Lesson 14: Sampling methods
• Subjective vs. objective sampling
• Centralized replicate, random, and
systematic sampling approaches
• The relevé method
• Cover
– Cover estimates
– Measuring cover, point sampling, line
intercept
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Density
Frequency
Basal area
Count-plot method
Distance methods
Subjective vs. objective sampling
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Subjective sampling
– Sample sites are consciously chosen as representative of
predetermined vegetation classes.
– Most flexible sampling scheme
– Allows for experience and decision making ability of the
investigator
– Best used in areas where there are clear boundaries between
plant communities
– Good approach for vegetation classification
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Objective sampling
– Sample sites are chosen according to chance (i.e. random
sampling)
– Essential if probability statistics are to be used to back up the
conclusions
– Best used in areas where boundaries between communities
are indistinct or where the objective is to determine the causes
of variation within a single plant community
– Good approach for ordination methods
Centralized replicate, random, and
systematic sampling approaches
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Centralized replicate
– Sample sites are chosen subjectively and centrally located within
representative homogeneous areas of predetermined vegetation types.
– This method is used in the relevé approach (more on this later).
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Random
– Sample sites are chosen according some randomizing method (e.g., dice,
random numbers). Any point is a possible sample point.
– In a complete random method plots are chosen completely randomly.
– In a stratified random approach, the research areas is first divided into
relatively similar classes based on some criteria, for example, landscape
units (floodplains, hills, mountains) or mapped vegetation units. Sample
sites are then randomly chosen in the various classes. This ensures that the
most common units are not over-sampled and the uncommon units under
sampled. The samples are dispersed throughout the entire survey area.
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Systematic
– Plots are located according to a regular system such as a grid or regular
intervals along a line. A stratified systematic approach is similar to the
stratified random approach except the sample sites are chosen according to
a systematic method (grids or linear transects) within each stratified class.
Random
Systematic
Sampling
designs
Stratified
random
Stratified
systematic
Sample size:
How many sample plots are needed for an accurate determination of cover?
• Take many cover samples within the vegetation type using a point sampling procedure.
• The running mean of cover is plotted for various numbers of samples.
• Fluctuaitons in cover are damped out as the number of quadrats increases.
• In this example from a sagebrush/grassland in the eastern Washington area,1--20 plots
might be sufficient to conduct the study, with diminishing reward for added effort beyond
that point.
Precision vs. Accuracy
• Precision is close agreement of sample
means to each other without reference
to the true mean.
• Accuracy is the close agreement of the
sample means to the true mean.
• In the diagram, the center represents
the true cover for a stand of vegetation,
and the radiating circles represent
departures up to 40% error. A and B are
both precise. A is accurate. C is neither
accurate nor precise.
The relevé method
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French term meaning a collection of data. Often used in terms of
surveys.
Developed by Josias Braun-Blanquet as a standard method of
sampling for vegetation classification according to the ZurichMontpellier School of phytosociology.
Recently has gained popularity in North America (e.g., Nature
Conservancy, California Department of Fish and Game, Talbot and
Talbot 1994, Walker et al. 1994, Komárková 1978, Rivas-Martinez
1997, Miyawaki et al. 1994, Klinka et al. 1996)
The quickest way to obtain detailed community information.
Does not necessarily involve sampling other components of the
site such as soils and site factors, although these are often
collected if environmental gradient analysis is part of the
research.
Subjective sampling (centralized replicate).
Qualitative in the sense that species cover is estimated instead of
measured.
Quantitative in the sense that it gives a complete list of species for
the plot.
Entitation and requirements of a relevé
Entitation
• “The process of subdividing the vegetation into recognizable
entities or preliminary vegetation types.”
• Reconnaissance essential (cannot be overemphasized) The better
your initial knowledge of an area, the better will be the subsequent
sampling.
• Important to avoid sampling ecotones or breaks between distinct
communities.
• Iterative process that may take several years to develop a good
concept of the communities.
Requirements of a sample site for a relevé
• 1. Homogeneity of the vegetation canopy.
• 2. Homogeneity of the soil and other site factors.
• 3. Large enough to contain all the species in the community.
• 4. Should be recognizable as unit that is repeated in other areas
of the landscape, i.e. a repeating assemblage of species.
Size of plots: Minimal Area Method
Objective:
1. Determine the smallest area that is representative
of the plant community so as to minimize the
sampling effort. The plot should contain a very high
percentage of the total species in the community.
2. Minimize the problem of including areas that are
not representative of the plant community. Larger
areas tend to include multiple communities and
ecotonal areas.
Nested plot method :
1. A large example of the community in question
should be selected in order to permit many
doublings of plot size without crossing any
community boundaries.
2. A small plot (e.g. 0.25 m2) is laid out, and all the
species are recorded including cryptogams.
3. The plot is doubled in size, and any new species
are recorded.
4. This is continued until only 1 or two new species
are recorded in successive doublings.
Size of plots: Minimal Area Method
• The minimum plot size is the point on the
curve where the line most rapidly
approaches the horizontal. Another method
is to arbitrarily define the optimum plot size
as that where some objective percentage of
the total species encountered in the
community type occurs (e.g. 90 or 95%).
• However, in tropical communities neither
method works because the species-curve
does not appear to level off. However, it
undoubtedly does eventually, and MD&E
suggest that an appropriate plot size might
be about 5 ha (12.5 acres!). The task of
tallying all the species in such a large area
would be formidable indeed, and you may
want to compromise by doing many smaller
manageable plots.
Results for dune area in North Carolina (about 0.13 m2),
and English Woodland (100 m2) and a tropical forest in
Brunei (1000 m2).
Minimum area for common vegetation types
• The actual minimum
area used is usually
somewhat larger than
the graphical minimum
area.
• Minimal areas have been
established for a wide
variety of vegetation
types and so there are
certain guidelines that
can be followed when
there is not sufficient
time to establish the
minimal sample area.
Relevé sites
• Homogeneous areas of vegetation
• Homogenous environment
• Large enough to contain minimal area plus buffer
Example Relevé data
sheet
1. Header includes plot number, date,
observer , photo numbers, and a
description of the vegetation and the site.
2. Percent cover estimates are given for
each growth form category, also, rocks,
water, bare soil,
3. Plot size is recorded
4. A complete list of species is made for
vascular plants, bryophytes, and lichens.
5. Cover is estimated using the BraunBlanquet cover-abundance scores (see next
slide).
6. Samples of all species are collected as
vouchers.
7. Unknown plants are collected separately
and given a collection number.
Cover-abundance classes
Site-factor
data form
• A second data sheet is used to
describe the site, including soil
moisture regimes, wind regimes,
snow regimes, disturbance regimes,
slope, elevation, etc.
• The introduction of computers has
made it necessary to code the site
information as much as possible
using numeric codes. This sheet
shows the codes that were used for a
site near Happy Valley, Alaska.
• Note the place for notes at the
bottom. This is particularly important
because it can give important
observations that may not be noted
by simply filling out the codes.
Sample soil
description
form
• A third data sheet
is used to briefly
describe the soil.
• A collection of soil
is made from the
upper mineral
horizon.
Common parameters from plant community
analysis
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Species composition (total species list)
Cover
Density
Frequency
Basal area
Tree heights
Cover
“The area of ground covered by the vertical
projection of the aerial parts of plants of one or
more species. “
• An easily obtained index of plant biomass.
• Estimates of cover can be obtained by using
cover-abundance scores.
• Measures of cover can be made using point
sampling methods, line transect method, or
photos and planimeter or other direct measure of
cover.
Estimating percentage cover
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Cover is very difficult to accurately estimate. The use of cover-abundance scores greatly reduces
the variation in scores from observer to observer.
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For the relevé method, actual scores are not as important as the presence or absence of species.
Cover is a secondary consideration in the Braun-Blanquet method and rarely affects the outcome of
a table analysis.
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However, every attempt should be made to maintain consistency throughout the sampling
procedure.
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The method of estimating cover described in Barbour et al. is very difficult to apply in many
ecosystems because the actual rooting position is difficult to quickly ascertain, and overlap
between leaves of the same species are difficult to estimate.
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Generally a ball-park estimate is good enough (e.g., 20% for species B above. This falls in B-B cover
category 3, which is the same as the actual cover (33%) determined by measurement.)
Measuring cover: Line intercept method
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Generally used for tree and shrub cover or for measuring cover of clearly defined
vegetation types
A line is laid out along the ground and the line segments for each species or
vegetation type is recorded. Percent cover for each species is the total length of line
segments for each species divided by the total length of the transect.
Often, a lengthy line intercept is combined with quadrats for estimating density or
frequency that run alongside it. Cover is measured along the line, and density or
frequency is noted in the quadrats.
Measuring cover: Point sampling methods
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Cover of plants can also be quantitatively determined by point
sampling methods. There are several such methods. All of them,
record the vegetation intercepted at random points in the plant
canopy.
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Percent cover is calculated as:
% cover of species A = (No. of points that intercept species A at least once) X 100%
Total number of points
Point sampling methods:
I. Point frame
• The frame is set up over the vegetation and
the needles are lowered down through the
plant canopy.
• Every time the point of a needle touches a
plant, a “hit” is recorded with the species
name.
• The needle can make several hits before it
eventually touches the ground surface.
• % cover of species A = (No. of hits that
intercept species A)/ (No. of points)¸
• This is the only point sampling method that
can give an accurate estimate of absolute
cover of each species in multistratose
vegetation, and hence an estimate of total
leaf area for each species. All other methods
give relative percentage cover.
• It is, however, a very time consuming
method.
Electronic inclined point frame
Point Sampling methods:
II. Point quadrat
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This device is very
useful for low-growing
graminoid or dwarfshrub vegetation.
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It consists of a 1-m
frame with a double 10cm grid of strings.
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We record three things
at each of 100 points:
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Species at the top
of canopy
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Species at the
ground level.
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Distance to the top
of the plant canopy
from the bottom
string.
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Distance to the
ground from the
bottom string.
Point quadrat double grid
• In sampling a point,
the intersections
between strings in the
upper and lower grid
a visually aligned so
as to avoid the
problem of parallax.
• The percent cover for
a species in each
layer of the canopy is
simply the number of
hits out of 100.
Maps from point-quadrat data
Point sampling methods:
III. Buckner sampler
• Used for sampling along
transects and large plots
(e.g., 100 x 100m).
• It has a mirror that reflects
a vertical image of the
ground surface into a
telescope with a crosshairs in it. The plant at the
cross-hairs is recorded.
• A large number of point
samples is taken (usually
300-400 points per plot)
and relative cover for each
species is the percentage
of the total number of
points.
• Can also be used for
sampling tree canopies by
inverting the mirror to
look upward.
Point sampling
methods:
IV. methods for
tree canopy cover
Densitometer with single cross hairs
Moosehorn crow-cover estimator
Spherical densiometer
Density
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The number of plants per unit area. Expressed as number/square
meter, stems/acre, etc.
Most often used for trees or large plants.
An an easy concept to grasp, but very difficult to perform in some
types of vegetation because of:
(1) There is difficulty of defining an individual (e.g. caespitose growth
forms, plants with underground rhizomes, plants in peaty landscapes
often have complicated stems just beneath the surface of the moss
layer)
(2) Quadrat size affects density size because of problem of counting
large individuals near the boundary of the quadrat
(3) It is very time-consuming in graminoid dominated systems and lowgrowing vegetation.
Frequency
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Expressed as a percentage of plots (quadrats) of equal size in
which at least one individual of the species occurs in a stand.
It is a measure of the degree of uniformity with which individuals
of a species are distributed in an area, and more specifically a
stand.
Generally frequency quadrats are much smaller than quadrats
used to determine species composition in plant communities
(relevés).
Rule of thumb is that the frequency plot size should be at least
twice the size of the largest individual.
Frequency plots
• The various patterns represent
species.
• The little squares are small
frequency plots.
• Consider just the cross-hatch
polygons.
• The frequency of “cross
hatch” is the percent of plots
which have at least a little
cross-hatch pattern
• For the regular sampling
scheme: Frequency = 21/25 x
100% = 84%.
Questions:
What is the frequency for the random sampling scheme?
What would greatly affect the frequency determinations?
Basal area
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The cross-sectional area of tree stems at breast height per unit of
ground area (e.g., m2/ha)
A measure of dominance. Generally used for trees.
Methods of determining basal area:
– Measure tree diameters at breast height with a biltmore stick or
diameter tape. Area of each tree = (dbh/2)2. To calculate basal area
the area of the stems is calculated for a known area (count-plot
method) or by using distance methods (e.g.the point-centered quarter
method described in a later lesson).
– Bitterlich stick, or angle gauge to calculate m2/ha directly.
Diameter Tape
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A diameter tape (D-tape) is used by
foresters to measure the diameter of
a tree.
Since trees are swelled at the base,
measurements are made 4.5 feet
above the ground (breast height) in
order to give an average diameter
estimate.
The D-tape is wrapped around a tree
and is specially designed to convert
the tree circumferance to tree
diameter.
http://www.cnr.vt.edu/dendro/Forsite/dtape.htm
Biltmore Stick
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A Biltmore stickis one method used for measuring tree diameter and
height . From there, the total board feet of the tree can be established,
along with tonnage and cubic feet. It has specially calibrated scale to
measure diameter of trees directly.
1. Hold the stick at breast height (4.5 feet from the
ground), 25" from your eye, with the back of the stick
against the tree you are measuring.
2. Hold the stick at a right angle to the axis of the tree
and keep your eyes level with the stick.
3. Adjust the stick so that the left or zero is in line of sight
with the left side of the tree.
4. Without moving your head, shift the line of sight to the
right hand side of the trunk.
5. Read the diameter on the stick nearest the point at
which the line of sight crosses it.
http://extension.usu.edu/forestry/Management/Biltmore_UsingABiltmoreStick.htm
Bitterlich Stick method for determining basal
area directly
(a). The original bitterlich stick sight
device. This particular one will give
total basal area in square feet per acre
if the number of trees tallied is
multiplied by 10.
(b) A bird’s eye view of trees that
would be tallied as an observer at the
center point turns in a complete circle.
Trunk X (shaded) is tallied because its
trunk diameter exceeds the angle
projected by the sighting device, but
trees Y and Z (not shaded) are not
tallied. In one complete circle, the
observer would tally four trees (all
shaded). Basal area = 40 ft2/ acre.
(c ) The prism type of sighting device.
In this case, the lower trunk is not
completely displaced from the upper
trunk, therefore the tree would be
tallied.
Barbour et al. 1999, Fig. 9-13.
Measuring tree heights: Native American
Indian approach
Find a spot where, looking
under your legs (as shown),
you can just see the top of
the tree. The distance from
such a spot to the base of
the tree is approximately the
height of the tree.
Why does this work? For a
normal, healthy (limber) adult,
the angle formed by looking
under one's legs is
approximately 45˚. Hence, the
distance to the tree must be
around the same as the height
of the tree.
Trigonometric methods
Lots of trigonometric methods:
METHOD 1: Use a meter stick to measure the distance from your eye to your outstretched
fist (d). Hold the meter stick vertically at so the length d extends above your fist.
Back off from tree holding meter stick vertically in your extended hand, while
sighting the top of the tree. When the top of the tree is at the top of the meter stick.
Pace the distance to the tree. This distance is the same as the height of the tree.
METHOD 2: Tie a ribbon around tree at 2-m above the ground. Back off from the tree and
measure the apparent distance between the base of the tree and ribbon (r). Then
measure the apparent distance between the base of the tree and the top of the tree
(t). The ratio r/t = 2/T.
T
t
2m
r
Using the Biltmore stick to determine tree
height
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2.
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4.
5.
6.
Total tree height is measured from the ground to
the top of the tree. Merchantable tree height is
measured from the stump height to the point at
which the tree is no longer useable.
Stand 100 feet from the tree you are going to
measure. If the ground is not level, stand on a spot
which has about the same elevation as the base of
the tree.
Hold the stick vertical, 25" from your eye, with the
“Height of Tree” side facing toward you.
Align the base of the stick at the ground (or at your
estimated stump height for merchantable height).
Without moving your head, shift your line of sight
so you can read the height at the point where your
line of sight and the top of the tree intersect (or
merchantable height).
This can also be done opposite: Zero the stick at
the top of the tree and check height at the ground
http://extension.usu.edu/forestry/Management/Biltmore_UsingABiltmoreStick.htm
Measuring tree heights: Sunto Clinometer
• User measures a given
distance (20 or 15 m) from
the tree.
• Then sights and aligns a
cross hair with the top of
the tree. The tree height is
then read directly in the
viewer (if on level ground).
• If not level, the user then
sights the bottom of the
tree, and subtracts (if the
tree base is above the
user) or adds (if the tree
base is below the user) the
reading to the first
determination.
Measuring foliage heights: Portable LIDAR system for rapid
determination of forest canopy structure
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A narrow-beam rapidly pulsed first-return laser rangefinder coupled with a
data recording system.
Measures distance to overhead plant surfaces.
Parker, G.G., Harding, D.J. and Berger, M.L. 2004. Journal of Applied Ecology, 41: 755. doi:10.1111/j.0021-8901.2004.00925.x
Count-plot method
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Species are counted and measured within a specifically defined area (belt
transect or quadrat).
Used for determining density and basal area of trees.
Widely used method for forest inventory and long-term studies.
The main reason for doing a plot as opposed to a plotless methods are:
• It can also be used to sample the understory, and thus is useful for vegetation
classification.
• Record a wide variety of other properties, such as soils, site factors, and the plot can be
mapped for spatial studies.
• Sampling can be repeated on the same plots in future years.
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Useful for long-term studies where the same plot will be revisited in future
years.
Data obtained in the plot-count method
In the United States this is usually done in plots or belt transects
(e.g., a 10 x 20-m plot.
Sampling often includes:
(1) Number of individuals for each tree species above a predetermined
minimum diameter. From these data density of each species is
determined.
(2) Tree diameters at breast height (dbh) using a Biltmore stick or
diameter tape and grouped in diameter classes. From these data
basal area (cross-sectional area of tree stems at breast height/ha) for
each species is determined.
(3) Tree heights (e.g., with an inclinometer).
(4) Trees less than the minimum diameter are classed as seedlings or
saplings and grouped into 1 ft (30 cm) height classes.
Example of plot to determine density and basal area
Example forest plot from Hawaii:
1. Calculate the density of Acacia koa:
Area = 120 m2 = 1.2 ha
No .of ACAKOA = 4
Density = 4/1.2 = 3.3 plants/ha
2. Calculate the basal area of Acacia koa:
Basal area = (d/2)2
Basal areas is:
(202 + 11.52 + 7.52 + 382) cm2/ha = 6385.3 cm2/ha = 0.64 m2/ha
Distance Methods
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Developed by Cottam and Curtis in the 1950s to describe the forests of
Wisconsin.
Density is determined by first finding the average distance between trees,
and then squaring this distance to find the average area per tree. To find
the number of trees per unit area, divide the unit area (m2) by the area per
tree.
Frequency is determined by counting the number of points (sample sites)
at which a tree occurs (not the percentage of the total number of trees).
Dominance is calculated by first determining the mean basal area per tree
species and then multiplying by the density of that species.
Distance methods
Nearest individual - measure distance to the
nearest tree at each point (correction factor =
2).
Nearest neighbor - the nearest tree is
selected and the distance between it and its
nearest neighbor is measured. (correction
factor = 1.47).
Random pairs - a line from a random point
to the nearest tree is made and a 90˚
exclusion is erected on either side of the line.
The distance to the nearest tree outside the
exclusion angle is measured. (Correction
factor = 0.8)
Nearest individual
Point-centered quarter
Pont-centered quarter - a pair of
perpendicular lines are erected at the random
point, forming a cross with four quadrants.
The distances to the nearest tree in each
quadrant are measured.
The distances are calculated separately for
each tree species.
The squared distances are the areas
occupied by each tree.
If the average area per tree is divided into a
unit of area (e.g. ha), this will give the
density of the trees (trees/ha).
Nearest neighbor
Random pairs
Distance methods: Wandering quarter method (Bonham 1989)
• The most recent variation on the
distance methods is the wandering
quarter method suggest by Bonham.
• It does not require selection of any
random point except the first point.
• At each point a 90˚ angle is formed
centered on a given azimuth (e.g.
North). The distance to the nearest
tree within the angle is measured.
• That tree then becomes the next
point.
Bonham 1989 cited in Barbour et al. 1999
Importance Value
Used when a single number is needed to incorporate cover, density
and frequency (e.g., computerized ordination methods)
IVi = Dri + Fri + Bri
IV = importance value
i = species i
Dri = relative density of species i = (density of species i)/ (density of all species)
Fri = relative frequency of species i = (frequency of species i)/ (frequency of all species)
Bri = relative dominance of species i = (dominance of species i)/ (dominance of all
species)
Bisect Diagrams
Bisect diagrams are scale
drawings of the vegetation in
strips. As mentioned last lesson,
these were developed by British
ecologists working in the
tropics.
These diagrams show stands of
tropical rain forests in British
West Indies (a) and Borneo (b)
Bisect transect: Aracaria forest, Rio Negro,
Argentina
It helps to visuallize the 3dimensional aspect of the
stand to also show the plot
in planar view.
From Siebert, P. Carta de Vegetacion de region de El Bolson, Rio Negro Y su aplication a la planificacion de uso de la tierra.
Canopy profiles
• Each bar represents a different layer in the plant
canopy.
• The thickness of the horzontal bar represent the
span of the canopy height.
Eastern deciduous forest
• The length of the bar represents the percentage
cover of the layer.
• The eastern deciduous forest has four layers and
the canopy is taller. The boreal forest site has 3
layers.
Boreal forest
Summary Lesson 14: sampling
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Subjective vs. objective sampling
Centralized replicate, random, and systematic sampling approaches
Precision vs. accuracy
The relevé method
Cover
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Density
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Clinometer
Trigonometric methods (45˚ triangle)
Count-plot method for determining density and basal area of trees
Bisect transect (graphic portrayal of vertical and planar structure of sample transects)
Distance Methods
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Tree diameter measurements (diameter tape, Biltmore stick)
Bitterlich stick method of direct measurement
Tree height
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Frequency plots
Basal area
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Can be obtained from counting in plot count method, or by the distance methods
Frequency
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Estimate cover (Braun-Blanquet cover abundance scores or other class estimates)
Measure cover (Point sampling techniques, e.g., Line intercept method, point frame, point
quadrats, Buckner sampler)
Methods for tree canopies (Moosehorn crown cover estimator, densiometer, Buckner sampler)
Point-centered quarter method
Importance value for ordination methods
Literature for Lesson 14
Bonham, C.D. 1989. Measurement for terrestrial vegetation. New York: WileyInterscience.
Cottom, G. and J.T. Curtis. 1956. The use of distance measures in
phytosociological sampling. Ecology 37:451-460.
Westhoff. V. and van der Maarel, E. 1978. The Braun-Blanquet approach. In:
Whittaker, R.H. Classification of Plant Communities. The Netherlands:
Junk, p. 289-312 (Introduction, History, General Concepts, and Analytical
Research Phase)