example, Table 10.2 shows that the total tree density is 1663