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Complexity of Sampling Multiple Resources 1
W.E. Frayer2
Abstract-Experience with many inventories for single and multiple resources has resulted in suggestions to be considered when
sampling multiple resources. Discussion begins with the design of
the sampling unit and continues for such items as sampling
design, sampling over time and projections of future status. Specific recommendations are given for each area discussed.
Many inventories are originally designed to monitor status
and trends of a single resource. There have been inventories for
timber, wildlife, agricultural crops, wetlands and other resources.
In almost every case, those relying on information from the inventories have concluded that other information is needed. Plant and
animal responses are usually affected by their surroundings. Timber must be characterized by its environment in order to evaluate its
availability for harvest. Wildlife inventories usually must combine
habitat measures as well as population densities and trends. Before
long, it appears that there are many multi resource inventoriesthat each single-resource inventory has now become an inventory of
multiple resources. Then pressure is exerted or felt to combine these
inventories in order to eliminate waste and overlap. There are good
reasons for doing this as well as several reasons for being very
cautious in doing so. Unless there is agreement among users that
the information derived from a single multi resource inventory
meets their needs, the inventory may create more problems than it
solves. Putting many things together does not necessarily save
money. Larger field crews may be needed, and measurement times
may be greatly increased. What follows are some guidelines for a
multi resource inventory based on my experience with several
single-purpose inventories and some efforts to expand those inventories to multi resource inventories.
Sample Unit Size _ _ _ _ _ __
I shall start the discussion with the sampling unit. I know
it's desirable to define a sampling frame that consists of a
list of all sampling units so that the usual approach of
sample selection and use of finite population theory is easily
applied. It's not that easy with multi resources-although
it's been tried. Some have tried to collect more and more
information on the same plot-a plot (sampling unit) that
was originally designed for collection of data on one resource.
I believe that sampling units must be flexible so that they
can be optimized for collection of data on many resources. I
believe a useful procedure is to treat a sampling unit as the
list of data collected with reference to a point in space and
time. Timber information might be collected, in part, by a
Ipaper presented at the North American Science Symposium: Toward a
Unified Framework for Inventorying and Monitoring Forest Ecosystem
Resources, Guadalajara, Mexico, November 1-6, 1998.
2W.E. Frayer is Dean, School of Forestry and Wood Products, Michigan
Technological University, Houghton, MI, U.S.A. Phone: (906) 487-3604;
Fax: (906) 487-2915; e-mail: wefrayer@mtu.edu
USDA Forest Service Proceedings RMRS-P-12. 1999
point sample (probability proportional to basal area). Habitat data may be collected by delineating the boundaries of
the habitat the point is located within. Wetland data could
be a map of the wetland the point falls within, a description
of the type of wetland, distances to other wetlands and any
other features needed. Finite population corrections would
not be used, because, in essence, there are an infinite number
of points contained within the population. This could be
considered analogous to sampling with replacement.
1. Recommendation: Use points as sampling units.
Many configurations of areas around a point may
contribute to variable values for the sampling unit
(point).
Variation Within and Between
Sampling Units
As suggested, a sampling unit might be a point with data
associated with various resources collected around the point.
At any rate, the sampling unit may be complex. Many
inventories use a cluster of points/plots as a sampling unit.
For some reason, these clusters are often located close
together. This may give data gatherers the belief that
they're representing a fairly homogeneous area with the
data collected. For sampling precision, however, there are
very good arguments for maximizing the variation within
the clusters and minimizing variation between clusters.
The precision of population estimates is strongly dependent
on the variation between sampling units-this being a
strong argument in favor of absorbing as much variation as
possible within the units. It often takes considerable travel
time to locate the sampling unit. Why, then, confine the area
of the cluster on which measurements are made to an area
as small as an acre or a hectare? Spreading the measurements out over a larger area will, on the average, introduce
more variability into the cluster and less variability between
clusters. In some cases, transects may prove highly useful.
2. Recommendation: Design sampling units such
that variation is large within units and small between
units.
Movement of Sampling Units _ __
The concern here is similar to that of the previous discussion. Some inventory procedures have included the practice of moving sampling units (or portions of sampling units)
so that they have minimal variability-as in moving all
parts of a cluster into a single vegetative type. This not only
is counterproductive to obtaining precise estimates-it can
also be a real procedural problem in later inventories when
the sampling unit may again straddle vegetative conditions
that have changed since the previous inventory.
3. Recommendation: Do not move sampling units.
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Allocation of Sampling Units _ __
;:.:
Many designs have been tried for sampling single resources and multiple resources. Sampling with partial replacement (SPR) is one of the more complex designs used in
forestry (Ware and Cunia, 1962; Bickford et aI., 1963). With
most inventories there is an important component ofmonitoring change as well as assessing current status and perhaps forecasting future status under various assumptions.
Any time that sampling units are chosen with unequal
probability or a complex design like SPR is used, there is a
danger that the personnel who try to replicate the procedure
for the subsequent inventory will not follow the same, exact
procedure used before. Another potential hazard is the
change ofthings over time. What was originally an optimum
design based on varying probabilities may be far from
optimum unless the probabilities can be redefined-regardless of the design used. For example, stratified sampling can
become quite laborious to handle if stratum boundaries keep
changing. For these reasons, when possible, I believe it best
to "keep it simple" and use proportional allocation when
there is not a distinct, overriding disadvantage.
4. Recommendation: Use proportional allocation.
Sampling Designs _ _ _ _ _ __
As indicated earlier, complex designs like SPR have been
used in forest sampling. Multi stage designs up to four stages
have been attempted (Schreuder et al. 1992b). A three-phase
design using high-altitude photography for an unsupervised
classification, low-altitude photography for a more derailed
stratification and ground plots for measurement was shown
to be advantageous when compared to double sampling for
stratification with low-altitude photography and ground
plots (Kent et aI., 1979). Stratified sampling with either
known or estimated stratum sizes has stood the test of time.
The procedure when estimating stratum sizes generally
uses some type of remotely sensed data (be it satellite
imagery, or aerial photography). Known stratum sizes may
be delineated by political boundaries (states, counties), physiographic provinces, or any land classification that proves
useful. Multi resource inventories conducted by US Forest
Service Experiment Stations all use a form of stratified
sampling with estimated stratum weights. Wetland inventories conducted by the US Fish and Wildlife Service use
stratified sampling with strata formed by cross sections of
political boundaries and physiographic subdivisions.
5. Recommendation: Use designs/procedures that
are as simple as possible.
Random vs. Systematic
Samples _ _ _ _ _ _ _ _ __
Sample points could be located systematically or at random. If located systematically, caution should be used to
avoid the potential bias of that approach. For example, you
wouldn't want to locate sampling units on a systematic grid
if some of the data you want to collect are located on a grid
as well. An example of the potential danger would be school
lands or railroad holdings in the western United States, both
164
of which were originally laid out in a systematic grid. Other
examples of potential problems are roads, fence lines, canals
and other features located in periodic fashion. If transects
are used, there may be certain instances in which measurements might be more efficient if not equally spaced.
6. Recommendation: Use a systematic design, but
with caution.
Sampling Over Time _ _ _ _ __
Inventories of natural resources are usually carried out to
monitor status and trends. Many designs were adopted
because of their precision in estimating status (estimating
current values of population parameters). Sampling unit
design has often been dependent primarily on how well it
could be used to collect data on current values. Point sampling for timber volume (which samples trees with probability proportional to basal area is such an example). If the
trends are of much importance, it may make sense to use a
sampling design that is optimum for estimating changes.
The solution is fairly simple. Ware and Cunia (1962) showed
that a complete remeasurement design is optimum for
estimating change if the measurements on successive occasions are correlated. Thus, regardless of the exact design
used, it is highly recommended that all sampling units be
remeasured.
7. Recommendation: Remeasure all sampling units.
Changes in Strata Over Time _ __
If stratification is useful-and it generally is as discussed
earlier-there must be some acceptable procedure for handling the problem of changing stratum boundaries over
time. If working with complete stratification and complete
remeasurement of sampling units, the units can be characterized by the stratum at the first or second occasion. For
additivity with results from the previous inventory, the
original stratification can be used. Post stratification (using
the strata as delineated at the second occasion) will provide
better correlation with current status and would generally
be more precise for estimates of trends as well as status. If
the stratum sizes are estimated from a primary sample, the
ground plots must be stratified in the same fashion and
should truly represent a subsample of the primary sample.
In this case also, there are different estimates available
depending on the stratification used for the estimation. In
this case, too, the most recent stratification is recommended.
8. Recommendation: Use the most recent stratification for all estimates.
Future Status _ _ _ _ _ _ _ __
Information on change has assumed more importance in
recent years. Presumably, there is reasonably good information on current status and attention has turned to change
and how to manage it. Change estimates are often based on
average annual change between inventories. Projections
are another estimate of change and are becoming more
common and of vital use in soliciting funding for affecting
future status. Agricultural and forestry organizations have
USDA Forest Service Proceedings RMRS-P-12. 1999
routinely dealt with projections. It has been common to
project 10, 20, even 50 years into the future. Others have
only recently attempted this. The latest status and trends
study of U.S. Wetlands used a Markov process for estimation of future status and trends. Without some indication of
future status, it was feared that there was little information
on which to base federal policies and programs. Given that
projections are useful, they should be made with caution.
Monte Carlo studies andjackknife estimates have indicated
that rates of change used in projection procedures must be
very precise for the projections to have any validity at all
even for only a few years into the future.
9. Recommendation: Projections should be made
with caution.
In Summary
The recommendations made are based on the experiences
of the author. Some individuals may have a different opinion
on one or more of these. I believe they form a reasonable set
of guidelines, especially for those with very little personal
experience who find that they must design a multi resource
inventory. When in that situation, an additional recommendation is in order:
10. Seek advice from those with experience!
The recommendations given in the paper are summarized
here:
1. Recommendation: Use points to derme sampling
units. Many configurations of areas around a point
may contribute to variable values for the sampling
unit.
USDA Forest Service Proceedings RMRS-P-12. 1999
2. Recommendation: Design sampling units such
that variation is large within units and small between
units.
3. Recommendation: Do not move sampling units.
4. Recommendation: Use proportional allocation.
5. Recommendation: Use designs/procedures that
are as simple as possible.
6. Recommendation: Use a systematic design, but
with caution.
7. Recommendation: Remeasure all sampling units.
8. Recommendation: Use the most recent stratification for all estimates.
9. Recommendation: Projections should be made
with caution.
10. Seek advice from those with experience!
Literature Cited
Bickford, C. A., C. E. Mayer, and K. D. Ware. 1963. An efficient
sampling design for forest inventory: the Northeastern forest
resurvey. J. For. 61:826-833.
Kent, B., D. Johnston, and W. E. Frayer. 1979. The applications of
three-phase sampling for stratification to multi-resource inventories. In: Proceedings, Forest Resource Inventories. Colorado
State University. pp. 993-1000.
Schreuder, H. T., V. J. LaBau, andJ.W. Hazard. 1992b. The Alaska
four-phase sampling design. Submitted to Photogramm. Eng.
Rem.Sens.
Ware, K. D., and T. Cunia. 1962. Continuous forest inventory with
partial replacement of samples. Forest Science Monograph No.3.
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