Rangeland Ecology & Management

Get reliable science

Distance Methods

Distance methods to determine density that involve plotless sampling regimes are based on determining the mean area associated with each plant by measuring the spacing between them. This approach builds on the pattern that when plants are crowded together in dense vegetation there is a small distance between individuals.

Distance methods are most commonly used in forests and shrublands (although some have been tried in bunchgrass), and work best when estimating the density of a single key species. These methods are usually adopted when a large area must be sampled, where it is difficult to follow the counting individual plants approach which requires that we delineate boundaries and methodically count all individuals. Inaccuracies caused by boundary decisions should also be prevented using a plotless method.

Nonetheless, distance methods can also be time consuming and arduous, and a second person may be needed to identify the correct neighboring plant and accurately measure the distance. This is especially true in dense vegetation, where it can be troublesome to see the key species or difficult to choose between several plants that are a similar distance from the sampling point. In contrast, excessive time may be spent scouting for individuals of an infrequently occurring species or in less dense vegetation.

However, the greatest shortcoming of many distance methods is the assumption that the sampled key species follow a random spatial pattern. This assumption rarely holds for herbaceous plants or shrubs (but is more likely to be tenable for some tree species) and nonrandom psatial patterns cause density to be underestimated. Some distance methods have been developed in an attempt to circumvent this assumption (Table 1).

Table 1. Plotless or distance methods developed to estimate density
Method Spatial Patterns Should be Random Reference
Closest Individual Method yes Cottam and Curtis (1956)
Nearest Neighbor Method yes Clark and Evans (1954)
Random Pairs Method yes Cottam and Curtis (1949)
Point Centered Quarter Method yes Cottam and Curtis (1956)
Wandering Quarter Method no Catana (1953)
Angle Order Method no Morisita (1957)
Corrected Point Distance Method no Bachelor (1971)

To provide an idea of the concepts and procedures involved with distance methods, three techniques are described in greater detail.

References and Further Reading

(Note: pdf files require Adobe Acrobat (free) to view)

Bachelor, C.L. 1971. Estimating density from a sample of joint point and nearest-neighbor distances. Ecology 52:703-709.

Bonham, C.D. 1989. Measurements for terrestrial vegetation. John Wiley Sons, New York. pp. 148-177.

Catana, A.J. 1953. The wandering quarter method of estimating population density. Ecology 44:349-360.

Clark, P.J., and F.C. Evans. 1954. Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology 35:445-453.

Cook, C.W., and J. Stubbendieck. (eds). 1986. Range research: Basic problems and techniques. Society for Range Management, Denver, CO. pp. 62-63.

Cottam, G., and J.T. Curtis. 1949. A method for making rapid surveys of woodlands by means of pairs of randomly selected trees. Ecology 30:101-104.

Cottam, G., and J.T. Curtis. 1956. The use of distance measures in phytosociological sampling. Ecology 37:451-460.

Greig-Smith, P. 1983. Quantitative plant ecology. Blackwell Scientific Publications, Oxford.3rd ed. pp. 47-53.

Laycock, W.A. 1965. Adaptation of distance measurements for range sampling. Journal of Range Management 18:205-211. (pdf)

Laycock, W.A. 1985. Density as a Method for Measuring Rangeland Vegetation. In W.C. Krueger (Chairman) Symposium on use of frequency and sensity for rangeland monitoring. Proceeding 38th Annual Meeting, Society for Range Management, Salt Lake City, UT, February 1985. pp. 93-96.

Mueller-Dombois, D., and H. Ellenburg. 1974. Aims and methods of vegetation ecology. John Wiley Sons, New York. pp. 68-70.

Morisita, M. 1957. A new method for the estimation of density by the spacing method applicable to non-randomly distributed populations. Physiology and Ecology 7:134-144. (In Japanese)