Chapter Two

Plant Frequency Sampling for Monitoring Rangelands

D.W. Despain, P.R. Ogden, and E.L. Smith

Federal and State land management agencies in the U.S. are actively involved in monitoring the effects of management practices and climatic fluctuations on western rangelands. A widely used method for monitoring vegetation changes on these rangelands is plant frequency sampling. Frequency has become popular primarily because it is relatively simple and objective.

Definitions

The concept of frequency as a parameter for quantifying vegetation is generally credited to the Scandinavian researcher, Raunkiaer (1909). Frequency is defined as the number of times a plant species is present within a given number of sample quadrats of uniform size placed repeatedly across a stand of vegetation (Mueller-Dombois and Ellenberg 1974, Daubenmire 1968). It is generally expressed as a percentage of total placements and reflects the probability of encountering a particular species at any location within the stand (Greig-Smith 1983).

Only species presence within the bounds of the sample quadrat is recorded, with no regard to size or number of individuals. Plant frequency is a function of quadrat size and reflects both plant density and dispersion. The sensitivity of frequency data to density and dispersion make frequency a useful parameter for monitoring and documenting changes in plant communities. If information is needed as to the specific attribute or attributes which contribute to the change, this must be accomplished by interpretation of data in the field or by collecting additional data which are specific for each attribute. Plant frequency, by itself, is useful for monitoring vegetation changes over time at the same locations or for comparisons of different locations. Plant frequency is less useful in descriptive studies except in conjunction with other parameters.

Sampling Procedures

Quadrat Size

Quadrat size is an important consideration in quadrat frequency sampling. The size of the quadrat influences the probability of each species occurring within the quadrat. Small quadrats result in low frequencies for most species and many uncommon species will not be sampled except with large samples. Large quadrats will include most species but will include the most common species in every quadrat. This eliminates the ability to detect changes in abundance or pattern for those species (Brown 1954).

The choice of a suitable quadrat size is primarily a function of the average abundance per unit area. A change in the size of the quadrat usually has the most effect on frequency values for species of intermediate abundance. Less influence of quadrat size is noted for species of high or low prevalence (Mueller-Dombois and Ellenberg 1974). Frequency values of 100% indicate quadrat size exceeds the maximum size of gaps between individuals (Daubenmire 1968). If quadrat size greatly exceeds this, then even a considerable decrease in the relative abundance of the species will not be detected. The best sampling precision is reached for a particular species when it is present in 40% to 60% of the quadrats sampled. This will provide the most sensitivity to changes in frequency. Good sensitivity is obtained for frequency values between 20% and 80%. Frequency values between 10% and 90% are useful but data outside this range should be used only to indicate species presence. Ideally, each plant species should be sampled with a quadrat size best suited for it. Obviously this is impractical. As a compromise, a quadrat size is selected which will adequately sample as many species as possible. Generally, quadrat size should be kept as large as possible without frequency of the most abundant species approaching 100%. At the very least, sampling those species in which one is most interested should result in frequency values between 20% and 80%.

Figure 1 shows the total number of species encountered and percent frequency values for several species using various quadrat sizes at 5 locations in Arizona. In general, quadrats larger than .10 m2 are necessary to sample the most important species at each location. Roughly half of the species encountered occur in more than 5% of the quadrats. For the remaining species, frequency sampling indicates only their presence. Based on these

examples and others, a square quadrat 40 or 50 centimeters on a side is generally appropriate and is easily handled in the field. Quadrats greater than 1 m2 are unwieldy and are not recommended. If a species of primary interest is not sampled adequately (>10%) by a practical sized quadrat, a different method should be considered for documenting changes in that species.

Situations arise where one species is very abundant and occurs almost continuously throughout a community with small spacing between individuals. Examples of this are illustrated in Figures 1d and Figures 1f. In Figures 1f, blue grama is highly abundant and dominates the stand. Other species such as squirreltail, a grass, and winterfat, a small woody plant, are common but not nearly as common as blue grama. In this case, a quadrat larger than .1 m2 would be adequate for most major species, but too large for blue grama. A large quadrat would be necessary if there is concern for sampling a less abundant species such as snakeweed. A quadrat small enough to appropriately sample blue grama would be too small for winterfat. In this case, "nested quadrats" could be used. A small quadrat is nested in the corner of a large quadrat (Figure 2) and frequency of the most abundant species is recorded in the small quadrat at the same time other species are recorded for the large quadrat. More than two quadrat sizes will rarely be necessary.

Although a particular sized quadrat might be adequate at the beginning of a study or monitoring program, large increases in the abundance of plants may cause frequencies to approach 100% at some later date. At this point, the ability to track further increases in species frequency is lost and attention can be shifted to a smaller nested quadrat. By recording these species in both sizes of quadrats concurrently for at least one sampling period, time continuity in the data is maintained.

Quadrat Shape

Numerical results of frequency sampling are also dependent on quadrat shape, though to a lesser extent than size. Therefore, as with quadrat size, the same quadrat shape must be used for all sampling for which data are to be compared. Any conventional quadrat shape will provide satisfactory results (The term "quadrat" is loosely defined here to included circular sample units). However, there are some considerations.

Since individuals of a species tend to be symmetrical and often concentrate in patches, a rectangular frame is likely to assess a somewhat different frequency than an equally sized square or circular frame (Mueller-Dombois and Ellenburg, 1974). For sampling most vegetation parameters, a rectangular frame is generally considered the best shape because it least conforms to plant shapes and distribution patterns and samples more variability with each placement of the frame. However, a rectangular quadrat has a longer perimeter than a square or circular quadrat of equal area. Therefore, in frequency sampling, more judgement error is introduced in deciding if a plant is in or out of the quadrat boundaries. A circular frame has the least perimeter per unit area, but is probably the least preferred because the frame shape conforms to plant shape and distribution patterns. Also, a circular frame can be less practical in the field because one side cannot be left open to facilitate placement and still have plot boundaries easily defined. A square quadrat is recommended as a good compromise.

Basis For Recording Presence

The most common criteria for determining plant presence within a quadrat are a) rooted or basal frequency for which a plant must be rooted within the quadrat, and b) cover or shoot frequency for which a species is counted as present if any part of the plant hangs over or occurs within the bounds of the quadrat.

Some have distinguished rooted and basal frequency by defining rooted frequency as using the center of a stem or clump as the criterion of inclusion, and basal frequency as considering any part of the stem or clump. In practice, the distinction is rarely made. Generally, a plant is recorded as present if any part of the plant is rooted within the quadrat. Stoloniferous plants require some judgement as to whether to include rooted nodes or not. Rooted nodes are generally included because it is easier to be consistent and because an individual plant can develop from a rooted node in the event the stolons are severed.

Sample Size and Design

Experience with frequency sampling has shown that vegetation changes often occur as relatively large changes. Regular frequency measurements can provide the signal that a change has occurred, and field observation can determine if the signal is biologically realistic.

The number of quadrats to be sampled depends upon the objectives of the sampling and is usually determined as a balance between a practical number which can be sampled on a regular basis and a number which is statistically sensitive to changes. Two hundred quadrats appears to be a reasonable compromise between data needs for statistical rigor and needs to identify biologically meaningful changes. Generally, it is better to take samples of this size on a regular basis than to undertake a more ambitious sampling program which dies because too much effort is involved. One hundred quadrats is the minimum number recommended at each sample location. If frequency data are analyzed strictly on a statistical basis and the objective is to identify small magnitudes of change with a high degree of probability, large samples of 500 to 1000 quadrats may be required (Wysong and Brady 1987).

Sampling design or arrangement of quadrats at a sample location or macroplot also is a matter of both statistical validity and practical application. Frequency data are enumeration data (presence or absence) and are discrete. Such data fit a binomial population distribution and statistical analyses may utilize binomial confidence intervals or Chi-square analyses. The sampling unit in this situation is the individual quadrat and strict statistical theory requires that each quadrat be independent and randomly located within the macroplot. The macroplot may be divided into a limited number of blocks and each block sampled with random placement of quadrats.

If normal statistics (t and F tests) are used to evaluate the statistical validity of differences among blocks within macroplots, years or sample areas, a sampling design which groups quadrats into transects may be used with the transect mean or total used for analysis. In this case, data are continuous and transect means should approach a normal distribution. The design should maximize the number of transects (to maximize the number of degrees of freedom for error) but should include enough quadrats in each transect so that few transects have zero values for any species of interest. For 200 quadrats, 10 transects of 20 quadrats each is often a reasonable choice (Tueller et al. 1972). The transect is the sample unit for analysis, and statistical theory requires that transects be randomly and independently located within the macroplot to be sampled.

In the field, strict randomization of quadrats or transects is rarely practical. Generally, quadrats or transects are located systematically from random or systematic starting points. If quadrats are at least one or two paces apart, they probably very nearly meet the independence criterion (Yavitt 1979). Systematic sampling usually will yield data which are more precise than random sampling (Cochran, 1977). However, exact confidence limits are not known and systematic sampling can be criticized as incorrect for strict statistical interpretation.

A practical sampling design when using binomial statistics with the quadrat as the sample unit, is to divide a macroplot into about four blocks. Samples within each block should at least approach being random and independent. If normal statistics are to be used for analysis, the data may be collected by transects with starting points located systematically or randomly along a baseline. Orientation of the baseline and subsequent placement of quadrats should fit the area to be sampled.

Statistical analysis methods and examples are given in Appendix A.

Recording Data

The first time a location or macroplot is sampled, ground rules should be clearly established and recorded for future reference. Later adjustments should likewise be noted. Ground rules to consider include:

  • Criteria for determining presence for each species or life form.

  • Which species, if any, are to be lumped together (e.g., annual forbs or species difficult to distinguish such as 3-awns or some gramas).

  • Whether to include seedlings and whether to separate any species into age classes. Seedlings, especially for species with low rates of seedling survival, may by excluded from the sampling or tallied separately to avoid wide fluctuations in the data which are season or climate related.

  • Are annuals to be recorded, and if so, do they have to be alive and green or dry but rooted and standing.

  • Sampling design, including any portions of the site to be avoided in sampling such as inclusions of atypical soil or vegetation.

Generally, data should be collected on a species by species basis. Consistency in species identification and use of criteria for determining presence or absence are essential. Rooted frequency is recommended for herbaceous plants and small shrubs and half-shrubs. Canopy frequency is suggested for larger shrubs. For intermediate sized shrubs or half-shrubs, the criteria for determining presence may depend on shrub density. Often, cover frequency is used for all shrubs in the interest of simplicity and consistency.

Summaries of data from previous sampling periods should be taken into the field for reference to assist in maintaining consistency in species identification. Having previous years data in the field also helps to interpret causes for observed changes while at the monitoring site. Recording species observed in previous sampling periods on field forms prior to sampling helps observers with consistency in identification. It also helps with on site comparison of current years data with previous years because species are in approximately the same order on the data sheets as on previous years summaries.

Perhaps the most common and significant problem in comparing data over time is in treatment of similar species. For example, two similar species may be separately identified on one occasion and combined as one species on another. Or, attempts may have been made to separate the species on each occasion, but the data reveal those attempts to be inconsistent. In these situations it is necessary to combine data for the two species and evaluate them as a complex. However, this can only be done if the data are collected on a quadrat by quadrat basis rather than tallied. When both species are recorded for the same quadrat, credit can be given for only one hit when the data are combined. Therefore, frequency values cannot be directly summed, but must be redetermined from the recorded hits for each individual quadrat.

Appendix D includes an example of a BLM form used for recording frequency on a quadrat by quadrat basis. This form does not allow for nested quadrats, but in combination with other examples in Appendix D, provides ideas for developing appropriate forms for particular needs. Data entry using hand held computers or data loggers may facilitate quadrat by quadrat entries and summary.

When nested quadrats are used, it is sometimes useful to collect data for the same species in both quadrats concurrently. In this case, a plant present in the nested quadrat can be recorded for the small quadrat only, as it automatically occurs in the larger quadrat. Frequency for that species in the large quadrat is then determined by summing the hits for the large and small quadrats. Appendix D includes a form used by the BLM for recording frequency in nested quadrats.

Analysis and Interpretation

An emphasis on interpretation of frequency changes while at the site of measurement has already been suggested. It is important to have data from previous years in a form that can readily be compared with current year data while at the monitoring location. A summary of data for the monitoring location, such as shown in Appendix B, is satisfactory for this purpose and is easily updated. A major benefit of a monitoring program is the discussion of data at the collection site by interested parties at the time the data are collected.

Data should be compared for frequency changes from one year to the next on a species by species basis. Binomial confidence intervals (Appendix C) can be utilized to help identify the magnitude of changes which indicate a change greater than what might be expected from sampling variation. For example, the data in Figure 3 (from Appendix B) are from a 200 quadrat sample at the 95% confidence level. Frequency of hairy grama for 1982 is 25% with confidence limits from 19% to 31%. In 1983, frequency of hairy grama was 36% with confidence limits of 29% to 43%. Confidence intervals overlap, so the difference could be due to sampling variation. Confidence intervals do not overlap at a probability of 80%. Statistical analyses of data for this species are detailed in Appendix A.

This change is large enough that observations of this species in the field should be made to determine if there might be some explanation for the change, such as an indication of new plants in the system. This was the case in this situation and a note was made that numerous young plants were observed. That these young plants probably maintained themselves and additional recruitment occurred is substantiated in the 1984 data where frequency of hairy grama increased to 49%. A similar observation was made for plains lovegrass for the 1982-1984 period (Appendix B). These changes were interpreted as a response to summer deferment of grazing in 1981 and 1982, heavy grazing with favorable precipitation in 1983, followed by summer deferment and favorable precipitation in 1984. It was concluded that the changes were desirable and that the deferred rotation grazing system, utilization levels and favorable rainfall were providing for upward trend at the monitoring location.

As was pointed out, frequency is a combination of species attributes including density, dispersion and cover. The relationship of frequency to plant density is curvilinear. Frequency changes should not be expressed as percentage changes in density. A change in frequency at low values does not reflect density changes of the same magnitude as changes at high frequency values. For randomly distributed plants, the curvilinear relationship between frequency and density are given in Figure 4.

Advantages and Disadvantages

As with all vegetation sampling methods, the frequency approach has both advantages and disadvantages.

Advantages

  1. Objectivity
    No estimation or subjective evaluation is necessary. The only decisions made by the observer is whether a particular plant is present within the quadrat and the identity of the plant. Objectivity provides better repeatability of results over time and among different observers.

  2. Rapidity
    Quadrat frequency is a relatively rapid approach to monitoring vegetation changes with respect to value of the data collected.

  3. Simplicity
    Relatively little training or practice is necessary for consistent application of frequency procedures and the data obtained are easily summarized and evaluated.

  4. Low sensitivity to periodic fluctuations
    Rooted frequency data are relatively insensitive to periodic fluctuations in vegetation structure due to grazing or changes in phenology. This is less true for cover frequency.

  5. No distinction of individuals
    There is no need to distinguish individuals in frequency sampling which can be a problem with indefinite individuals such as sod-forming grasses. This is an advantage only in comparison with density techniques.

  6. Function of both density and dispersion
    Frequency values depend upon both the density and the dispersion or distribution of individuals. Therefore, frequency will detect changes in plant distribution as well as abundance. This can also be a disadvantage as pointed out below.

Disadvantages

  1. Function of both density and dispersion
    Sensitivity of frequency to both density and dispersion can be a disadvantage as well as an advantage. It is difficult to determine which characteristic is indicated by changes observed in the data without supporting data from other parameters. Long term range health is, overall, more a concern of abundance than of dispersion. Frequency data can show significant changes in percentage values where no real changes in abundance actually exist. This problem arises more often when comparing two stands for differences than when observing one stand for changes over time.

  2. Data are non-absolute
    Though often correlated, frequency does not necessarily relate directly to more concrete parameters such as density, weight, height, volume or any criteria related to the amount of a species present at a location. Species frequency data are not generally useful for evaluating vigor, production, or dominance. This limits the use of frequency to comparisons in space or time such as monitoring trends in abundance related to loss and recruitment (confounded with changes in distribution patterns). Also, different species cannot be readily compared with each other unless their size and structure are similar, or when frequency is combined with other data or knowledge relating to size of the plant.

  3. Values dependent on quadrat size
    Frequency values are dependent upon the size of the quadrat used in sampling. Therefore, data collected with different sized quadrats are not comparable.

  4. Not well suited to larger shrubs
    Because of wide spacing of large species, a quadrat large enough to adequate-ly sample these species becomes unwieldy or impossible to use. Use of shoot or cover frequency can often be useful for evaluating shrubs, but where indi-vidual plants are widely scattered, may still be inadequate. The same can be said about uncommon, small species, but the issue of large shrubs is usually more important because of potentially strong influence on the community des-pite fewness of numbers. Quadrat frequency procedures are generally not well suited to shrubland vegetation types such as chaparral or Sonoran shrub types.

Appropriate Use of Frequency for Range Monitoring

Each parameter sampled and each method used to sample it have their advantages and disadvantages and have purposes to which they are most suited. The same is true of frequency data. Plant frequency data are useful because they are relatively easy and fast to collect, can be statistically evaluated, and indicate changes in species abundance and distribution. Because frequency data are non-absolute, they only indicate a change is occurring and which species are changing. The nature of those changes is not very well established from frequency data alone.

Frequency is an appropriate "indicator" of range trend, but unwarranted conclusions should not be drawn from frequency values alone. Other parameters provide more information than frequency alone and should be used where necessary. Frequency combined with other parameters is especially useful. However, other parameters are more expensive to obtain and are not always practical for wide spread monitoring.

A good analogy has been used to describe the appropriate use of frequency monitoring. A doctor monitors a patients blood pressure for indication of heart problems. When an increase in blood pressure is detected, the doctor does not immediately perform open heart surgery. Rather, additional tests are run to confirm and pinpoint the cause of the rise in blood pressure. Then appropriate action is taken.

Frequency monitoring should be considered in range management in a similar way as blood pressure monitoring is used by a doctor. When a consistent change in frequency of one or more species occurs, it may be necessary to take a closer look to determine the nature and cause of those changes. This may require performing additional "tests" such as more intensive monitoring of additional parameters. Lack of consistent trends in frequency values indicate little change in the vegetation and efforts can be concentrated elsewhere where frequency values are changing.

Frequency should be used only in those vegetation types and situations where it is appropriate (RISC 1983). Results should not be inappropriately extrapolated beyond the location sampled.

Comparison with Other Monitoring Methods

How does frequency sampling using quadrats compare with other methods commonly used to monitor rangelands? There is not as much difference as it may seem for many of these methods. Some of the most common methods used by range managers now and in the past can be compared with frequency to assist in understanding use of the method. Also, the use of ground cover sampling popularly included with frequency sampling will be briefly discussed.

Point Methods

Various "point" sampling procedures, such as the "step-point" and "Parker 3-step" methods, have been used extensively by land management agencies for monitoring trends in range condition. The basic concept behind these procedures is essentially the same as that of quadrat frequency except that a point is used as the sample or sub-sample unit rather than a quadrat. In fact, data collected with point sampling methods can be evaluated as frequency data; i.e. the number of hits on a plant species as a percentage of the total number of points read. However, because a point is essentially dimensionless, the data are usually used as absolute measures of cover, basal area or whatever the criteria used for determining "hits".

There are advantages to the direct quantitative information provided by point procedures as opposed to the relative nature of frequency data. However, disadvantages of point sampling often out-weigh the advantages. The main disadvantage of point procedures is the large number of sample points usually required for an adequate sample size. Large sample sizes are required because many placements of the point encounter no plants at all.

Another disadvantage of point methods relates to lack of repeatability over time and between observers. It is difficult to place a point without any bias. The slightest shifting of a point may change the reading and two observers may see it differently anyway.

Point Frame

One approach that is occasionally used to help overcome disadvantages of point sampling is to place a series of pins in a frame. These "point frames" allow for rapid sampling of points by providing several sample points at each placement of the frame. At the same time, the pins are held rigid in position such that there is less bias in the placement of the pin for sampling. The main drawback to this approach is that the sample points within each group or frame placement are so close together as to lack independence. In other words, the points are not independent of each other as related to size of a plant or patterns of plant distribution. For example, all or a portion of the points in the frame may hit the same shrub. This can cause biased sampling results with the principal bias in favor of large or aggregated species.

Step-Point

Another common attempt to remedy the drawbacks of point methods is to record the nearest plant to the sample point whenever a direct hit is not made. This gives a recorded hit each time the point is placed, reducing the number of points that must be sampled and reducing observer inconsistencies or errors in reading the hits.

This approach has several problems stemming from the fact that the method is not really a point method. It is a quadrat based frequency method except that the quadrat varies in size with each placement of the point (quadrat). The size of the quadrat at each placement is determined by the distance to the nearest plant. The quadrat is circular in shape, or a half-circle when only plants in front of the point are considered (such as when the tip of the boot is used as the point). If the closest plant is determined based on any plant part, it is cover frequency. If the criterion is the closest plant at its rooting point, it is rooted frequency.

There are three problems with nearest plant frequency data. First, each "quadrat" is of a different size such that the data have no meaning until combined for determining composition. Second, when composition is determined, the data for each species are no longer independent. A change in the density of one particular species will cause a change in data values for other species regardless of whether the abundance of the other species has changed or not. This means it is impossible to determine which species are changing and whether they are increasing, decreasing, or some of each. Third, small, dense species such as some grasses and small annual forbs are greatly overemphasized.

Parker 3-Step

The Parker 3-step method (Parker 1951), widely used by the USFS, is another attempt at overcoming disadvantages of point sampling. In the Parker method, the size of the "point" is increased to 3/4 inches in diameter to reduce error in determining hits. The "point" is kept consistent in size and is kept small so that the data can be evaluated as cover data. Increasing the size of the "point" such that it has dimensions creates a bias in the data when interpreted as cover data. Thus, an estimate of cover by the Parker method is considered a biased estimate of cover. This bias is generally not considered high enough to cause significant problems in interpreting the data, although at times it can be significant.

A major disadvantage of the small 3/4 loop used in the Parker method is that although slightly increasing the size of the "point" helps increase repeatability in sampling, it does not greatly reduce the sample size required for adequacy of sample. The 300 points typically sampled are often inadequate.

Since only species presence or absence is recorded, data collected with the Parker method using a 3/4 loop can appropriately be analyzed as frequency data. However, the 3/4 inch loop is too small for most species to be useful for frequency data.

Ground Cover

A popular addition to monitoring plant frequency has been point sampling of ground cover. Usually, one or more points are marked on the quadrat frame. At each placement, the type of ground cover occurring beneath each point is recorded. Cover type categories are usually general, e.g. bare ground, rock, litter, etc.. Although a reading is obtained at every placement of a point (unlike plant cover), point sampling of ground cover still often requires a larger sample size than quadrat frequency. One remedy is to read more than one point per placement of the quadrat. This results in a clustered sampling and may result in bias due to lack of independence between points.

Ground cover data are useful, and may also indicate changes in range trend. Ultimately, ground cover or other soil features may be the best indicator of long term site stability and potential productivity. However, our current understanding of what parameters to monitor and how to monitor them is still limited.

It should be emphasized that point sampling of ground cover involves a different parameter and is a procedure additional to, rather than a part of, plant frequency sampling. Therefore, the proper sampling and evaluation of ground cover must be considered separately from frequency in selecting the best methods. Then it can be considered how best to simultaneously handle the two procedures most effectively in the sampling scheme.

 

 

Literature Cited

  1. Brown, D. 1954. Methods of surveying and measuring vegetation. Jarrold and Sons Ltd., Norwich. (1957 printing). 223 pp.

  2. Cochran, W.G. 1977. Sampling techniques. John Wiley and Sons, New York.

  3. Cook, C.W. and J. Stubbendieck, eds. 1986. Range research: Basic problems and techniques. Soc. for Range Mgmt., Denver, CO. 317 pp.

  4. Daubenmire, R.F. 1968. Plant communities: A textbook of plant synecology. Harper and Row, New York. 300 pp.

  5. Despain, D.W. and E.L. Smith. 1987. "The comparative yield method for estimating range production." Univ. of Arizona. (See Chapter Four.)

  6. Greig-Smith, P. 1983. Quantitative plant ecology. 3rd ed. Blackwell Sci. Publ., Oxford. 359 pp.

  7. Hironaka, M. 1985. "Frequency approaches to monitor rangeland vegetation." Proc. 38th annual meeting Soc. for Range Mgmt. pp 84-86.

  8. Hyder, D.N., C.E. Conrad, P.T. Tueller, L.D. Calvin, C.E. Poulton and F.A. Sneva. 1963. "Frequency sampling in sagebrush-bunchgrass vegetation." Ecology 44(4):740-746.

  9. Hyder, D.N., R.E. Bement, E.E. Remmenga and C. Terwilliger, Jr. 1966. "Vegetation-soils and vegetation-grazing relations from frequency data." J. Range Mgmt. 19:11-17.

  10. Mueller-Dombois, D. and H. Ellenberg. 1974. Aims and methods of vegetation ecology. John Wiley and Sons, New York. 547 pp. .pa

  11. Parker, K.W. 1951. "A method for measuring trend in range condition on National Forest ranges." U.S.D.A. Forest Service. Mimeo.

  12. Raunkiaer, C. 1909. "Formation sun der sogelse og formation statistik." Bot. Tidsskr. 30:20-80.

  13. RISC (Range Inventory Standardization Committee.) 1983. Guidelines and Terminology for Range Inventories and Monitoring. Denver: Society for Range Management, 13 pp.

  14. Smith, E.L. and D.W. Despain. 1987. "The dry-weight-rank method of estimating species composition." Univ. of Arizona. (See Chapter Three.)

  15. Smith, S.D., S.C. Bunting and M. Hironaka. 1986. "Sensitivity of frequency plots for detecting vegetation change." Northwest Sci. 60(4):279-286.

  16. Snedecor, G.W. and W.G. Cochran. 1980. Statistical methods. Iowa State Univ. Press, Ames, IO.

  17. Tueller, P.T., G. Loraine, K. Kipping and C. Wilkie. 1972. Methods for measuring vegetation changes on Nevada Rangelands. Max C. Fleischman College of Agric. Agric. Exper. Stn., Reno NV. 55 pp.

  18. West, N.E. 1985. "Shortcomings of plant frequency-based methods for range condition and trend." Proc. 38th annual meeting Soc. for Range Mgmt. pp 87-90.

  19. Whysong, G.L. and W.W. Brady. 1987. "Frequency sampling and type II errors." J. Range Mgmt. 40(5):472-474.

  20. Yavitt, J.B. 1979. Quadrat frequency sampling in a semi-desert grassland. M.S. Thesis. Univ. of Arizona, Tucson.


This document is part of AZ9043, "Some Methods For Monitoring Rangelands and Other Natural Area Vegetation"
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